Weak Solution for Stochastic Partial Differential Equations Driven by a Fractional Brownian Sheet withMonotone Drift

2019 ◽  
Vol 08 (11) ◽  
pp. 1766-1774
Author(s):  
晓宇 夏
Keyword(s):  
Weak Solution ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Brownian Sheet ◽  
Fractional Brownian Sheet ◽  
Partial Differential

Hyperbolic Stochastic Partial Differential Equations with Additive Fractional Brownian Sheet

2003 ◽  
Vol 03 (02) ◽  
pp. 121-139 ◽  
Author(s):  
Mohamed Erraoui ◽  
Youssef Ouknine ◽  
David Nualart
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Strong Solution ◽  
Stochastic Partial Differential Equations ◽  
Existence And Uniqueness ◽  
Approximation Scheme ◽  
Borel Function ◽  
Brownian Sheet ◽  
Fractional Brownian Sheet ◽  
Partial Differential

Let [Formula: see text] be a fractional Brownian sheet with Hurst parameters H, H′ ≤ 1/2. We prove the existence and uniqueness of a strong solution for a class of hyperbolic stochastic partial differential equations with additive fractional Brownian sheet of the form [Formula: see text], where b(ζ, x) is a Borel function satisfying some growth and monotonicity assumptions. We also prove the convergence of Euler's approximation scheme for this equation.

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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