scholarly journals Existence and Uniqueness of a Stationary Solution of a Nonlinear Stochastic Differential Equation with Memory

2003 ◽  
Vol 47 (4) ◽  
pp. 684-688
Author(s):  
Yu. Bakhtin
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Stationary Solution ◽  
Existence And Uniqueness ◽  
Nonlinear Stochastic Differential Equation ◽  
With Memory

Lévy-type nonlinear stochastic dynamic model, method and analysis

2019 ◽  
Vol 19 (05) ◽  
pp. 1950033
Author(s):  
Gangarm S. Ladde ◽  
Youngsoo Seol
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Dynamic Model ◽  
Existence And Uniqueness ◽  
Type Theorem ◽  
Main Idea ◽  
Stochastic Dynamic ◽  
Innovative Idea ◽  
The One ◽  
Nonlinear Stochastic Differential Equation

In this work, we consider a prototype stochastic dynamic model for dynamic processes in biological, chemical, economic, financial, medical, military, physical and technological sciences. The dynamic model is described by Lévy-type nonlinear stochastic differential equation. The model validation is established by the usage of Lyapunov-like function. The basic innovative idea is to transform a nonlinear Lévy-type nonlinear stochastic differential into a simpler stochastic differential equation that is easily tested for the existence and uniqueness theorem. Using the nature of Lyapunov-like function, the existence and uniqueness of solution of the original Lévy-type nonlinear stochastic differential equation is established. The main idea of the proof is based on the property of the one-to-one and onto transformation. As the byproduct of the analysis, it is shown that the closed-form implicit solution of transformed stochastic differential equation is a positive martingale. Furthermore, using the change of measure, a Girsanov-type theorem for Lévy-type nonlinear stochastic dynamic model is established.

scholarly journals Lp (p ≥ 1) solutions of multidimensional BSDEs with monotone generators in general time intervals

2014 ◽  
Vol 15 (01) ◽  
pp. 1550002 ◽  
Author(s):  
Li-Shun Xiao ◽  
Sheng-Jun Fan ◽  
Na Xu
Keyword(s):  
Differential Equation ◽  
Weak Convergence ◽  
Stochastic Differential Equation ◽  
Existence And Uniqueness ◽  
Additional Assumption ◽  
Backward Stochastic Differential Equation ◽  
Time Interval ◽  
Time Intervals ◽  
Lipschitz Continuous ◽  
General Time

In this paper, we are interested in solving general time interval multidimensional backward stochastic differential equation in Lp (p ≥ 1). We first study the existence and uniqueness for Lp (p > 1) solutions by the method of convolution and weak convergence when the generator is monotonic in y and Lipschitz continuous in z both non-uniformly with respect to t. Then we obtain the existence and uniqueness for L1 solutions with an additional assumption that the generator has a sublinear growth in z non-uniformly with respect to t.

BSDE with rcll reflecting barrier driven by a Lévy process

2020 ◽  
Vol 28 (1) ◽  
pp. 63-77 ◽  
Author(s):  
Mohamed El Jamali ◽  
Mohamed El Otmani
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Existence And Uniqueness ◽  
Lévy Process ◽  
Backward Stochastic Differential Equation ◽  
American Option ◽  
Levy Process ◽  
Fair Price ◽  
Penalization Method ◽  
Uniqueness Of A Solution

AbstractIn this paper, we study the solution of a backward stochastic differential equation driven by a Lévy process with one rcll reflecting barrier. We show the existence and uniqueness of a solution by means of the penalization method when the coefficient is stochastic Lipschitz. As an application, we give a fair price of an American option.

Fractional anticipated BSDEs with stochastic Lipschitz coefficients

2018 ◽  
Vol 26 (3) ◽  
pp. 143-161
Author(s):  
Ahmadou Bamba Sow ◽  
Bassirou Kor Diouf
Keyword(s):  
Differential Equation ◽  
Brownian Motion ◽  
Stochastic Differential Equation ◽  
Fractional Brownian Motion ◽  
Comparison Theorem ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equation ◽  
Hurst Parameter ◽  
Uniqueness Of A Solution

Abstract In this paper, we deal with an anticipated backward stochastic differential equation driven by a fractional Brownian motion with Hurst parameter {H\in(1/2,1)} . We essentially establish existence and uniqueness of a solution in the case of stochastic Lipschitz coefficients and prove a comparison theorem in a specific case.

scholarly journals Monte-Carlo Galerkin Approximation of Fractional Stochastic Integro-Differential Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Abdallah Ali Badr ◽  
Hanan Salem El-Hoety
Keyword(s):  
Differential Equation ◽  
Stochastic Process ◽  
Monte Carlo ◽  
Stochastic Differential Equation ◽  
Galerkin Method ◽  
Existence And Uniqueness ◽  
Galerkin Approximation ◽  
Integro Differential Equation ◽  
Uniqueness Of The Solution ◽  
Time Continuum

A stochastic differential equation, SDE, describes the dynamics of a stochastic process defined on a space-time continuum. This paper reformulates the fractional stochastic integro-differential equation as a SDE. Existence and uniqueness of the solution to this equation is discussed. A numerical method for solving SDEs based on the Monte-Carlo Galerkin method is presented.

scholarly journals INFINITELY MANY BROWNIAN GLOBULES WITH BROWNIAN RADII

2010 ◽  
Vol 10 (04) ◽  
pp. 591-612
Author(s):  
MYRIAM FRADON ◽  
SYLVIE RŒLLY
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Strong Solution ◽  
Local Time ◽  
Existence And Uniqueness ◽  
Infinite System ◽  
Time Dependent ◽  
Initial Condition ◽  
Infinite Dimensional ◽  
Time Existence

We consider an infinite system of non-overlapping globules undergoing Brownian motions in ℝ3. The term globules means that the objects we are dealing with are spherical, but with a radius which is random and time-dependent. The dynamics is modelized by an infinite-dimensional stochastic differential equation with local time. Existence and uniqueness of a strong solution is proven for such an equation with fixed deterministic initial condition. We also find a class of reversible measures.

scholarly journals Multidimensional BSDE with Poisson jumps of Osgood type

2019 ◽  
Vol 4 (2) ◽  
pp. 387-394 ◽  
Author(s):  
Yaya Sagna
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Finite Time ◽  
Existence And Uniqueness ◽  
Time Horizon ◽  
Linear Growth ◽  
Backward Stochastic Differential Equation ◽  
Uniqueness Of Solution ◽  
Poisson Jumps ◽  
Finite Time Horizon

AbstractThis paper is devoted to solve a multidimensional backward stochastic differential equation with jumps in finite time horizon. Under linear growth generator, we prove existence and uniqueness of solution.

Sign in / Sign up

Export Citation Format

Share Document