Titlebook: Malliavin Calculus and Stochastic Analysis; A Festschrift in Hon Frederi Viens,Jin Feng,Eulalia Nualart Conference proceedings 2013 Spring

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2194-1009 of David Nualart‘s career, on March 19-21, 2011, at the University of Kansas, USA. These scholars and other top-level mathematicians have kindly contributed research articles for this refereed volume..978-1-4899-9657-2978-1-4614-5906-4Series ISSN 2194-1009 Series E-ISSN 2194-1017

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Dilation Vector Field on Wiener Spacee heat kernel measures (ν.).. We project down “through a nondegenerate map .”, Ornstein–Uhlenbeck operators defined on Ω by .. We obtain a first-order partial differential equation for the density of the random vector .. We compare this differential equation to the heat equation and to Stein’s equation for the density.

Aphorism

The Calculus of Differentials for the Weak Stratonovich Integralection term which is a classical Itô integral and which is related to the so-called signed cubic variation of .(.). Finally, we derive a surprising formula for calculating with differentials. We show that if .. = ..., then ... can be written as ... minus a stochastic correction term which is again related to the signed cubic variation.

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On the Stochastic Navier–Stokes Equation Driven by Stationary White Noiseon. The perturbed equation is solved in the space of generalized stochastic processes using the Cameron–Martin version of the Wiener chaos expansion and generalized Malliavin calculus. We also study the accuracy of the Galerkin approximation of the solutions of the unbiased stochastic Navier–Stokes equations.

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Generalized Stochastic Heat Equationsr, in space, Hölder’s parameter has a different behavior depending on the fractional parameter. Finally, we show that the law of the solution is absolutely continuous with respect to Lebesgue’s measure and its density is infinitely differentiable.

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