Stochastic partial differential equations (SPDEs)

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Programme theme

Stochastic Partial Differential Equations are used to model many physical systems subjected to the influence of internal, external or environmental noise. They also arise when considering deterministic models from random initial conditions, or as tractable approximations to complex deterministic systems. In many cases the presence of noise leads to new phenomena with many recent examples in the physical sciences, biology and financial modelling.

The goal of the programme is to bring together the world leaders in Stochastic Partial Differential Equations working on various aspects of the theory, numerical approximations and applications, as well as in related scientific areas.

The following will be included as themes for the 6-month-long programme.

The study of classical problems (well-posedness, ergodicity, etc.): Kolmogorov equations, equations with constraints, analysis of operators on infinite dimensional spaces, control theory, stochastic viscosity solutions, equations with non-Gaussian or non time-decorrelated noise.
Applications: Stochastic models in fluid flow, stochastic nonlinear Schrödinger equation, stochastic Landau-Lifshitz equations, plasmas turbulence, stochastic porous media equations, branching diffusions, stochastic growth and disintegration models, interacting species models, epidemic modelling, financial modelling
Approximation methods: Numerical schemes (including finite element, splitting etc.), rates of convergence (theory and simulations), multiscale and asymptotic problems, particle approximations, perturbation problems.

Self-financing Participants

The Institute has some space available for participants who will not require financial assistance towards their subsistence, accommodation or travel costs. People who are interested in participating in the programme and who can find their own financial support are asked to contact the organisers by the end of January 2009. The researchers invited on that basis will be offered the use of the library, shared computer facilities and/or access to the wireless network, and help, if required, in finding accommodation.

