Stochastic analysis and stochastic control for symmetric Markov processes

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For a general symmetric Markov process X(t) and a function u in the associated quasi-regular Dirichlet space, the head investigator succeeded to give a quite useful necessary and sufficient conditions for the composite process u(X(t)) to be a semimartingale.Then he cooperates with other investigators to apply the above mentioned general criteria first for symmetric diffusion processes in finite dimensions to identify necessary and sufficient smoothness for a function to make Ito's formula invariant. Second, finite dimensional notions of BV functions are extended to the infinite dimensional abstract Wiener space and the associated Gauss formula and the Skorohod 1 equations are exploited. The head investigator also has written a joint paper on a singular control problem with Professor Taksar by extending a previous paper by Taksar considerably, combining it with a Nagai-Zabczyk characterization of a stochastic zero sum game by a Dirichelt form.