On the first quasiderivatives of solutions of itÔ stochastic equations

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Abstract

In the study of smoothness of probabilistic solutions of differential equations an important role is played by the derivatives of the solutions of stochastic equations with respect to the initial data. In this article the possibility of replacing them by other processes called quasiderivatives is considered. As examples of the advantage of such a substitution, the intrinsic smoothness of probabilistic solutions in a domain is proved in several cases.

Original languageEnglish (US)
Pages (from-to)377-403
Number of pages27
JournalIzvestiya Mathematics
Volume40
Issue number2
DOIs
StatePublished - Apr 30 1993

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