Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Some variational formulas on additive functionals of symmetric Markov chains

Authors: Daehong Kim, Masayoshi Takeda and Jiangang Ying
Journal: Proc. Amer. Math. Soc. 130 (2002), 2115-2123
MSC (2000): Primary 60F10, 60J20; Secondary 31C25
Published electronically: December 20, 2001
MathSciNet review: 1896048
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For symmetric continuous time Markov chains, we obtain some formulas on total occupation times and limit theorems of additive functionals by using large deviation theory.

References [Enhancements On Off] (What's this?)

  • [1] Cinlar, E.: Introduction to Stochastic Processes, Prentice-Hall, Inc., Englewood Cliffs, N. J., 1975. MR 52:1809
  • [2] Dembo, A., Zeitouni, O.: Large Deviations Techniques and Applications, Second edition. Applications of Mathematics, 38. Springer-Verlag, New York, 1998. MR 99d:60030
  • [3] Ellis, R. S.: Large deviations for a general class of random vectors, Ann. Probab. 12 (1984), 1-12. MR 85e:60032
  • [4] Fitzsimmons, P. J.: On the quasi-regularity of semi-Dirichlet forms, preprint.
  • [5] Freedman, D.: Approximating Countable Markov Chains, Holden-Day, 1972. MR 55:1493
  • [6] Fukushima, M., Oshima, Y., Takeda, M.: Dirichlet Forms and Symmetric Markov Processes, de Gruyter Studies in Mathematics, 19, Walter de Gruyter $\&$ Co., Berlin, 1994. MR 96f:60126
  • [7] Kim, D.: Asymptotic properties for continuous and jump type's Feynman-Kac functionals, Osaka J. Math. 37 (2000), 147-173. CMP 2000:10
  • [8] Kato, T.: A Short Introduction to Perturbation Theory for Linear Operators, Springer-Verlag, 1982. MR 83m:47015
  • [9] Sharpe, M.: General Theory of Markov Processes, Academic Press, 1988. MR 89m:60169
  • [10] Silverstein, M.: Symmetric Markov Processes, Springer Lect. Notes in Math. 426, 1974. MR 52:6891
  • [11] Takeda, M.: On a large deviation for symmetric Markov processes with finite lifetime, Stochastics and Stochastic Reports 59 (1996), 143-167. MR 98b:60057
  • [12] Takeda, M.: Exponential decay of life times and a theorem of Kac on total occupation times, Potential Analysis 11 (1999), 235-247. MR 2000i:60084
  • [13] Ying, J.: Bivariate Revuz measures and the Feyman-Kac formula, Ann. Inst. Henri Poincare, 32 (1995), 251-287. MR 97j:60139

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 60F10, 60J20, 31C25

Retrieve articles in all journals with MSC (2000): 60F10, 60J20, 31C25

Additional Information

Daehong Kim
Affiliation: Department of Mathematics, Pusan National University, Pusan, 609–735, Korea
Address at time of publication: Department of Systems and Information, Graduate School of Science and Technology, Kumamoto University, Kurokami, 2-39-1, Kumamoto 860-8555, Japan

Masayoshi Takeda
Affiliation: Mathematical Institute, Tohoku University, Sendai 980–8578, Japan

Jiangang Ying
Affiliation: Department of Mathematics, Zhejiang University, Hangzhou 310027, People’s Republic of China

Keywords: Additive functional, Dirichlet form, large deviation, symmetric Markov chain
Received by editor(s): May 20, 2000
Received by editor(s) in revised form: January 29, 2001
Published electronically: December 20, 2001
Additional Notes: The first author’s research was supported in part by Brain Korea 21
Communicated by: Claudia M. Neuhauser
Article copyright: © Copyright 2001 American Mathematical Society

American Mathematical Society