Lower bounds for the density of locally elliptic Itô processes

Annals of Probability

Volumn 34, Issue 6, 2006, Pages 2406-2440

  Bally, Vlad ^a,b  

^a UNIVERSITÉ GUSTAVE EIFFEL   (France)

^b UFR des Sciences et Technologie   (France)

Author keywords

Density of the low; It processes; Lower bounds; Malliavin calculus

Indexed keywords

EID: 33947522214     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/009117906000000458     Document Type: Article

References (17)

1. AIDA, S., KUSUOCKA, S. and STROOCK, D. (1993). On the support of Wiener functionals. In Asymptotic Problems in Probability Theory: Wiener Functional and Asymptotics (K. D. Elworthy and N. Ikeda, eds.). Pitman Res. Notes Math. Ser. 284 3-34. Longman Sc. Tech., Harlow. MR1354161
2. BALLY, V. (2003). Lower bounds for the density of the law of locally elliptic Itôprocesses. Preprint 4887, INRIA.
3. BALLY, V. and PARDOUX, E. (1998). Malliavin calculus for white noise driven parabolic SPDEs. Potential Anal. 9 27-64. MR1644120
4. BASS, R. F. (1997). Diffusions and Elliptic Operators. Probability and Its Applications. Springer, New York. MR1483890
5. BEN-AROUS, G. and LEANDRE, R. (1991). Decroissance exponentille du noyau de la chaleur sur la diagonale. II. Probab. Theory Related Fields 90 377-402. MR1133372
6. DALANG, R. and NUALART, E. (2004). Potential theory for hyperbolic SPDEs. Ann. Probab. 32 2099-2148. MR2073187
7. FEFFERMAN, C. L. and SANCHEZ-CALLE, A. (1986). Fundamental solutions of second order subelliptic operators. Ann. of Math. (2) 124 247-272. MR0855295
8. FRIEDMAN, A. (1975). Stochastic Differential Equations and Applications. Academic Press, New York. MR0494490
9. GUÉRIN, H., MÉLÉARD, S. and NULALART, E. (2006). Estimate for the density of a nonlinear Landau proccess. J. Funct. Anal. 238 649-677.
10. HÖRMANDER, L. (1990). The Analysis of Linear Partial Differential Operators. I, 2nd ed. Springer, Berlin. MR1065993
11. KUSUOKA, S. and STROOCK, D. (1985). Applications of the Malliavin calculus, part II. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 32 1-76. MR0783181
12. KUSUOKA, S. and STROOCK, D. (1987). Applications of the Malliavin calculus, part III. J. Fac. Sci. Univ. Tokyo Sect. IA Math. 34 391-442. MR0914028
13. KOHATSU-HIGA, A. (2003). Lower bounds for densities of uniform elliptic random variables on Wiener space. Probab. Theory Related Fields 126 421-457. MR1992500
14. IKEDA, N. and WATANABE, S. (1989). Stochastic Differential Equations and Diffusion Processes, 2nd ed. North-Holland, Amsterdam. MR1011252
15. MILLET, A. and SANZ, M. (1997). Points of positive density for the solutions to a hyperbolic SPDE. Potential Anal. 7 623-659. MR1473646
16. NUALART, D. (1995). The Malliavin Calculus and Related Topics. Springer, New York. MR1344217
17. SANCHEZ-CALLE, A. (1986). Fundamental solutions and geometry of the sum of square of vector fields. Invent. Math. 78 143-160. MR0762360