scholarly journals An Adaptive Euler--Maruyama Scheme for Stochastic Differential Equations with Discontinuous Drift and its Convergence Analysis

2019 ◽  
Vol 57 (1) ◽  
pp. 378-403 ◽  
Author(s):  
Andreas Neuenkirch ◽  
Michaela Szölgyenyi ◽  
Lukasz Szpruch
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Convergence Analysis ◽  
Discontinuous Drift

Convergence of Recent Multistep Schemes for a Forward-Backward Stochastic Differential Equation

2015 ◽  
Vol 5 (4) ◽  
pp. 387-404 ◽  
Author(s):  
Jie Yang ◽  
Weidong Zhao
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Differential Equations ◽  
Convergence Rate ◽  
Stochastic Differential Equation ◽  
Stochastic Differential Equations ◽  
Convergence Analysis ◽  
Stochastic Control ◽  
Backward Stochastic Differential Equation ◽  
Order Convergence

AbstractConvergence analysis is presented for recently proposed multistep schemes, when applied to a special type of forward-backward stochastic differential equations (FB-SDEs) that arises in finance and stochastic control. The corresponding k-step scheme admits a k-order convergence rate in time, when the exact solution of the forward stochastic differential equation (SDE) is given. Our analysis assumes that the terminal conditions and the FBSDE coefficients are sufficiently regular.

scholarly journals The Existence of Strong Solutions for a Class of Stochastic Differential Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-5
Author(s):  
Junfei Zhang
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Strong Solution ◽  
Strong Solutions ◽  
Lipschitz Continuous ◽  
Discontinuous Drift ◽  
Increasing Function

In this paper, we will consider the existence of a strong solution for stochastic differential equations with discontinuous drift coefficients. More precisely, we study a class of stochastic differential equations when the drift coefficients are an increasing function instead of Lipschitz continuous or continuous. The main tools of this paper are the lower solutions and upper solutions of stochastic differential equations.

scholarly journals On the existence of solutions for stochastic differential equations driven by fractional Brownian motion

Filomat ◽  
2019 ◽  
Vol 33 (6) ◽  
pp. 1695-1700
Author(s):  
Zhi Li
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Fractional Brownian Motion ◽  
Growth Condition ◽  
Linear Growth ◽  
Existence Of Solutions ◽  
Hurst Parameter ◽  
Linear Growth Condition ◽  
Discontinuous Drift

In this paper, we are concerned with a class of stochastic differential equations driven by fractional Brownian motion with Hurst parameter 1/2 < H < 1, and a discontinuous drift. By approximation arguments and a comparison theorem, we prove the existence of solutions to this kind of equations under the linear growth condition.

scholarly journals A study on stochastic differential equation

2021 ◽  
Vol 5 (2) ◽  
pp. 68-75
Author(s):  
Govindaraju P ◽  
Senthil Kumar
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Stochastic Differential Equation ◽  
Stochastic Differential Equations ◽  
Density Function ◽  
Discontinuous Drift ◽  
Point Of Departure

In this paper we study solutions to stochastic differential equations (SDEs) with discontinuous drift. In this paper we discussed The Euler-Maruyama method and this shows that a candidate density function based on the Euler-Maruyama method. The point of departure for this work is a particular SDE with discontinuous drift.

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