## Weak approximations. A Malliavin calculus approach

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- by Arturo Kohatsu-Higa;
- Math. Comp.
**70**(2001), 135-172 - DOI: https://doi.org/10.1090/S0025-5718-00-01201-1
- Published electronically: March 2, 2000

## 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 may be 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.## References

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## Bibliographic Information

**Arturo Kohatsu-Higa**- Affiliation: Universitat Pompeu Fabra. Departament d’Economia. Ramón Trias Fargas 25-27. 08005 Barcelona. Spain
- Email: kohatsu@upf.es
- Received by editor(s): June 9, 1998
- Received by editor(s) in revised form: March 2, 1999
- Published electronically: March 2, 2000
- Additional Notes: This article was partially written while the author was visiting the Department of Mathematics at Kyoto University with a JSPS fellowship. His research was partially supported by a DGES grant.
- © Copyright 2000 by Arturo Kohatsu-Higa
- Journal: Math. Comp.
**70**(2001), 135-172 - MSC (2000): Primary 60H07, 60H35, 65C30, 34B99
- DOI: https://doi.org/10.1090/S0025-5718-00-01201-1
- MathSciNet review: 1680895