Comparison theorem and estimates for transition probability densities of diffusion processes |
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| Authors: | Email author" target="_blank">Zhongmin?QianEmail author Francesco?Russo Weian?Zheng |
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| Institution: | (1) Laboratoire de statistique et probabilités, Université Paul-Sabatier, 118, route de Narbonne, 31062 Toulouse and CNRS, France;(2) Institut Galilée, Mathématiques, Université de Paris, 13, 99, av. J.B. Clément, 99430 Villetaneuse, France;(3) Department of Statistics, East China Normal University, Shanghai, China;(4) Department of Mathematics, University of California, Irvine, CA, 92697 USA |
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| Abstract: | We establish several comparison theorems for the transition probability density p
b
(x,t,y) of Brownian motion with drift b, and deduce explicit, sharp lower and upper bounds for p
b
(x,t,y) in terms of the norms of the vector field b. The main results are obtained through carefully estimating the mixed moments of Bessel processes. All constants are explicit in our lower and upper bounds, which is different from most of the previous estimates, and is important in many applications for example in statistical inferences for diffusion processes.Research partially supported by N.S.F. Grants DMS-0203823, and by Doctoral Program Fundation of the Ministry of Education of China, Grant No. 20020269015.
Mathematics Subject Classification (2000): Primary: 60H10, 60H30; Secondary: 35K05 |
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| Keywords: |  Transition probabilities" target="_blank">gif" alt="ensp" align="MIDDLE" BORDER="0">Transition probabilities Diffusion processes Comparison theorems Bessel processes |
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