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Levy processes with jumps can be formulated following the Levy-kinchkine representation, which provide a decomposition of the characteristic function into three factors corresponding to the diffusion (...

Given an SDE with a Lévy process with a drift $b(x,t)$ the reverse SDE will have a drift, $\tilde{b}(x,t)$, given by the relation: $$\tilde{b}(x,t) = - b(x,t) + \int_{\mathbb{R}} y \left( 1 + \frac{...

Suppose we call a real valued stochastic process $\{Z_t\}$ to be distributed as ${\cal S}\alpha{\cal S}(\sigma)$ if each of the characteristic functions is $\phi_{Z_t}(u) = \exp\left\{-t\vert \sigma u ...

I know there are Itô formulas for cylindrical Brownian motions with values in a Hilbert space and Itô formulas for Lévy processes in $\mathbb{R}^d$. My question is: does there exist an Itô formula ...