Short Communications

On a type of stochastic differential equations with anticipation

A. A. Dorogovtsev

Institute of Mathematics, Ukrainian National Academy of Sciences

Abstract: We consider equations analogous to Itф stochastic differential equations but which contain the stochastic derivative instead of the stochastic differential. We prove the existence of a solution and also the preservation of peculiarities of equations that contain an extended stochastic integral.

Keywords: stochastic derivative, extended stochastic integral, equations with anticipation.

Received: 12.05.1993

 English version: Theory of Probability and its Applications, 1995, 40:4, 753–756

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