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Dynkin’s isomorphism without symmetry. (English) Zbl 1167.60016

Arous, Gerard Ben (ed.) et al., Stochastic analysing in mathematical physics. Proceedings of a satellite conference of ICM 2006, Lisbon, Portugal, September 4–8, 2006. Selected papers. Hackensack, NJ: World Scientific (ISBN 978-981-279-154-2/hbk). 43-53 (2008).
This article proposes an extension to Dynkin isomorphism with functionals of the occupation field of a symmetric Markov process with non polar points and of the associated Gaussian field to a suitable class of non symmetric Markov processes. The current approach does not rely on Grassmann variables and it works in general on finite space and on infinite spaces under some additional assumptions.
The second section deals with the finite case and it contains a direct extension of Dynkin’s isomorphism by means: of a complex “twisted” Gaussian field. In the last section an extension to the infinite-dimensional case is provided under some assumptions that allow the energy to control the skew symmetric part of the generator.
For the entire collection see [Zbl 1141.60002].

MSC:

60J05 Discrete-time Markov processes on general state spaces
60J25 Continuous-time Markov processes on general state spaces
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