Paper #358

Title:

Weak approximations. A Malliavin calculus approach

Author:

Arturo Kohatsu

Date:

February 1999

Abstract:

We introduce a variation of the proof for weak approximations that is suitable for studying the densities of stochastic processes which are evaluations of the flow generated by a stochastic differential equation on a random variable that maybe anticipating. Our main assumption is that the process and the initial random variable have to be smooth in the Malliavin sense. Furthermore if the inverse of the Malliavin covariance matrix associated with the process under consideration is sufficiently integrable then approximations for densities and distributions can also be achieved. We apply these ideas to the case of stochastic differential equations with boundary conditions and the composition of two diffusions.

Keywords:

Stochastic differential equations, boundary conditions, weak approximation, numerical analysis

JEL codes:

C15

Area of Research:

Statistics, Econometrics and Quantitative Methods

Published in:

Mathematics of Computation, 70, (2001), pp. 135-172

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