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Weak approximations. A Malliavin calculus approach
Author(s):
Arturo
Kohatsu-Higa.
Journal:
Math. Comp.
70
(2001),
135-172.
MSC (2000):
Primary 60H07, 60H35, 65C30, 34B99
Posted:
March 2, 2000
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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.
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Additional Information:
Arturo
Kohatsu-Higa
Affiliation:
Universitat Pompeu Fabra. Departament d'Economia. Ramón Trias Fargas 25-27. 08005 Barcelona. Spain
Email:
kohatsu@upf.es
DOI:
10.1090/S0025-5718-00-01201-1
PII:
S 0025-5718(00)01201-1
Keywords:
Stochastic differential equations,
boundary conditions,
weak approximation,
numerical analysis
Received by editor(s):
June 9, 1998 and, in revised form March 2, 1999
Posted:
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 of article:
Copyright
2000,
by Arturo Kohatsu-Higa
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