Donsker's delta functions and approximation of heat kernels by the time discretization methods

Kyoto Journal of Mathematics

Volumn 36, Issue 3, 1996, Pages 499-518

  Hu, Yaozhong ^a   Watanabe, Shinzo ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040656038     PISSN: 0023608X     EISSN: None     Source Type: Journal    
DOI: 10.1215/kjm/1250518506     Document Type: Article

References (11)

1. V. Bally and D. Tallay, The law of the Euler scheme for stochastic differential equations (II): convergence rate of the density, preprint (1995).
2. A. M. Garsia, Martingale inequalities, Mathematics Lecture Note Series, Benjamin, 1973.
3. Y. Z. Hu, Strong and weak order of time discretization schemes of stochastic differential equations, Sém. Prob. XXI, LNM 1626, Springer (1996), 218-227.
4. N. Ikeda and S. Watanabe, Stochastic differential equations and diffusion processes, second edition, North Holland, 1989.
5. P. E. Kloeden and E. Platen, Numerical solutions of stochastic differential equations, Springer, 1992.
6. A. Kohatsu-Higa, High order Itô-Taylor approximations to the density of a diffusion, Preprint (1995).
7. S. Kusuoka an D. W. Stroock, Applications of Malliavin calculus, part II, J. Fac. Sci. Univ. Tokyo, Sect. IA, Math., 32 (1985), 1-76.
8. R. Léandre, Minoration en temps petit de la densité d'une diffusion dégénérée, Journ. Funct. Anal., 74 (1987), 399-414.
9. k-hypoellicipticity with degeneracy, Stochastic Analysis (ed. A. Friedman and M. Pinsky), Academic Press (1978), 199-214, 327-340.
10. S. Watanabe, Stochastic differential equation and Malliavin calculus, Tata Institute of Fundamental Research, Springer, 1984.
11. S. Watanabe, Fractional order Sobolev spaces on Wiener space, Probab. Theory Relat. Fields, 95 (1993), 175-198.