Tohoku Mathematical Journal
- Tohoku Math. J. (2)
- Volume 71, Number 2 (2019), 221-241.
The conservativeness of Girsanov transformed symmetric Markov processes
In this paper, we study those Girsanov transformations of symmetric Markov processes which preserve the symmetry. Employing a criterion for uniform integrability of exponential martingales due to Chen , we identify the class of transformations which transform the original process into a conservative one, even if the original one is explosive. We also consider the class of transformations which transform to a recurrent one. In [14, 22], the same problems are studied for symmetric diffusion processes. Our main theorem is an extension of their results to symmetric Markov processes with jumps.
Tohoku Math. J. (2), Volume 71, Number 2 (2019), 221-241.
First available in Project Euclid: 21 June 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 31C25: Dirichlet spaces
Secondary: 60J25: Continuous-time Markov processes on general state spaces
Miura, Yusuke. The conservativeness of Girsanov transformed symmetric Markov processes. Tohoku Math. J. (2) 71 (2019), no. 2, 221--241. doi:10.2748/tmj/1561082597. https://projecteuclid.org/euclid.tmj/1561082597