The evolution of the Skorokhod integral

2016 ◽  
pp. 321-328
Author(s):  
Anatolii V. Skorokhod
Keyword(s):  
Skorokhod Integral

scholarly journals Extensions of the Hitsuda–Skorokhod Integral

2017 ◽  
Vol 11 (4) ◽  
Author(s):  
Peter Parczewski
Keyword(s):  
Skorokhod Integral

scholarly journals Transformations of index set for Skorokhod integral with respect to Gaussian processes

1999 ◽  
Vol 12 (2) ◽  
pp. 105-111 ◽  
Author(s):  
Leszek Gawarecki
Keyword(s):  
Gaussian Process ◽  
Gaussian Processes ◽  
Fundamental Theorem ◽  
Index Set ◽  
Diffusion Type ◽  
Line Integral ◽  
Fundamental Theorem Of Calculus ◽  
Skorokhod Integral ◽  
Uniqueness Of The Solution

We consider a Gaussian process {Xt,t∈T} with an arbitrary index set T and study consequences of transformations of the index set on the Skorokhod integral and Skorokhod derivative with respect to X. The results applied to Skorokhod SDEs of diffusion type provide uniqueness of the solution for the time-reversed equation and, to Ogawa line integral, give an analogue of the fundamental theorem of calculus.

scholarly journals A unified approach to stochastic evolution equations using the Skorokhod integral

2009 ◽  
Vol 54 (2) ◽  
pp. 288-303 ◽  
Author(s):  
С В Лотоцкий ◽  
S V Lototskii ◽  
Борис Л Розовский ◽  
Boris L Rozovskii
Keyword(s):  
Evolution Equations ◽  
Stochastic Evolution ◽  
Stochastic Evolution Equations ◽  
Unified Approach ◽  
Skorokhod Integral

scholarly journals Chaos expansion methods for stochastic differential equations involving the Malliavin derivative, Part I

2011 ◽  
Vol 90 (104) ◽  
pp. 65-84 ◽  
Author(s):  
Tijana Levajkovic ◽  
Dora Selesi
Keyword(s):  
Hilbert Space ◽  
White Noise ◽  
Orthogonal Basis ◽  
Chaos Expansion ◽  
Charlier Polynomials ◽  
Malliavin Derivative ◽  
Second Moments ◽  
Skorokhod Integral ◽  
Relationship Of ◽  
The Relationship

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.

scholarly journals Stochastic Fractional Heat Equations Driven by Fractional Noises

2015 ◽  
Vol 2015 ◽  
pp. 1-16
Author(s):  
Xichao Sun ◽  
Ming Li
Keyword(s):  
Hilbert Space ◽  
Lyapunov Exponent ◽  
The Other ◽  
Hurst Parameter ◽  
Heat Equations ◽  
Fractional Noise ◽  
Fractional Heat Equation ◽  
Skorokhod Integral ◽  
Time Parameters ◽  
Fractional Noises

This paper is concerned with the following stochastically fractional heat equation on(t,x)∈[0,T]×Rddriven by fractional noise:∂u(t,x)/∂t=Dδαu(t,x)+WH(t,x)⋄u(t,x), where the Hurst parameterH=(h0,h1,…,hd)and⋄denotes the Skorokhod integral. A unique solution of that equation in an appropriate Hilbert space is constructed. Moreover, the Lyapunov exponent of the solution is estimated, and the Hölder continuity of the solution on both space and time parameters is discussed. On the other hand, the absolute continuity of the solution is also obtained.

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