Dirichlet Forms for Poisson Measures and Lévy Processes: The Lent Particle Method

Bouleau, Nicolas; Denis, Laurent

doi:10.1007/978-3-0348-0097-6_1

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Comparison With Chaos Expansions and Mass Addition1

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2015

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Cited by 2 publications

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“…This "addition of mass" approach through a creation and annihilation operator appears in other approaches such as the "lent-particle method" (Bouleau-Denis [5]).…”

Section: Comparison With Chaos Expansions and Mass Additionmentioning

confidence: 99%

Functional calculus and martingale representation formula for integer-valued measures

Blacque-Florentin¹,

Cont²

2015

Preprint

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We develop a calculus for functionals of integer-valued measures, which extends the Functional Itô calculus to functionals of Poisson random measures in a pathwise sense. We show that smooth functionals in the sense of this pathwise calculus are dense in the space of square-integrable (compensated) integrals with respect to a large class of integer-valued random measures. As a consequence, we obtain an explicit martingale representation formula for all square-integrable martingales with respect to the filtration generated by such integer-valued random measures. Our representation formula extends beyond the Poisson framework and allows for random and time-dependent compensators.

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“…This "addition of mass" approach through a creation and annihilation operator appears in other approaches such as the "lent-particle method" (Bouleau-Denis [5]).…”

Section: Comparison With Chaos Expansions and Mass Additionmentioning

confidence: 99%