Click here to download the programme's final scientific report

Preprints

Title	Year	Programme
Local existence and uniqueness in the largest critical space for a surface growth model Authors: Marco Romito, Dirk Blömker Download PDF	2009	SPD
Pathwise uniqueness and continuous dependence for SDEs with nonregular drift Authors: Franco Flandoli, E Fedrizzi Download PDF	2009	SPD
Rough path stability of SPDEs arising in non-linear filtering Authors: Harald Oberhauser, Peter Friz Download PDF	2009	SPD
Matematica - Existence for semilinear parabolic stochastic equations Authors: Giuseppe Da Prato, Viorel Barbu Download PDF	2009	SPD
Internal stabilization by noise of the Navier-Stokes equation Authors: Giuseppe Da Prato, Viorel Barbu Download PDF	2009	SPD
Lattice embeddings in percolation Authors: AE Holroyd, Geoffrey Grimmett Download PDF	2009	SPD
Plaquettes, spheres, and entanglement Authors: AE Holroyd, Geoffrey Grimmett Download PDF	2009	SPD
Conditional distributions, exchangable particle systems, and stochastic partial differential equations Authors: Thomas Kurtz, Wonjung Lee, Dan Crisan Download PDF	2009	SPD
Master-slave synchronization and invariant manifolds for coupled stochastic systems Authors: B Schmalfuss, Igor Chueshov Download PDF	2009	SPD
Strong uniqueness for both Dirichlet operators and stochastic dynamics to Gibbs measures on a path space with exponential interactions Authors: Sergio Albeverio, Michael Roeckner, Hiroshi Kawabi Download PDF	2009	SPD
Singular pertubations to semilinear stochastic heat equations Authors: Martin Hairer Download PDF	2009	SPD
Approximations to the stochastic Burgers equation Authors: Jochen Voss, Martin Hairer Download PDF	2009	SPD
SPDE in Hilbert space with locally monotone coefficients Authors: Wei Liu, Michael Roeckner Download PDF	2009	SPD
Potential theory of infinite dimensional Lévy processes Authors: A Cornea, Michael Roeckner, L Beznea Download PDF	2009	SPD
BV functions in a Gelfand triple and the stochastic reflection problem on a convex set of a Hilbert space Authors: Xiangchan Zhu, Xiangchan Zhu, Michael Roeckner Download PDF	2009	SPD
Dimension-independent Harnack inequalities for subordinated semigroups Authors: Michael Roeckner, Jin Wang, M Gordina Download PDF	2009	SPD
Uniqueness for solutions of Fokker-Planck equations on infinite dimensional spaces Authors: Giuseppe Da Prato, Michael Roeckner, Vladimir Igorevich Bogachev Download PDF	2009	SPD
The global random attractor for a class of stochastic porous media equations Authors: Benjamin Gess, P Lescot, Michael Roeckner, W-J Beyn Download PDF	2009	SPD
Explosive solutions of stochastic reaction-diffusion equations in mean $\it L^p$-norm Authors: Pao-Liu Chow Download PDF	2009	SPD
Wick product in the stochastic Burgers equation: A curse or a cure? Authors: Sergey Lototsky, S Kaligotla Download PDF	2009	SPD
Weak solutions to stochastic wave equations with values in Riemannian manifolds Authors: Martin Ondreját, Z Brzezniak Download PDF	2009	SPD
A note on generalized Malliavin calculus Authors: BL Rozovskii, Sergey Lototsky, D Selesi Download PDF	2009	SPD
On quantized stochastic Navier-Stokes equations Authors: Remigijus Mikulevicius, BL Rozovskii Download PDF	2009	SPD
Smooth solutions for the dyadic model Authors: F Morandin, Marco Romito, D Barbato Download PDF	2009	SPD
Approximation of invariant foliations for stochastic dynamical systems Authors: X Kan, X Sun, Jinqiao Duan Download PDF	2009	SPD
Effective dynamics of a coupled microscopic-macroscopic stochastic system Authors: H Fu, Jinqiao Duan, J Ren, D Cao Download PDF	2009	SPD
Geometric shape of invariant manifolds for a class of stochastic partial differential equations Authors: Jinqiao Duan, Xin Chen, Tusheng Zhang Download PDF	2009	SPD
Maximal inequality of stochastic convolution driven by compensated Poisson random measures in Banach spaces Authors: Erika Hausenblas, Z Brzezniak, Xiangchan Zhu Download PDF	2009	SPD
Inviscid large deviation principle and the 2D Navier-Stokes equations with a free boundary condition Authors: Annie Millet, H Bessaih Download PDF	2009	SPD
Cores for generators of some Markov semigroups Authors: Michael Roeckner, Giuseppe Da Prato Download PDF	2009	SPD
Regularity analysis for stochastic partial differential equations with nonlinear multiplicative trace class noise Authors: Michael Roeckner, Arnulf Jentzen Download PDF	2009	SPD
A mild Itô formula for SPDEs Authors: Michael Roeckner, Arnulf Jentzen, Giuseppe Da Prato Download PDF	2009	SPD
Non-time-homogeneous generalized Mehler semigroups and applications Authors: Shunxiang Ouyang, Michael Roeckner Download PDF	2009	SPD
The stochastic reflection problem on an infinite dimensional convex set and BV functions in a Gelfand triple Authors: Michael Roeckner, Xiangchan Zhu, Xiangchan Zhu Download PDF	2009	SPD
Random attractors for a class of stochastic partial differential equations driven by general additive noise Authors: Wei Liu, Michael Roeckner, Benjamin Gess Download PDF	2009	SPD
Harnack inequalities and applications for Ornstein-Uhlenbeck semigroups with jump Authors: Michael Roeckner, Jin Wang, Shunxiang Ouyang Download PDF	2009	SPD
Pathwise uniqueness for singular SDEs driven by stable processes Authors: Enrico Priola Download PDF	2009	SPD
On local mixing conditions for SDE approximations Authors: A Yu Veretennikov, SA Klokov Download PDF	2009	SPD
On asymptotics for Vaserstein coupling of a Markov chain Authors: A Yu Veretennikov, OA Butkovsky Download PDF	2009	SPD
Hitting probabilities for non-linear systems of stochastic waves Authors: Robert Dalang, Marta Sanz-Solé Download PDF	2009	SPD
Hitting probabilities for systems of non-linear stochastic heat equations in spatial dimension $\it k$ $\geq 1$ Authors: Robert Dalang, Davar Khoshnevisan, Eulalia Nualart Download PDF	2009	SPD
On the stochastic Strichartz estimates and the stochastic nonlinear Schrödinger equation on a compact riemannian manifold Authors: Z Brzezniak, Annie Millet Download PDF	2009	SPD
Global solutions of the random vortex filament equation Authors: Z Brzezniak, M Gubinelli, Mikhail Neklyudov Download PDF	2009	SPD
Existence and convergence results for infinite dimensional nonlinear stochastic equations with multiplicative noise Authors: Viorel Barbu, Z Brzezniak, Erika Hausenblas, L Tubaro Download PDF	2009	SPD

