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Journal of Applied Mathematics and Stochastic Analysis - Volume 7 1994, Issue 3, Pages 239-246



Ukranian Academy of Science, Institute of Mathematics, Kiev, Ukraine

Michigan State University, Department of Mathematics, East Lansing 48824, MI, USA

Received 1 February 1994; Revised 1 April 1994

Copyright © 1994 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider transformations of the formTaxt=xt+∫0tas,xdson the space C of all continuous functions x=xt:0,1→ℝ, x0=0, where as,xis a measurable function 0,1×C→ℝ which is 𝒞˜s-measurable for a fixed s and 𝒞˜sis the σ-algebra generated by {xu,u≤t}. It is supposed that Ta maps the Wiener measure μ0 on C,𝒞˜s into a measure μa which is equivalent with respect to μ0. We study some conditions of invertibility of such transformations. We also consider stochastic differential equations of the formdyt=dwt+at,ytdt, y0=0where wt is a Wiener process. We prove that this equation has a unique strong solution if and only if it has a unique weak solution.





Author: Anatoli V. Skorokhod

Source: https://www.hindawi.com/



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