Stochastic integration for Lévy processes with values in Banach spaces
The aim of the authors is to define a stochastic integral with respect to a Banach space \(B\)-valued Lévy process \((L_t)\), and to use it, in order to get a Lévy-Itô decomposition (extending the classical finite-dimensional one) for \((L_t)\), and finally to solve Cauchy problems of type: \[ dY_t= AY_t dt+ \int H(u)\,dL_t, \] for some generator \(A\) and \(L^2\) function \(H\). These goals are achieved, essentially by considering systematically the weak version (with respect to the dual of \(B\)) of the above objects, and by restricting to deterministic Banach valued integrands.
scientific article; zbMATH DE number 5561597
scientific article