# ICP

## Seminar

### Precision of Disorders Detection

Seminar Room 1, Newton Institute

#### Abstract

The lecture presents the results on the problem of change point detection for Markov processes generalizing the results contained in the publications [2], [4], [3] and [1]. The short description are as follows. A random sequence having segments being the homogeneous Markov processes is registered. Each segment has his own transition probability law and the length of the segment is unknown and random. The transition probabilities of each process are known and joint a priori distribution of the disorder moments is given. The detection of the disorder rarely is precise. The decision maker accepts some deviation in estimation of the disorder moment. In the models taken into account the aim is to indicate the change point with xed, bounded error with maximal probability. The case with various precision for over and under estimation of this point is analysed including situation when the disorder does not appears with positive probability is also included. The observed sequence, when the change point is known, has the Markov properties. The results explain the structure of optimal detector in various circumstances and shows new details of the solution construction as well insignicantly extends range of application. The motivation for this investigation is the modelling of the attacks in the node of networks. The objectives is to detect one of the attack immediately or in very short time before or after it appearance with highest probability. The problem is reformulated to optimal stopping of the observed sequences. The detailed analysis of the problem is presented to show the form of optimal decision function.Key Words: disorder problem, sequential detection, optimal stopping, multi-variate optimization

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