Chaos Expansion Methods for Stochastic Differential Equations Involving the Malliavin Derivative–part I
نویسندگان
چکیده
We consider Gaussian, Poissonian, fractional Gaussian and fractional Poissonian white noise spaces, all represented through the corresponding orthogonal basis of the Hilbert space of random variables with finite second moments, given by the Hermite and the Charlier polynomials. There exist unitary mappings between the Gaussian and Poissonian white noise spaces. We investigate the relationship of the Malliavin derivative, the Skorokhod integral, the Ornstein–Uhlenbeck operator and their fractional counterparts on a general white noise space.
منابع مشابه
Chaos Expansion Methods for Stochastic Differential Equations Involving the Malliavin Derivative–part Ii
We solve stochastic differential equations involving the Malliavin derivative and the fractional Malliavin derivative by means of a chaos expansion on a general white noise space (Gaussian, Poissonian, fractional Gaussian and fractional Poissonian white noise space). There exist unitary mappings between the Gaussian and Poissonian white noise spaces, which can be applied in solving SDEs.
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