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Let $X$ be a Levy diffusion of the form $$dX_t = \mu(t, X_t) \, dt + \sigma(t, X_t) \, dW_t + \int_{\mathbb R} \, c(t, z) \overline N (dt, dz)$$ where $\ overline N (dt, dz)$ is a compensated Poisson random measure with finite Levy measure. Is it true that $$\mathbb E\big[ \int_{\mathbb R^2} X_t^2 \,c(t, z) \, \overline N(dt, dz)] < \infty?$$
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Sun, 10 Oct 2021 01:21 GMT