Workshops

SPDW01

Seminars

Thursday 14th January 2010
16:30 to 17:30	Jan van Neerven Delft University of Technology Domain identification for analytic Ornstein-Uhlenbeck operators	Room 2

Thursday 21st January 2010
11:30 to 12:30	Sergei Fedotov University of Manchester Continuous time random walk and non-linear reaction-transport equations	Room 1

Friday 22nd January 2010
11:30 to 12:30	Anne de Bouard Centre de Physique Théorique de l’Ecole Polytechnique (CPHT) Stochastic nonlinear Schrodinger equations and modulation of solitary waves	Room 1

Wednesday 3rd February 2010
11:30 to 12:30	Robert Dalang Intermittency properties in a hyperbolic Anderson model	Room 1

Thursday 4th February 2010
11:30 to 12:30	Szymon Peszat Polish Academy of Sciences Central limit theorems for additive functionals of stable processes	Room 1

Wednesday 17th February 2010
11:30 to 12:30	Andreas Prohl Eberhard Karls Universität Tübingen On operator-splitting methods to solve the stochastic incompressible Stokes equations	Room 1

Thursday 18th February 2010
10:15 to 11:15	Lorenzo Zambotti Université Pierre et Marie Curie Paris An entropic functional on families of random variables from theoretical biology	Room 1
11:30 to 12:30	Yoshiki Otobe Shinshu University Recurrence properties for quantum dynamics	Room 1

Tuesday 23rd February 2010
10:00 to 10:50	Leonid Mytnik Technion - Israel Institute of Technology Infinite rate mutually catalytic branching model	Room 1
11:00 to 12:00	Tadahisa Funaki University of Tokyo Brascamp-Lieb inequality and Wiener integrals for centred Bessel processes	Room 1

Thursday 25th February 2010
11:00 to 12:00	Stella Brassesco Instituto Venezolano de investigaciones Científicas (IVIC) The stochastic Allen-Cahn equation with Dobrushin boundary conditions	Room 1

Tuesday 2nd March 2010
11:00 to 12:30	Martin Ondreját Academy of Sciences of the Czech Republic Nonlinear stochastic wave equations I	Room 1

Wednesday 3rd March 2010
11:00 to 12:30	Martin Ondreját Academy of Sciences of the Czech Republic Nonlinear stochastic wave equations II	Room 1

Thursday 4th March 2010
11:00 to 12:00	Salah-Eldin Mohammed Southern Illinois University Carbondale Linear SPDE's	Room 1
14:00 to 15:00	Dirk Blömker Universität Augsburg The effect of degenerate noise on dominant modes for SPDEs	Room 2

Tuesday 9th March 2010
11:30 to 12:30	Stochastic processes in magnetism; basic approaches	Room 2
15:00 to 16:00	Asymptotic coupling	Room 2

Wednesday 10th March 2010
10:30 to 11:15	Omar Lakkis University of Sussex Computing the stochastic Allen-Cahn problem	Room 2
11:30 to 12:30	Multiscale approaches to sub-picosecond heat driven magnetism reversal	Room 2

Friday 12th March 2010
10:30 to 11:15	Mamadou Sango University of Pretoria Homogenisation of a semilinear stochastic evolution problem in a perforated domain	Room 2

Thursday 18th March 2010
11:00 to 12:30	Giuseppe Da Prato Scuola Normale Superiore di Pisa Kolmogorov equations in Hilbert spaces I	Room 2

Friday 19th March 2010
11:00 to 12:30	Giuseppe Da Prato Scuola Normale Superiore di Pisa Kolmogorov equations in Hilbert spaces II	Room 1
14:15 to 15:15	Eulalia Nualart Université Paris 13 Strict positivity of the density for spatially homogeneous SPDEs	Room 1

Thursday 25th March 2010
11:00 to 12:30	Giuseppe Da Prato Scuola Normale Superiore di Pisa Kolmogorov equations in Hilbert spaces III	Room 2

Friday 26th March 2010
11:00 to 12:30	Giuseppe Da Prato Scuola Normale Superiore di Pisa Kolmogorov equations in Hilbert spaces IV	Room 2

