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.

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.

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 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 Conditions to Guarantee the Existence of the Solution to Stochastic Differential Equations of Neutral Type

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1613
Author(s):  
Mun-Jin Bae ◽  
Chan-Ho Park ◽  
Young-Ho Kim
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Existence And Uniqueness ◽  
Neutral Type ◽  
Sufficient Conditions ◽  
Exponential Estimates ◽  
Analysis Theory ◽  
Linear Growth Condition ◽  
Uniqueness Of The Solution ◽  
The Uniqueness Theorem

The main purpose of this study was to demonstrate the existence and the uniqueness theorem of the solution of the neutral stochastic differential equations under sufficient conditions. As an alternative to the stochastic analysis theory of the neutral stochastic differential equations, we impose a weakened Ho¨lder condition and a weakened linear growth condition. Stochastic results are obtained for the theory of the existence and uniqueness of the solution. We first show that the conditions guarantee the existence and uniqueness; then, we show some exponential estimates for the solutions.

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 .

scholarly journals A Picard Theorem for iterative differential equations

2009 ◽  
Vol 42 (2) ◽  
Author(s):  
Wen-rong Li ◽  
Sui Sun Cheng
Keyword(s):  
Differential Equations ◽  
Uniqueness Theorem ◽  
Existence And Uniqueness ◽  
Existence And Uniqueness Theorem ◽  
Picard Theorem ◽  
Iterative Differential Equations

AbstractA Picard type existence and uniqueness theorem is established for iterative differential equations of the form

scholarly journals Existence and uniqueness theorem for a solution of fuzzy differential equations

1999 ◽  
Vol 22 (2) ◽  
pp. 271-279 ◽  
Author(s):  
Jong Yeoul Park ◽  
Hyo Keun Han
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Differential Equations ◽  
Uniqueness Theorem ◽  
Successive Approximation ◽  
Existence And Uniqueness ◽  
Fuzzy Differential Equation ◽  
Existence And Uniqueness Theorem ◽  
Uniqueness Of A Solution

By using the method of successive approximation, we prove the existence and uniqueness of a solution of the fuzzy differential equationx′(t)=f(t,x(t)),x(t0)=x0. We also consider anϵ-approximate solution of the above fuzzy differential equation.

scholarly journals Convergence Theorems for Operators Sequences on Functionals of Discrete-Time Normal Martingales

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Jinshu Chen
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Discrete Time ◽  
Existence And Uniqueness ◽  
Continuous Dependence ◽  
Functional Space ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient ◽  
Convergence Of Operators

We aim to investigate the convergence of operators sequences acting on functionals of discrete-time normal martingales M. We first apply the 2D-Fock transform for operators from the testing functional space S(M) to the generalized functional space S⁎(M) and obtain a necessary and sufficient condition for such operators sequences to be strongly convergent. We then discuss the integration of these operator-valued functions. Finally, we apply the results obtained here and establish the existence and uniqueness of solution to quantum stochastic differential equations in terms of operators acting on functionals of discrete-time normal martingales M. And also we prove the continuity and continuous dependence on initial values of the solution.

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