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https://projecteuclid.org/euclid.aop/1176992255
Keywords Sobolev spaces of Wiener functionals generalized Wiener functionals pull-back of Schwartz distributions asymptotic expansion of Wiener functionals heat kernels short-time asymptotics. CitationCited by: 312
https://arxiv.org/abs/0707.0154
Abstract: Malliavin Calculus is about Sobolev-type regularity of functionals on Wiener space, the main example being the Ito map obtained by solving stochastic differential equations. Rough path analysis is about strong regularity of solution to (possibly stochastic) differential equations. We combine arguments of both theories and discuss existence of a density for solutions to stochastic ...Cited by: 1
https://www.encyclopediaofmath.org/index.php/Brownian_functional
Although the set of these regular Brownian paths is negligible with respect to the Wiener measure, certain Brownian functionals are completely determined by their restriction to this set. This fact is the keystone of several recent works on the concept of a skeleton of a Brownian functional, , .
https://www.sciencedirect.com/science/article/pii/S0079816908602779
This chapter discusses the Fourier transforms of distributions with compact support and Paley-Wiener theorem. This chapter considers a continuous function f with compact support in R n.The chapter mentions that the Fourier transform of a continuous function with compact support can be extended to the complex space C n, as an entire analytic function of exponential type.
https://link.springer.com/article/10.1007/BF01192259
Sep 01, 1994 · In this paper we prove Stroock-Varadhan type theorems for the topological support of a hyperbolic stochastic partial differential equation in the α-Hölder norm, for α∈(0, 1/2). Our approach is based on absolutely continuous transformations of Ω defined using non-homogeneous approximations of the Brownian sheet.Cited by: 21
https://projecteuclid.org/download/pdf_1/euclid.ejp/1463434887
The distributions of Wiener functionals of second order are infinitely divisible. An explicit expression of the associated Lévy measures in terms of the eigenvalues of the corresponding Hilbert-Schmidt operators on the Cameron-Martin subspace is presented. In some special cases, a formula for the densities of the distributions is given.Cited by: 13
https://www.sciencedirect.com/science/article/pii/0016003266900640
This paper gives new results on the application of Volterra-Wiener functionals to the analysis of nonlinear systems. Part I deals with the convergence properties of the Volterra-Wiener functional series both in the deterministic case and the stochastic case.Cited by: 70
http://faculty.virginia.edu/melcher/Mall_Lie2.pdf
MALLIAVIN CALCULUS FOR LIE GROUP-VALUED WIENER FUNCTIONS TAI MELCHER Abstract. Let G be a Lie group equipped with a set of left invariant vector fields. These vector fields generate a function ξ on Wiener space into G via the stochastic version of …
https://www.researchgate.net/publication/263752743_Double_integral_transforms_and_double_convolution_products_of_functionals_on_abstract_Wiener_space
Double integral transforms and double convolution products of functionals on abstract Wiener space Article (PDF Available) in Integral Transforms and Special Functions 24(11) · November 2013 with ...
https://www.researchgate.net/publication/264153398_Fourier-type_functionals_on_Wiener_space
In this paper, we consider the Fourier-type functionals introduced in [Chung HS, Tuan VK. Fourier-type functionals on Wiener space. Bull Korean Math Soc. 2012;49:609–619] and used in [Lee IY ...
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