Weak Dirichlet processes with jumps

Abstract : This paper develops systematically 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. In particular, 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 X_t = u(t, X_t) which stands in applications for a chain Itô type rule.
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Contributor : Francesco Russo <>
Submitted on : Wednesday, March 1, 2017 - 11:23:36 AM
Last modification on : Monday, September 30, 2019 - 9:12:05 AM
Long-term archiving on : Tuesday, May 30, 2017 - 3:22:46 PM

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  • HAL Id : hal-01241073, version 3
  • ARXIV : 1512.06236

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Elena Bandini, Francesco Russo. Weak Dirichlet processes with jumps. 2017. ⟨hal-01241073v3⟩

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