## Tohoku Mathematical Journal

### The conservativeness of Girsanov transformed symmetric Markov processes

Yusuke Miura

#### Abstract

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 [3], 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.

#### Article information

Source
Tohoku Math. J. (2), Volume 71, Number 2 (2019), 221-241.

Dates
First available in Project Euclid: 21 June 2019

https://projecteuclid.org/euclid.tmj/1561082597

Digital Object Identifier
doi:10.2748/tmj/1561082597

Mathematical Reviews number (MathSciNet)
MR3973250

Zentralblatt MATH identifier
07108038

Subjects
Primary: 31C25: Dirichlet spaces
Secondary: 60J25: Continuous-time Markov processes on general state spaces

#### Citation

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

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