Infinite-dimensional stochastic partial differential equations with multiparametric Brownian motion

Cybernetics ◽  
1977 ◽  
Vol 12 (4) ◽  
pp. 597-606
Author(s):  
L. L. Ponomarenko
Keyword(s):  
Brownian Motion ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Partial Differential ◽  
Infinite Dimensional

Moderate deviation principle for a class of stochastic partial differential equations

2016 ◽  
Vol 53 (1) ◽  
pp. 279-292 ◽  
Author(s):  
Parisa Fatheddin ◽  
Jie Xiong
Keyword(s):  
Brownian Motion ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Moderate Deviation ◽  
Partial Differential ◽  
Moderate Deviation Principle ◽  
Lipschitz Continuous ◽  
Deviation Principle ◽  
Super Brownian Motion

Abstract We establish the moderate deviation principle for the solutions of a class of stochastic partial differential equations with non-Lipschitz continuous coefficients. As an application, we derive the moderate deviation principle for two important population models: super-Brownian motion and the Fleming–Viot process.

scholarly journals On a Theorem by A.S. Cherny for Semilinear Stochastic Partial Differential Equations

2021 ◽  
Author(s):  
David Criens ◽  
Moritz Ritter
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Strong Uniqueness ◽  
Partial Differential ◽  
Infinite Dimensional ◽  
Dual Version ◽  
Martingale Problems ◽  
Weak Uniqueness ◽  
Strong Existence

AbstractWe consider analytically weak solutions to semilinear stochastic partial differential equations with non-anticipating coefficients driven by a cylindrical Brownian motion. The solutions are allowed to take values in Banach spaces. We show that weak uniqueness is equivalent to weak joint uniqueness, and thereby generalize a theorem by A.S. Cherny to an infinite dimensional setting. Our proof for the technical key step is different from Cherny’s and uses cylindrical martingale problems. As an application, we deduce a dual version of the Yamada–Watanabe theorem, i.e. we show that strong existence and weak uniqueness imply weak existence and strong uniqueness.

Reflected stochastic partial differential equations with jumps

2021 ◽  
pp. 2250002
Author(s):  
Hongchao Qian ◽  
Jun Peng
Keyword(s):  
Brownian Motion ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Existence And Uniqueness ◽  
Random Measure ◽  
Poisson Random Measure ◽  
Uniqueness Of Solutions ◽  
Partial Differential ◽  
Penalization Method

In this paper, we establish the existence and uniqueness of solutions of reflected stochastic partial differential equations (SPDEs) driven both by Brownian motion and by Poisson random measure in a convex domain. Penalization method plays a crucial role.

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