scholarly journals Existence and uniqueness results for semilinear stochastic partial differential equations

1998 ◽  
Vol 73 (2) ◽  
pp. 271-299 ◽  
Author(s):  
István Gyöngy
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Existence And Uniqueness ◽  
Partial Differential ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results

scholarly journals Mean-Field Forward-Backward Doubly Stochastic Differential Equations and Related Nonlocal Stochastic Partial Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Qingfeng Zhu ◽  
Yufeng Shi
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Existence And Uniqueness ◽  
Mean Field ◽  
Partial Differential ◽  
Existence And Uniqueness Results ◽  
Doubly Stochastic ◽  
Uniqueness Results

Mean-field forward-backward doubly stochastic differential equations (MF-FBDSDEs) are studied, which extend many important equations well studied before. Under some suitable monotonicity assumptions, the existence and uniqueness results for measurable solutions are established by means of a method of continuation. Furthermore, the probabilistic interpretation for the solutions to a class of nonlocal stochastic partial differential equations (SPDEs) combined with algebra equations is given.

scholarly journals BSDEs with polynomial growth generators

2000 ◽  
Vol 13 (3) ◽  
pp. 207-238 ◽  
Author(s):  
Philippe Briand ◽  
René Carmona
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Existence And Uniqueness ◽  
Polynomial Growth ◽  
Probabilistic Representation ◽  
Existence And Uniqueness Results ◽  
State Variable ◽  
Cahn Equation ◽  
Uniqueness Results ◽  
Terminal Time

In this paper, we give existence and uniqueness results for backward stochastic differential equations when the generator has a polynomial growth in the state variable. We deal with the case of a fixed terminal time, as well as the case of random terminal time. The need for this type of extension of the classical existence and uniqueness results comes from the desire to provide a probabilistic representation of the solutions of semilinear partial differential equations in the spirit of a nonlinear Feynman-Kac formula. Indeed, in many applications of interest, the nonlinearity is polynomial, e.g, the Allen-Cahn equation or the standard nonlinear heat and Schrödinger equations.

DISSIPATIVE BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS IN INFINITE DIMENSIONS

2006 ◽  
Vol 09 (01) ◽  
pp. 155-168 ◽  
Author(s):  
FULVIA CONFORTOLA
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Hilbert Spaces ◽  
Stochastic Partial Differential Equations ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equations ◽  
Uniqueness Result ◽  
Infinite Dimensions ◽  
Partial Differential

We prove an existence and uniqueness result for a class of backward stochastic differential equations (BSDE) with dissipative drift in Hilbert spaces. We also give examples of stochastic partial differential equations which can be solved with our result.

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.

scholarly journals Stationary in Distributions of Numerical Solutions for Stochastic Partial Differential Equations with Markovian Switching

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Yi Shen ◽  
Yan Li
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Existence And Uniqueness ◽  
Numerical Solutions ◽  
Mild Solutions ◽  
Sufficient Conditions ◽  
Markovian Switching ◽  
Partial Differential ◽  
Stationary Distributions

We investigate a class of stochastic partial differential equations with Markovian switching. By using the Euler-Maruyama scheme both in time and in space of mild solutions, we derive sufficient conditions for the existence and uniqueness of the stationary distributions of numerical solutions. Finally, one example is given to illustrate the theory.

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 Elliptic stochastic partial differential equations with two reflecting walls

2014 ◽  
Vol 17 (04) ◽  
pp. 1450025
Author(s):  
Wen Yue ◽  
Tusheng Zhang
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Existence And Uniqueness ◽  
Multiplicative Noise ◽  
Partial Differential

In this paper, we study elliptic stochastic partial differential equations with two reflecting walls h1 and h2, driven by multiplicative noise. The existence and uniqueness of the solutions are established.

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