The technique of the exponential change of measure for Markov processes

is a true martingale for a positive function h 2 D(A). We demonstrate that the process X (t) is a Markov process on the probability space (U, F , fF tg, ~ P), we find its extended generator ~ A and provide sufficient conditions under which D(~ A) 1⁄4 D(A). We apply this result to continuous-time Markov chains, to piecewise deterministic Markov processes and to diffusion processes (in this case a special choice of h yields the classical Cameron–Martin–Girsanov theorem).

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