Comparison theorem and estimates for transition probability densities of diffusion processes in memory of professor paul-andre meyer

Probability Theory and Related Fields

Volumn 127, Issue 3, 2003, Pages 388-406

  Qian, Zhongmin ^a,b   Russo, Francesco ^c   Zheng, Weian ^d,e  

^a INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

^b CNRS   (France)

^c UNIVERSITÉ PARIS 13   (France)

^d EAST CHINA NORMAL UNIVERSITY   (China)

^e UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Bessel processes; Comparison theorems; Diffusion processes; Transition probabilities

Indexed keywords

EID: 0344982920     PISSN: 01788051     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00440-003-0291-1     Document Type: Article

References (19)

1. Azencott, R.: Grandes déviations et applications. Ecoles d'Eté de Probabilités de Saint-Flour VIII-1978, P. L. Hennequin (ed.), Lecture Notes in Math. 774, Springer, Berlin, pp. 1-176, 1980
2. Aronson, D.G.: Non-negative solutions of linear parabolic equation. Ann. Sci. Norm. Sup. Pisa 22, 607-694 (1967)
3. Davies, E.B.: Heat Kernels and Spectral Theory. Cambridge Tracts in Math. 92, Cambridge University Press, 1989
4. Gradinaru, M., Herrmann, S., Roynette, B.: A singular large deviations phenomenon. Ann. Inst. H. Poincaré Probab. Stat. 37(5), 555-580 (2001)
5. Karatzas, I., Shreve, S.E.: Brownian Motion and Stochastic Calculus. Springer-Verlag, 1988
6. Kendall, D.: Pole-seeking Brownian motion and bird navigation. J. Royal Stat. Soc., Series B 36(3), 365-417 (1974)
7. Ladyženskaja, O.A., Solonnikov, V.A., Ural'ceva, N.N.: Linear and Quasi-linear Equations of Parabolic Type. Translations of Mathematical Monographs, Volume 23, AMS, 1968
8. Lyons, T.J., Zheng, W.A.: On conditional diffusion processes. Proc. Royal Soc. Edinburgh 115A, 243-255 (1990)
9. Nash, J.: Continuity of solutions of parabolic and elliptic equations. Am. J. Math. 80, 931-954 (1958)
10. Norris, J.R.: Long time behavior of heat flow: global estimates and exact asymptotics. Arch. Rational Mech. Anal. 140, 161-195 (1997)
11. Norris, J.R., Stroock, D.W.: Estimates on the fundamental solution to heat flows with uniformly elliptic coefficients. Proc. London Math. Soc. 62(3), 373-402 (1991)
12. Pitman, J., Yor, M.: Bessel processes and infinitely divisible laws. In: "Stochastic Integrals", Lecture Notes in Math. D. Williams (ed.), 851, Springer, 1981
13. Prakasa Rao, B.L.S.: Statistical Inference for Diffusion Type Processes. Arnold, Oxford University Press Inc., New York, 1998
14. Qian, Z., Zheng, W.: Sharp bounds for transition probability densities of a class of diffusions. C. R. Acad. Sci. Paris, Ser. I 335, 953-957 (2002)
15. Revuz, D., Yor, M.: Continuous Martingales and Brownian Motion. Springer-Verlag, 1991
16. Shiga, T., Watanabe, S.: Bessel diffusions as a one-parameter family of diffusion processes. Z. F. W. 27, 37-46 (1973)
17. Yor, M.: On square root boundaries for Bessel processes and pole seeking Brownian motion. In: "Stochastic Analysis and Applications", Lecture Notes in Math. 1095, Springer, 1984
18. Yor, M.: Local Times and Excursions for Brownian Motion: a concise introduction. Leccions en Matemáticas, Número 1, 1996, Universidad Central de Venezuela, 1995
19. Yor, M.: Some Aspects of Brownian Motion Part I: Some Special Functionals. Birkhäuser Verlag, Basel, Boston, Berlin, 1992