scholarly journals Lp - estimates of solutions of backward doubly stochastic differential equations

Filomat ◽  
2017 ◽  
Vol 31 (8) ◽  
pp. 2365-2379
Author(s):  
Jasmina Djordjevic
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Large Class ◽  
General Type ◽  
Lp Estimates ◽  
Estimates Of Solutions ◽  
Doubly Stochastic ◽  
Lipschitz Conditions

This paper deals with a large class of nonhomogeneous backward doubly stochastic differential equations which have a more general form of the forward It? integrals. Terms under which the solutions of these equations are bounded in the Lp-sense, p ? 2, under both the Lipschitz and non-Lipschitz conditions, are given, i.e. Lp - stability for this general type of backward doubly stochastic differential equations is established.

scholarly journals BSDE associated with Lévy processes and application to PDIE

2003 ◽  
Vol 16 (1) ◽  
pp. 1-17 ◽  
Author(s):  
K. Bahlali ◽  
M. Eddahbi ◽  
E. Essaky
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Large Class ◽  
Unique Solution ◽  
Lipschitz Constant ◽  
Probabilistic Interpretation ◽  
Locally Lipschitz ◽  
Independent Brownian Motion ◽  
Lipschitz Conditions

We deal with backward stochastic differential equations (BSDE for short) driven by Teugel's martingales and an independent Brownian motion. We study the existence, uniqueness and comparison of solutions for these equations under a Lipschitz as well as a locally Lipschitz conditions on the coefficient. In the locally Lipschitz case, we prove that if the Lipschitz constant LN behaves as log(N) in the ball B(0,N), then the corresponding BSDE has a unique solution which depends continuously on the on the coefficient and the terminal data. This is done with an unbounded terminal data. As application, we give a probabilistic interpretation for a large class of partial differential integral equations (PDIE for short).

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.

scholarly journals Comparison Theorems for the Multidimensional BDSDEs and Applications

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Bo Zhu ◽  
Baoyan Han
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Comparison Theorem ◽  
Existence Of Solutions ◽  
Minimal Solution ◽  
Comparison Theorems ◽  
Doubly Stochastic

A class of backward doubly stochastic differential equations (BDSDEs) are studied. We obtain a comparison theorem of these multidimensional BDSDEs. As its applications, we derive the existence of solutions for this multidimensional BDSDEs with continuous coefficients. We can also prove that this solution is the minimal solution of the BDSDE.

L2-regularity result for solutions of backward doubly stochastic differential equations

2019 ◽  
Vol 20 (02) ◽  
pp. 2050012
Author(s):  
Achref Bachouch ◽  
Anis Matoussi
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Rate Of Convergence ◽  
Numerical Scheme ◽  
Regularity Result ◽  
Time Discretization ◽  
Lipschitz Continuous ◽  
Doubly Stochastic

We prove an [Formula: see text]-regularity result for the solutions of Forward Backward doubly stochastic differential equations (F-BDSDEs) under globally Lipschitz continuous assumptions on the coefficients. As an application of our result, we derive the rate of convergence in time for the (Euler time discretization-based) numerical scheme for F-BDSDEs proposed by Bachouch et al. (2016) under only globally Lipschitz continuous assumptions.

scholarly journals Comparison theorems for anticipated backward doubly stochastic differential equations with non-Lipschitz coefficients

2020 ◽  
Vol 28 (1) ◽  
pp. 19-26
Author(s):  
Sadibou Aidara
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Comparison Theorems ◽  
Doubly Stochastic

AbstractIn this work, we prove some comparison theorems of anticipated backward doubly stochastic differential equations with non-Lipschitz coefficients.

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