Tohoku Mathematical Journal

The conservativeness of Girsanov transformed symmetric Markov processes

Yusuke Miura

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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

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

First available in Project Euclid: 21 June 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

symmetric Markov process Girsanov transform Dirichlet form Schrödinger form


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.

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