Lp-Solutions of backward doubly stochastic differential equations with stochastic Lipschitz condition and p ∈ (1,2)

2017 ◽  
Vol 21 ◽  
pp. 168-182 ◽  
Author(s):  
Jean-Marc Owo
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Lipschitz Condition ◽  
Doubly Stochastic ◽  
Lp Solutions

scholarly journals Lp Solutions of BSDEs with Stochastic Lipschitz Condition

2007 ◽  
Vol 2007 ◽  
pp. 1-14 ◽  
Author(s):  
Jiajie Wang ◽  
Qikang Ran ◽  
Qihong Chen
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Lipschitz Condition ◽  
Existence And Uniqueness ◽  
Special Class ◽  
Lipschitz Continuity ◽  
Backward Stochastic Differential Equations ◽  
Uniqueness Of The Solution ◽  
Lp Solutions

We are concerned with the solutions of a special class of backward stochastic differential equations which are driven by a Brownian motion, where the uniform Lipschitz continuity is replaced by a stochastic one. We prove the existence and uniqueness of the solution in Lp with p>1.

scholarly journals Backward Doubly Stochastic Differential Equations with Markov Chains and a Comparison Theorem

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 1953
Author(s):  
Ning Ma ◽  
Zhen Wu
Keyword(s):  
Differential Equations ◽  
Markov Chains ◽  
Stochastic Differential Equations ◽  
Comparison Theorem ◽  
Lipschitz Condition ◽  
Existence And Uniqueness ◽  
Comparison Theorems ◽  
Yosida Approximation ◽  
Uniqueness Of Solutions ◽  
Doubly Stochastic

In this paper we study the existence and uniqueness of solutions for one kind of backward doubly stochastic differential equations (BDSDEs) with Markov chains. By generalizing the Itô’s formula, we study such problem under the Lipschitz condition. Moreover, thanks to the Yosida approximation, we solve such problem under monotone condition. Finally, we give the comparison theorems for such equations under the above two conditions respectively.

scholarly journals Lp-SOLUTIONS OF BACKWARD DOUBLY STOCHASTIC DIFFERENTIAL EQUATIONS

2012 ◽  
Vol 12 (03) ◽  
pp. 1150025 ◽  
Author(s):  
AUGUSTE AMAN
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Existence And Uniqueness ◽  
A Priori Estimates ◽  
A Priori ◽  
Stochastic Calculus ◽  
Technical Aspects ◽  
Doubly Stochastic ◽  
Priori Estimates ◽  
Lp Solutions

The goal of this paper is to solve backward doubly stochastic differential equations (BDSDEs, in short) under weak assumptions on the data. The first part is devoted to the development of some new technical aspects of stochastic calculus related to this BDSDEs. Then we derive a priori estimates and prove the existence and uniqueness of solution in Lp, p ∈ (1, 2), extending the work of Pardoux and Peng (see [12]).

scholarly journals Lp solutions of infinite time interval backward doubly stochastic differential equations

Filomat ◽  
2017 ◽  
Vol 31 (7) ◽  
pp. 1857-1868 ◽  
Author(s):  
Zhaojun Zong ◽  
Feng Hu
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Uniqueness Theorem ◽  
Existence And Uniqueness ◽  
Time Interval ◽  
Existence And Uniqueness Theorem ◽  
Infinite Time ◽  
Doubly Stochastic ◽  
Infinite Time Interval ◽  
Lp Solutions

In this paper, we study the existence and uniqueness theorem for Lp (1 < p < 2) solutions to a class of infinite time interval backward doubly stochastic differential equations (BDSDEs). Furthermore, we obtain the comparison theorem for 1-dimensional infinite time interval BDSDEs in Lp.

scholarly journals A Type of Time-Symmetric Stochastic System and Related Games

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 118
Author(s):  
Qingfeng Zhu ◽  
Yufeng Shi ◽  
Jiaqiang Wen ◽  
Hui Zhang
Keyword(s):  
Nash Equilibrium ◽  
Time Delay ◽  
Differential Equations ◽  
Equilibrium Point ◽  
Stochastic Differential Equations ◽  
Stochastic System ◽  
Stochastic Systems ◽  
Necessary Condition ◽  
Nash Equilibrium Point ◽  
Doubly Stochastic

This paper is concerned with a type of time-symmetric stochastic system, namely the so-called forward–backward doubly stochastic differential equations (FBDSDEs), in which the forward equations are delayed doubly stochastic differential equations (SDEs) and the backward equations are anticipated backward doubly SDEs. Under some monotonicity assumptions, the existence and uniqueness of measurable solutions to FBDSDEs are obtained. The future development of many processes depends on both their current state and historical state, and these processes can usually be represented by stochastic differential systems with time delay. Therefore, a class of nonzero sum differential game for doubly stochastic systems with time delay is studied in this paper. A necessary condition for the open-loop Nash equilibrium point of the Pontriagin-type maximum principle are established, and a sufficient condition for the Nash equilibrium point is obtained. Furthermore, the above results are applied to the study of nonzero sum differential games for linear quadratic backward doubly stochastic systems with delay. Based on the solution of FBDSDEs, an explicit expression of Nash equilibrium points for such game problems is established.

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