Electronic Journal: Southwest Journal of Pure and Applied Mathematics Internet: http://rattler.cameron.edu/swjpam.html ISSN 1083-0464 Vol. No. 01, 1995, pp. 17–26 Submitted: June 11, 1995. Published: September 5, 1995.

STOCHASTIC CALCULUS AND INITIAL VALUE

ANALYSIS ON THE ONE DIMENSIONAL DIFFUSIONS

Dražen Pantić

Abstract. Stochastic calculus and initial value analysis are used for complete description of distribution type of diffusion processes with Lipschitz coefficients. Sufficient conditions so that the solutions of stochastic differential equations posses absolutely continuous one dimensional distribution are given. For stochastic differential equations with uniformly elliptic coefficients probability density is investigated in detail. Also, the distribution of inverse process is given.

(1991) A.M.S. Subject Classification Codes. 60H07, 60H10.

Key Words and Phrases. Malliavin calculus, solutions of stochastic differential equations, point distributions.

Department of Mathematics, University of Belgrade, Studentski trg 16, 11000 Beograd, Yugoslavia E-mail Address: epantidr@ubbg.etf.bg.ac.yu \begin{matrix}c \\ ◯ \end{matrix}1995 Cameron University

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