Displaying similar documents to “Moments of stochastic processes governed by Poisson random measures”

Invariance of Poisson measures under random transformations

Nicolas Privault (2012)

Annales de l'I.H.P. Probabilités et statistiques

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We prove that Poisson measures are invariant under (random) intensity preserving transformations whose finite difference gradient satisfies a cyclic vanishing condition. The proof relies on moment identities of independent interest for adapted and anticipating Poisson stochastic integrals, and is inspired by the method of Üstünel and Zakai ( (1995) 409–429) on the Wiener space, although the corresponding algebra is more complex than in the Wiener case. The examples of...

Moments of some random functionals

K. Urbanik (1997)

Colloquium Mathematicum

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The paper deals with nonnegative stochastic processes X(t,ω)(t ≤ 0) not identically zero with stationary and independent increments right-continuous sample functions and fulfilling the initial condition X(0,ω)=0. The main aim is to study the moments of the random functionals 0 f ( X ( τ , ω ) ) d τ for a wide class of functions f. In particular a characterization of deterministic processes in terms of the exponential moments of these functionals is established.