Weak Dirichlet processes with jumps

2015/12/19 by Bandini, Elena, Russo, Francesco
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1512.06236

Abstract

This paper develops systematically the stochastic calculus via regularization in the case of jump processes. In particular one continues the analysis of real-valued càdlàg weak Dirichlet processes with respect to a given filtration. Such a process is the sum of a local martingale and an adapted process A such that [N,A] = 0, for any continuous local martingale N. Given a function u:[0,T] × ℝ → ℝ, which is of class C^0,1 (or sometimes less), we provide a chain rule type expansion for u(t,X_t) which stands in applications for a chain Itô type rule.

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