RESEARCH ARTICLE

Algebraic convergence of diffusion processes on Rn with radial diffusion and drift coefficients

  • Yutao MA ,
  • Yingzhe WANG
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  • School of Mathematical Sciences & Laboratory of Mathematics and Complex Systems of Ministry of Education, Beijing Normal University, Beijing 100875, China

Received date: 16 Apr 2015

Accepted date: 20 Apr 2015

Published date: 05 Jun 2015

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

We consider the diffusion process Xt on n with radial diffusion and drift coefficients. We prove that once the one-dimensional diffusion |Xt| has algebraic L2-convergence, so does Xt. And some classical examples are discussed.

Cite this article

Yutao MA , Yingzhe WANG . Algebraic convergence of diffusion processes on Rn with radial diffusion and drift coefficients[J]. Frontiers of Mathematics in China, 2015 , 10(4) : 965 -984 . DOI: 10.1007/s11464-015-0476-9

1
Bobkov S G. Spectral gap and concentration for some spherically symmetric probability measures. In: Geometric Aspects of Functional Analysis. Lecture Notes in Math, Vol 1807. Berlin: Springer, 2003, 37-43

DOI

2
Bobkov S G, Ledoux M. Weighted Poincaré-type inequalities for Cauchy and other convex measures. Ann Probab, 2009, 37: 403-427

DOI

3
Bonnefont M, Joulin A, Ma Y T. Spectral gap for spherically symmetric log-concave probability measures, and beyond. Preprint, 2014

4
Chen M F. From Markov Chains to Non-equilibrium Particle Systems. Singapore: World Scientific, 1992

DOI

5
Chen M F. Analytic proof of dual variational formula for the first eigenvalue in dimension one. Sci Sin A, 1999, 42(8): 805-815

6
Chen M F, Li S F. Coupling Methods for Multidimensional diffusion processes. Ann Probab, 1989, 17(1): 151-177

DOI

7
Chen M F, Wang Y Z. Algebraic convergence of Markov chains. Ann Appl Probab, 2003, 13(2): 604-627

DOI

8
Deuschel J D. Algebraic L2-decay of attractive critical processes on the lattice. Ann Probab, 1994, 22(1): 264-283

DOI

9
Djellout H, Wu L M. Lipschitzian norm estimate of one-dimensional Poisson equations and applications. Ann Inst Henri Poincaré Probab Stat, 2011, 47(2): 450-465

DOI

10
Ikeda N, Watanabe S. Stochastic Differential Equations and Diffusion Processes. Tokyo: Kodansha Ltd, 1981

11
Liggett T M. L2 Rates of convergence for attractive reversible nearest particle systems: the critical case. Ann Probab, 1991, 19(3): 935-959

DOI

12
Lindvall T, Rogers L C G. Coupling of multidimensional diffusions by reflection. Ann Probab, 1986, 14: 860-872

DOI

13
Rockner M, Wang F-Y. Weak Poincaré inequalities and L2-convergence rates of Markov semigroup. J Funct Analysis, 2011, 185(2): 564-603

DOI

14
Wang Y Z. Algebraic convergence of diffusion processes on a real line. J Beijing Normal Univ, 2003, 39: 448-456

15
Wang Y Z. Algebraic convergence of diffusion processes on ℝn. Acta Math Sinica (Chin Ser), 2004, 47(5): 1001-1012 (in Chinese)

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