Research for Stochastic Processes

This objectives of this paper are to calculate the probability that a given ship in a formation is targeted by a given number of incoming ASMs, and to calculate the probability that a given ship will survive the raid.

The expanded version of a set of lecture notes, this work is concerned with mathematical analysis, and not modeling target motion or detection functions, and not with the development of computer codes.

Some apparent contradictions in the operations research literature of search theory and information theory are reviewed, and the source of the conflict is isolated. The information processes connected with a search operation are examined by studying the geometric properties of information surfaces in search-allocation space. Some new theorems are developed which show that the connection between search and information theory is much stronger than previously believed. It is demonstrated that the amount of search effort, C is a critical parameter in the relation between search and information gain. For very small values of C, there is no unique relation between detection probability and information gain; for very large values of C, the optimal whereabouts search policy produces the greatest information gain; for a broad intermediate range of C (including many cases of practical interest) the optimal detection search policy produces the greatest information gain.

This paper considers the effects of fluctuations on chemical systems that have multiple steady states. The paper considers experiments beginning near the deterministic separatrix, and formulates a stochastic first exit problem.