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Items for "formula"

A note on the Itô formula of stochastic integrals in Banach spaces

Let E and Z be separable Banach spaces, E be of M type p, 1 ≤ p ≤ 2, and X = {X(t), 0 ≤ t ≤ T} be an E–valued stochastic process given by

where is progressive measurable process and is a càglàd process defined later, is a compensated Poisson random measure with characteristic Lévy–measure such that

We verify the Itô formula for X under certain conditions in M type p Banach spaces.

Keywords: Stochastic integration, It, formula, Poisson random measures

03/2006 | Random Operators and Stochastic Equations, Walter de Gruyter
Anticipating integrals and martingales on the Poisson space

Let t be a standard compensated Poisson process on [0, 1]. We prove a new characterization of anticipating integrals of the Skorokhod type with respect to , and use it to obtain several counterparts to well established properties of semimartingale stochastic integrals...

Keywords: Poisson processes, Malliavin Calculus, Skorokhod integrals, It, formula, Burkholder inequalities

11/2007 | Random Operators and Stochastic Equations, Walter de Gruyter