scholarly journals A Unique Solution of Stochastic Partial Differential Equations with Non-Local Initial condition

2019 ◽  
Vol 16 ◽  
pp. 8226-8233
Author(s):  
Mahmoud Mohammed Mostafa El-Borai ◽  
A. Tarek S.A.
Keyword(s):  
Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Differential Equation ◽  
Unique Solution ◽  
Stochastic Partial Differential Equations ◽  
Pathwise Uniqueness ◽  
Initial Condition ◽  
Partial Differential ◽  
Non Local

In this paper, we shall discuss the uniqueness ”pathwise uniqueness” of the solutions of stochastic partial differential equations (SPDEs) with non-local initial condition,We shall use the Yamada-Watanabe condition for ”pathwise uniqueness” of the solutions of the stochastic differential equation; this condition is weaker than the usual Lipschitz condition. The proof is based on Bihari’sinequality.

scholarly journals Stochastic Measure Diffusion Processes

1979 ◽  
Vol 22 (2) ◽  
pp. 129-138 ◽  
Author(s):  
Donald A. Dawson
Keyword(s):  
Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Differential Equation ◽  
Stochastic Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Diffusion Processes ◽  
Partial Differential ◽  
Stochastic Measure ◽  
Recent Developments

The purpose of this article is to give an introduction to the study of a class of stochastic partial differential equations and to give a brief review of some of the recent developments in this field. This study has evolved naturally out of the theory of stochastic differential equations initiated in a pioneering paper of K. Itô [13]. In order to set this review in its appropriate setting we begin by considering a simple scalar stochastic differential equation.

scholarly journals Stochastic partial differential equations driven by space-time fractional noises

2019 ◽  
Vol 19 (02) ◽  
pp. 1950012
Author(s):  
Ying Hu ◽  
Yiming Jiang ◽  
Zhongmin Qian
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Space Time ◽  
Partial Differential ◽  
The Family ◽  
Non Local ◽  
Fractional Noises

In this paper, we study a class of stochastic partial differential equations (SPDEs) driven by space-time fractional noises. Our method consists in studying at first the non-local SPDEs and thereafter showing the convergence of the family of these equations. The limit gives the solution of the SPDE.

Two Contrasting Properties of Solutions for One-Dimensional Stochastic Partial Differential Equations

1994 ◽  
Vol 46 (2) ◽  
pp. 415-437 ◽  
Author(s):  
Tokuzo Shiga
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Stochastic Partial Differential Equation ◽  
Partial Differential ◽  
One Dimensional ◽  
Noise Term

AbstractThe paper is concerned with the comparison of two solutions for a one-dimensional stochastic partial differential equation. Noting that support compactness of solutions propagates with passage of time, we define the SCP property and show that the SCP property and the strong positivity are two contrasting properties of solutions for one-dimensional SPDEs, which are due to degeneracy of the noise-term coefficient

scholarly journals Relations between Stochastic and Partial Differential Equations in Hilbert Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
I. V. Melnikova ◽  
V. S. Parfenenkova
Keyword(s):  
Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Differential Equation ◽  
Hilbert Spaces ◽  
Probability Characteristic ◽  
Partial Differential

The aim of the paper is to introduce a generalization of the Feynman-Kac theorem in Hilbert spaces. Connection between solutions to the abstract stochastic differential equation and solutions to the deterministic partial differential (with derivatives in Hilbert spaces) equation for the probability characteristic is proved. Interpretation of objects in the equations is given.

scholarly journals Existence of affine realizations for stochastic partial differential equations driven by Lévy processes

2015 ◽  
Vol 471 (2178) ◽  
pp. 20150104 ◽  
Author(s):  
Stefan Tappe
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Lévy Processes ◽  
Stochastic Partial Differential Equation ◽  
Levy Processes ◽  
Natural Sciences ◽  
Partial Differential

The goal of this paper is to clarify when a semilinear stochastic partial differential equation driven by Lévy processes admits an affine realization. Our results are accompanied by several examples arising in natural sciences and economics.

scholarly journals Existence of weak solutions to SPDEs with fractional Laplacian and non-Lipschitz coefficients

2021 ◽  
Author(s):  
Shohei Nakajima
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Weak Solutions ◽  
Stochastic Partial Differential Equations ◽  
Fractional Laplacian ◽  
Existence Of Solutions ◽  
Partial Differential ◽  
Continuity Theorem ◽  
Existence Of Weak Solutions ◽  
One Dimensional

AbstractWe prove existence of solutions and its properties for a one-dimensional stochastic partial differential equations with fractional Laplacian and non-Lipschitz coefficients. The method of proof is eatablished by Kolmogorov’s continuity theorem and tightness arguments.

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