Representation of functions of Markov processes as solutions of stochastic equations |
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Authors: | William J Anderson Abraham Boyarsky |
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Institution: | Department of Mathematics, McGill University, Montreal 101, Quebec, Canada;Department of Mathematics, Sir George Williams University, Montreal, Canada |
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Abstract: | Let Xt be a homogeneous Markov process generated by the weak infinitesimal operator A. Let be the class of functions f such that f, f2?DA, the domain of A. The main result of this paper states that for ? ∈ can be represented by a stochastic integral and other terms. If the process is generated by a second order differential operator (with ‘poor’ coefficients possibly) on C02(Rd) then the process itself can be represented as the solution of an Itô stochastic differential equation. |
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