Wednesday 7th April 2010
17:30 to 18:30	Pierre-Louis Lions CNRS & Université Paris-Dauphine Mean field games	Room 1

Monday 12th April 2010
17:00 to 18:30	Hypoelliptic SPDEs and ergodicity	Room 1

Friday 16th April 2010
16:30 to 17:30	Arnaud Debussche ENS de Cachan On the nonlinear Schridinger equation with white noise dispersion	Room 1
17:30 to 18:30	Mikhail Neklyudov University of York Ergodicity of infinite particle systems with locally conserved quantities	Discussion Room

Wednesday 21st April 2010
11:30 to 12:30	Erika Hausenblas Montanuniversität Leoben Maximum Inequality and Maximum Regularity of SPDEs driven by jump processes	Room 1
14:00 to 15:00	Viorel Barbu Universitatea Alexandru Ioan Cuza Stochastic nonlinear PDEs versus deterministic infinite dimensional Cauchy problem I	Room 1

Thursday 22nd April 2010
11:00 to 12:30	Jerzy Zabczyk Polish Academy of Sciences On the Musiela SPDE with Levy noise	Room 1
14:00 to 15:00	Nigel Cutland University of York Global attractors for 3D stochastic Navier-Stokes equations	Room 1

Monday 26th April 2010
11:30 to 12:30	Samy Tindel Université Henri Poincaré On rough PDEs	Room 1

Tuesday 27th April 2010
11:30 to 12:30	Mike Tehranchi University of Cambridge Hedging in variance swap markets	Room 1
14:00 to 15:00	Viorel Barbu Universitatea Alexandru Ioan Cuza Stochastic nonlinear PDEs versus deterministic infinite dimensional Cauchy problems II	Room 1

Wednesday 28th April 2010
11:30 to 12:30	Roger Moser University of Bath Ginzburg-Landau vortices driven by Landau-Lifshitz equation	Room 1

Thursday 29th April 2010
14:00 to 15:00	Viorel Barbu Universitatea Alexandru Ioan Cuza Stochastic nonlinear PDEs versus deterministic infinite dimensional Cauchy problem III	Room 1

Thursday 6th May 2010
14:00 to 15:00	Sergei Turitsyn Aston University Dissipative solitons and coherent structures in fibre lasers	Room 1

Friday 7th May 2010
14:00 to 15:00	Rainer Buckdahn Université de Bretagne Occidentale On regularity properties of a class of Hamiltonian-Jacobi-Bellman equations	Room 1

Tuesday 11th May 2010
11:30 to 12:30	Aaron Yip Yip Indiana University-Purdue University Indianapolis Some recent investigations on interfacial propagation in inhomogeneous medium	Room 1

Wednesday 12th May 2010
16:00 to 17:00	Mauro Mariani Université Paul Cézanne Aix-Marseille III The random vortexes model and the 2D Navier-Stokes equation	Room 1

Thursday 13th May 2010
14:00 to 15:00	Marta Sanz-Solé Universitat de Barcelona A class of stochastic partial differential equations driven by a fractional noise	Room 1

Friday 14th May 2010
14:00 to 15:00	Hongwei Long Florida Atlantic University Invariant measures for stochastic evolution equations in M-type 2 Banach spaces	Room 1
15:00 to 16:00	Andrey A. Dorogovtsev National Academy of Sciences of Ukraine Stochastic calculus for flows with singularities	Room 1

Tuesday 18th May 2010
14:00 to 15:00	Mauro Mariani Université Paul Cézanne Aix-Marseille III Large deviations for stochastic conservation laws	Room 1
15:15 to 16:15	Yana Belopolskaya St. Petersburg State Polytechnical University Stochastic approaches to fully nonlinear PDEs	Room 1

Thursday 20th May 2010
11:30 to 12:30	Yuri Kondratiev Universität Bielefeld Kinetic equations from stochastic dynamics in continuum	Room 1

Friday 21st May 2010
11:30 to 12:30	Michael Rockner Universität Bielefeld Potential theory on Wiener space revisited	Room 1
14:00 to 15:00	Michael Rockner Universität Bielefeld Singular stochastic equations on Hilbert spaces: Harnack inequality, ultraboundedness and other recent results	Room 1
15:30 to 16:30	Feng-Yu Wang Swansea University Harnack inequality for diffusion semigroups with non-constant difussion coefficients	Room 1

