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 Anticipated Generalized Backward Doubly Stochastic Differential Equations

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 114
Author(s):  
Tie Wang ◽  
Jiaxin Yu
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Uniqueness Theorem ◽  
Comparison Theorem ◽  
Existence And Uniqueness ◽  
Comparison Theorems ◽  
Existence And Uniqueness Theorem ◽  
New Class ◽  
Doubly Stochastic ◽  
Increasing Process

In this paper, we explore a new class of stochastic differential equations called anticipated generalized backward doubly stochastic differential equations (AGBDSDEs), which not only involve two symmetric integrals related to two independent Brownian motions and an integral driven by a continuous increasing process but also include generators depending on the anticipated terms of the solution (Y, Z). Firstly, we prove the existence and uniqueness theorem for AGBDSDEs. Further, two comparison theorems are obtained after finding a new comparison theorem for GBDSDEs.

Infinite Time Interval BSDEs Driven by a Lévy Process

2011 ◽  
Vol 50-51 ◽  
pp. 293-297
Author(s):  
Shi Qiu Zheng ◽  
Ai Min Yang ◽  
Dian Xuan Gong ◽  
Qiu Mei Liu ◽  
Ya Mian Peng
Keyword(s):  
Uniqueness Theorem ◽  
Existence And Uniqueness ◽  
Lévy Process ◽  
Continuous Dependence ◽  
Levy Process ◽  
Time Interval ◽  
Existence And Uniqueness Theorem ◽  
Infinite Time ◽  
Infinite Time Interval ◽  
Continuous Dependence Theorem

In this paper, we study the infinite time interval backward stochastic differential equations (BSDEs) driven by a Lévy process. A existence and uniqueness theorem for solution of the BSDEs is established, which can be considered a generalization of existence and uniqueness theorem of BSDEs. A continuous dependence theorem for solutions of the BSDEs is also given.

scholarly journals Existence and Uniqueness Theorem for Stochastic Differential Equations with Self-Exciting Switching

2011 ◽  
Vol 2011 ◽  
pp. 1-12
Author(s):  
Guixin Hu ◽  
Ke Wang
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Uniqueness Theorem ◽  
Existence And Uniqueness ◽  
Sufficient Condition ◽  
Existence And Uniqueness Theorem ◽  
Uniqueness Of The Solution

We introduce a new kind of equation, stochastic differential equations with self-exciting switching. Firstly, we give some preliminaries for this kind of equation, and then, we get the main results of our paper; that is, we gave the sufficient condition which can guarantee the existence and uniqueness of the solution.

Anticipated backward doubly stochastic differential equations driven by teugels martingales with or without reflecting barrier

2020 ◽  
pp. 1-21
Author(s):  
Mostapha Saouli ◽  
B. Mansouri
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Existence And Uniqueness ◽  
Time Interval ◽  
Present Value ◽  
Uniqueness Of Solutions ◽  
Doubly Stochastic ◽  
Teugels Martingales ◽  
The Fixed Point Theorem

We are interested in this paper on reflected anticipated backward doubly stochastic differential equations (RABDSDEs) driven by teugels martingales associated with Levy process. We obtain the existence and uniqueness of solutions to these equations by means of the fixed-point theorem where the coefficients of these BDSDEs depend on the future and present value of the solution $\left( Y,Z\right)$. We also show the comparison theorem for a special class of RABDSDEs under some slight stronger conditions. The novelty of our result lies in the fact that we allow the time interval to be infinite.

A Note on the Carathéodory Approximation Scheme for Stochastic Differential Equations under G-Brownian Motion

2012 ◽  
Vol 67 (12) ◽  
pp. 699-704 ◽  
Author(s):  
Faiz Faizullah
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Uniqueness Theorem ◽  
Unique Solution ◽  
Existence And Uniqueness ◽  
Approximation Scheme ◽  
Approximate Solutions ◽  
Existence And Uniqueness Theorem ◽  
Vector Valued

In this note, the Carathéodory approximation scheme for vector valued stochastic differential equations under G-Brownian motion (G-SDEs) is introduced. It is shown that the Carathéodory approximate solutions converge to the unique solution of the G-SDEs. The existence and uniqueness theorem for G-SDEs is established by using the stated method.

scholarly journals Infinite time interval BSDEs and the convergence of g-martingales

2000 ◽  
Vol 69 (2) ◽  
pp. 187-211 ◽  
Author(s):  
Zengjing Chen ◽  
Bo Wang
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Unique Solution ◽  
Backward Stochastic Differential Equations ◽  
Time Interval ◽  
Sufficient Condition ◽  
Infinite Time ◽  
Infinite Time Interval

AbstractIn this paper, we first give a sufficient condition on the coefficients of a class of infinite time interval backward stochastic differential equations (BSDEs) under which the infinite time interval BSDEs have a unique solution for any given square integrable terminal value, and then, using the infinite time interval BSDEs, we study the convergence of g-martingales introduced by Peng via a kind of BSDEs. Finally, we study the applications of g-expectations and g-martingales in both finance and economics.

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 Fuzzy Conformable Fractional Differential Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Atimad Harir ◽  
Said Melliani ◽  
Lalla Saadia Chadli
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Uniqueness Theorem ◽  
Fractional Differential Equations ◽  
Existence And Uniqueness ◽  
Existence And Uniqueness Theorem ◽  
Fractional Differential ◽  
Fractional Differentiability ◽  
Derivatives Of ◽  
Fuzzy Fractional Differential Equation

In this study, fuzzy conformable fractional differential equations are investigated. We study conformable fractional differentiability, and we define fractional integrability properties of such functions and give an existence and uniqueness theorem for a solution to a fuzzy fractional differential equation by using the concept of conformable differentiability. This concept is based on the enlargement of the class of differentiable fuzzy mappings; for this, we consider the lateral Hukuhara derivatives of order q ∈ 0,1 .

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