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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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Preprints, Working Papers, ...
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https://hal-ensta-paris.archives-ouvertes.fr//hal-01241073
Contributor : Francesco Russo Connect in order to contact the contributor
Submitted on : Friday, December 16, 2016 - 8:10:49 AM
Last modification on : Monday, November 30, 2020 - 3:38:06 PM
Long-term archiving on: : Monday, March 20, 2017 - 6:22:18 PM

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  • HAL Id : hal-01241073, version 2
  • ARXIV : 1512.06236

Citation

Elena Bandini, Francesco Russo. Weak Dirichlet processes with jumps. 2016. ⟨hal-01241073v2⟩

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