Monday 24th May 2010
11:30 to 12:30	Jason Swanson University of Central Florida A change of variable formula with It\^o correction term	Room 1
17:30 to 18:30	Yakov Sinai Princeton University Renormalisation Group Method in Fluid Dynamics	Room 1

Wednesday 26th May 2010
09:45 to 10:45	Pao-Liu Chow Wayne State University SPDEs and parabolic equations in Gauss-Sobolev spaces	Room 1

Friday 28th May 2010
09:45 to 10:45	Carlo Marinelli Rheinische Friedrich-Wilhelms-Universität Bonn Ergodicity for nonlinear stochastic evolution equations with multiplicative Poisson noise	Room 1

Tuesday 1st June 2010
11:30 to 12:30	Oleg Georgievich Smolyanov Institute of Mechanics of Moscow State University Liouville equations with respect to measures (as a way to get Bogoliubov) type equations	Room 1

Tuesday 8th June 2010
13:30 to 14:20	Nicolai Krylov University of Minnesota Stochastic partial differential equations and their applications	Room 1

Wednesday 9th June 2010
11:30 to 12:30	Yakov Sinai Princeton University The decay of Fourier modes of solutions	Room 1

Thursday 10th June 2010
11:30 to 12:30	Elliptic equations for measures and lower bounds for densities	Room 1

Friday 11th June 2010
11:30 to 12:30	Igor Chueshov Karazin Kharkov National University Synchronisation in coupled stochastic PDEs	Room 1

Friday 18th June 2010
11:30 to 12:30	Tomasz Szarek University of Gdansk Ergodic measures for Markov semigroups	Room 1
14:00 to 15:00	Bin Xie Shinshu University An SPDE with the laws of Levy processes as its invariant measures	Room 1

Monday 21st June 2010
14:00 to 15:30	Discussion	Room 2
16:00 to 16:45	Hakima Bessaih University of Wyoming On some stochastic shell models of turbulance	Room 1

Wednesday 23rd June 2010
17:00 to 18:00	Perturbation theory for systems with many invariant measures: Long-time effects (part I)	Room 1

Friday 25th June 2010
11:00 to 12:00	Thomas Wanner George Mason University Topology-Guided Sampling of Gaussian Random Fields	Room 2

Stochastic partial differential equations (SPDEs)

Organisers

Zdzislaw Brzezniak
Martin Hairer University of Warwick
Michael Rockner Universität Bielefeld
Takis Souganidis University of Chicago
Roger Tribe University of Warwick

Speakers

Viorel Barbu Universitatea Alexandru Ioan Cuza
Yana Belopolskaya St Petersburg State University of Technology and Design
Hakima Bessaih University of Wyoming
Dirk Blömker RWTH Aachen University
Stella Brassesco Instituto Venezolano de investigaciones Científicas (IVIC)
Rainer Buckdahn Université de Bretagne Occidentale
Pao-Liu Chow Wayne State University
Igor Chueshov Karazin Kharkov National University
Nigel Cutland University of York
Giuseppe Da Prato Scuola Normale Superiore di Pisa
Robert Dalang
Anne de Bouard Centre de Physique Théorique de l’Ecole Polytechnique (CPHT)
Arnaud Debussche ENS de Cachan
Andrey A. Dorogovtsev National Academy of Sciences of Ukraine
Sergei Fedotov University of Manchester
Tadahisa Funaki University of Tokyo
Erika Hausenblas Montanuniversität Leoben
Yuri Kondratiev Universität Bielefeld
Nicolai Krylov University of Minnesota
Omar Lakkis
Pierre-Louis Lions CNRS & Université Paris-Dauphine
Hongwei Long Florida Atlantic University
Mauro Mariani Université Paul Cézanne Aix-Marseille III
Carlo Marinelli Rheinische Friedrich-Wilhelms-Universität Bonn
Salah-Eldin Mohammed Southern Illinois University Carbondale
Roger Moser University of Bath
Leonid Mytnik Technion - Israel Institute of Technology
Mikhail Neklyudov University of York
Eulalia Nualart Université Paris 13
Martin Ondreját Academy of Sciences of the Czech Republic
Yoshiki Otobe Shinshu University
Szymon Peszat Polish Academy of Sciences
Andreas Prohl Eberhard Karls Universität Tübingen
Michael Rockner Universität Bielefeld
Mamadou Sango University of Pretoria
Marta Sanz-Solé Universitat de Barcelona
Yakov Sinai Princeton University
Oleg Georgievich Smolyanov Institute of Mechanics of Moscow State University
Jason Swanson University of Central Florida
Tomasz Szarek University of Gdansk
Mike Tehranchi Japan Atomic Energy Agency & University of Texas at Austin
Samy Tindel Université Henri Poincaré
Sergei Turitsyn Aston University
Jan van Neerven Delft University of Technology
Feng-Yu Wang Swansea University
Thomas Wanner George Mason University
Bin Xie Shinshu University
Aaron Yip Yip Indiana University-Purdue University Indianapolis
Jerzy Zabczyk Polish Academy of Sciences
Lorenzo Zambotti Université Pierre et Marie Curie Paris

