An Integrated Version of Varadhan’s Asymptotics for Lower-Order Perturbations of Strong Local Dirichlet Forms
- 222 Downloads
The studies of J. A. Ramírez, Hino–Ramírez, and Ariyoshi–Hino showed that an integrated version of Varadhan’s asymptotics holds for Markovian semigroups associated with arbitrary strong local symmetric Dirichlet forms. In this paper, we consider non-symmetric bilinear forms that are the sum of strong local symmetric Dirichlet forms and lower-order perturbed terms. We give sufficient conditions for the associated semigroups to have asymptotics of the same type.
KeywordsVaradhan’s asymptotics Short-time behavior Dirichlet form Intrinsic distance
Mathematics Subject Classification (2010)31C25 60J60 58J37 47D07
This study was supported by JSPS KAKENHI Grant Number JP15H03625.
- 2.Bauer, H.: Measure and integration theory. de Gruyter Studies in Mathematics, vol. 26. Walter de Gruyter, Berlin (2001)Google Scholar
- 3.Bouleau, N., Hirsch, F.: Dirichlet forms and analysis on Wiener Space. de Gruyter Studies in Mathematics, vol. 14. Walter de Gruyter, Berlin (1991)Google Scholar
- 4.Davies, E.B.: Heat kernels and spectral theory. Cambridge Tracts in Mathematics, vol. 92. Cambridge University Press, Cambridge (1990)Google Scholar
- 6.Fukushima, M., Oshima, Y., Takeda, M.: Dirichlet forms and symmetric Markov processes, 2nd edn. de Gruyter Studies in Mathematics, vol. 19. Walter de Gruyter, Berlin (2011)Google Scholar
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.