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Journal Articles Stochastic Processes and their Applications Year : 2017

Weak Dirichlet processes with jumps

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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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Dates and versions

hal-01241073 , version 1 (09-12-2015)
hal-01241073 , version 2 (16-12-2016)
hal-01241073 , version 3 (01-03-2017)

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Elena Bandini, Francesco Russo. Weak Dirichlet processes with jumps. Stochastic Processes and their Applications, 2017, 12, pp.4139-4189. ⟨10.1016/j.spa.2017.04.001⟩. ⟨hal-01241073v3⟩
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