Show All

Stochastic partial differential equations (SPDEs)

Programme theme

Self-financing Participants

Preprints

Local existence and uniqueness in the largest critical space for a surface growth model

Pathwise uniqueness and continuous dependence for SDEs with nonregular drift

Rough path stability of SPDEs arising in non-linear filtering

Matematica - Existence for semilinear parabolic stochastic equations

Internal stabilization by noise of the Navier-Stokes equation

Lattice embeddings in percolation

Plaquettes, spheres, and entanglement

Conditional distributions, exchangable particle systems, and stochastic partial differential equations

Master-slave synchronization and invariant manifolds for coupled stochastic systems

Strong uniqueness for both Dirichlet operators and stochastic dynamics to Gibbs measures on a path space with exponential interactions

Singular pertubations to semilinear stochastic heat equations

Approximations to the stochastic Burgers equation

SPDE in Hilbert space with locally monotone coefficients

Potential theory of infinite dimensional Lévy processes

BV functions in a Gelfand triple and the stochastic reflection problem on a convex set of a Hilbert space

Dimension-independent Harnack inequalities for subordinated semigroups

Uniqueness for solutions of Fokker-Planck equations on infinite dimensional spaces

The global random attractor for a class of stochastic porous media equations

Explosive solutions of stochastic reaction-diffusion equations in mean $\it L^p$-norm

Wick product in the stochastic Burgers equation: A curse or a cure?

Weak solutions to stochastic wave equations with values in Riemannian manifolds

A note on generalized Malliavin calculus

On quantized stochastic Navier-Stokes equations

Smooth solutions for the dyadic model

Approximation of invariant foliations for stochastic dynamical systems

Effective dynamics of a coupled microscopic-macroscopic stochastic system

Geometric shape of invariant manifolds for a class of stochastic partial differential equations

Maximal inequality of stochastic convolution driven by compensated Poisson random measures in Banach spaces

Inviscid large deviation principle and the 2D Navier-Stokes equations with a free boundary condition

Cores for generators of some Markov semigroups

Regularity analysis for stochastic partial differential equations with nonlinear multiplicative trace class noise

A mild Itô formula for SPDEs

Non-time-homogeneous generalized Mehler semigroups and applications

The stochastic reflection problem on an infinite dimensional convex set and BV functions in a Gelfand triple

Random attractors for a class of stochastic partial differential equations driven by general additive noise

Harnack inequalities and applications for Ornstein-Uhlenbeck semigroups with jump

Pathwise uniqueness for singular SDEs driven by stable processes

On local mixing conditions for SDE approximations

On asymptotics for Vaserstein coupling of a Markov chain

Hitting probabilities for non-linear systems of stochastic waves

Hitting probabilities for systems of non-linear stochastic heat equations in spatial dimension $\it k$ $\geq 1$

On the stochastic Strichartz estimates and the stochastic nonlinear Schrödinger equation on a compact riemannian manifold

Global solutions of the random vortex filament equation

Existence and convergence results for infinite dimensional nonlinear stochastic equations with multiplicative noise

Workshops

Stochastic partial differential equations (SPDEs)

Stochastic partial differential equations (SPDEs) and their applications

Rough paths, SPDEs and related topics

Satellite at the University of York

Workshop on filtering

Stochastic partial differential equations (SPDEs): approximation, asymtotics and computation

Stochastic PDEs

Seminars

Organisers

Speakers

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