Stochastic Processes with Short Memory

Details Stochastic Processes with Short Memory Stochastic Processes with Short Memory

2004-01-14

arxiv.org/abs/math/0401144v1

Mathematics

Probability

10 pages

Scientific paper

The mathematical model of a linear system with the short memory about own stochastic behavior is proposed. It is assumed that the system is under a continual influence of independent stochastic impulses. In a short memory approximation the expression of the stochastic process is found. An application of the model proposed to capital market processes is examined. The approach allows form a stochastic differential for processes concerned. The analog of the Black-Scholes equation for assets dealt on a market with the memory is expressed.

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