Tohoku Mathematical Journal
2019
June
SECOND SERIES VOL. 71, NO. 2

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

Title QUINARY LATTICES AND BINARY QUATERNION HERMITIAN LATTICES

Author Yusuke Miura

(Received January 20, 2017, revised March 21, 2017)
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.

Mathematics Subject Classification. Primary 31C25; Secondary 60J25.
Key words and phrases. Symmetric Markov process, Girsanov transform, Dirichlet form, Schrödinger form.

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