Abstract
Free Markov processes are investigated in Voiculescu’s free probability theory. We show that Voiculescu’s free Markov property implies a property called “weak Markov property”, which is the classical Markov property in the commutative case; while, in the general case, the “weak Markov property” is the same as the Markov property defined by Bozejko, Kummer, and Speicher. We also show that a kind of stochastic differential equations driven by free Levy processes has solutions. The solutions are free Markov processes.
Citation
Mingchu Gao. "Free Markov processes and stochastic differential equations in von Neumann algebras." Illinois J. Math. 52 (1) 153 - 180, Spring 2008. https://doi.org/10.1215/ijm/1242414126
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