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Stochastic Processes with Short Memory

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  • D. N. Zhabin

Abstract

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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  • D. N. Zhabin, 2004. "Stochastic Processes with Short Memory," Papers math/0401144, arXiv.org.
    • Handle: RePEc:arx:papers:math/0401144
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