stochastic integral
Recently Published Documents


TOTAL DOCUMENTS

488
(FIVE YEARS 54)

H-INDEX

26
(FIVE YEARS 4)

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
Sadibou Aidara ◽  
Ibrahima Sane

Abstract This paper deals with a class of deplay backward stochastic differential equations driven by fractional Brownian motion (with Hurst parameter H greater than 1 2 {\frac{1}{2}} ). In this type of equation, a generator at time t can depend not only on the present but also the past solutions. We essentially establish existence and uniqueness of a solution in the case of Lipschitz coefficients and non-Lipschitz coefficients. The stochastic integral used throughout this paper is the divergence-type integral.


Author(s):  
Kenza Benkirane ◽  
Abderrahim EL Adraoui ◽  
El Miloudi Marhrani

The aim of this paper is to prove a common random fixed-point and some random fixed-point theorems for random weakly contractive operators in separable Banach spaces. A random Mann iterative process is introduced to approximate the fixed point. Finally, the main result is supported by an example and used to prove the existence and the uniqueness of a solution of a nonlinear stochastic integral equation system.


2021 ◽  
Vol 60 (6) ◽  
pp. 5631-5636
Author(s):  
Amar Deep ◽  
Syed Abbas ◽  
Bhupander Singh ◽  
M.R. Alharthi ◽  
Kottakkaran Sooppy Nisar

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Mengting Deng ◽  
Guo Jiang ◽  
Ting Ke

This paper presents a valid numerical method to solve nonlinear stochastic Itô–Volterra integral equations (SIVIEs) driven by fractional Brownian motion (FBM) with Hurst parameter H ∈ 1 / 2 , 1 . On the basis of FBM and block pulse functions (BPFs), a new stochastic operational matrix is proposed. The nonlinear stochastic integral equation is converted into a nonlinear algebraic equation by this method. Furthermore, error analysis is given by the pathwise approach. Finally, two numerical examples exhibit the validity and accuracy of the approach.


Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2571
Author(s):  
A. M. A. El-Sayed ◽  
Hoda A. Fouad

The fractional stochastic differential equations had many applications in interpreting many events and phenomena of life, and the nonlocal conditions describe numerous problems in physics and finance. Here, we are concerned with the combination between the three senses of derivatives, the stochastic Ito^-differential and the fractional and integer orders derivative for the second order stochastic process in two nonlocal problems of a coupled system of two random and stochastic differential equations with two nonlocal stochastic and random integral conditions and a coupled system of two stochastic and random integral conditions. We study the existence of mean square continuous solutions of these two nonlocal problems by using the Schauder fixed point theorem. We discuss the sufficient conditions and the continuous dependence for the unique solution.


2021 ◽  
Vol 14 (5) ◽  
pp. 1443-1507
Author(s):  
Emiel Lorist ◽  
Mark Veraar

Author(s):  
A. M. A. El-Sayed ◽  
Hoda A. Foued

Here we are concerning with two problems of a coupled system of random and stochastic nonlinear differential equations with two coupled systems of nonlinear nonlocal random and stochastic integral conditions. The existence of solutions will be studied. The sufficient condition for the uniqueness of the solution will be given. The continuous dependence of the unique solution on the nonlocal conditions will be proved.


2021 ◽  
Vol 1964 (7) ◽  
pp. 072012
Author(s):  
B Sumathy ◽  
Kanagaraj Venusamy ◽  
D David Neels Ponkumar ◽  
P Malathi

Sign in / Sign up

Export Citation Format

Share Document