Results 11 to 20 of about 53,922 (203)

An explicit Euler scheme with strong rate of convergence for financial SDEs with non-Lipschitz coefficients [PDF]

SIAM Journal on Financial Mathematics, 2016
We consider the approximation of stochastic differential equations (SDEs) with non-Lipschitz drift or diffusion coefficients. We present a modified explicit Euler-Maruyama discretisation scheme that allows us to prove strong convergence, with a rate ...
Chassagneux, Jean-Francois, Jacquier, Antoine, Mihaylov, Ivo   +2 more
core   +3 more sources

A class of stochastic differential equations with super-linear growth and non-Lipschitz coefficients

Stochastics, 2015
The purpose of this paper is to study some properties of solutions to one dimensional as well as multidimensional stochastic differential equations (SDEs in short) with super-linear growth conditions on the coefficients.
Bahlali, Khaled, Hakassou, Antoine, Ouknine, Youssef   +2 more
core   +3 more sources

Euler–Maruyama approximations for SDEs with non-Lipschitz coefficients and applications

Journal of Mathematical Analysis and Applications, 2006
The author considers a \(d\)-dimensional system of Itô stochastic differential equations of the form \[ dX(t)= \sigma(X(t))dW(t) + b(X(t))dt,\quad X(0)=x,\;x\in R^d\tag{1} \] where \(W\) is an \(m\)-dimensional Brownian motion. The coefficient functions \(\sigma\) and \(b\) are supposed to satisfy the following non-Lipschitz conditions: \(\| \sigma(x)-\
Xicheng Zhang
openaire   +4 more sources

On the averaging principle for SDEs driven by G-Brownian motion with non-Lipschitz coefficients

Advances in Difference Equations, 2021
In this paper, we aim to develop the averaging principle for stochastic differential equations driven by G-Brownian motion (G-SDEs for short) with non-Lipschitz coefficients. By the properties of G-Brownian motion and stochastic inequality, we prove that
Wei Mao, Bo Chen, Surong You
doaj   +1 more source

On the Global Positivity Solutions of Non-homogeneous Stochastic Differential Equations

Frontiers in Applied Mathematics and Statistics, 2022
In this article, we treat the existence and uniqueness of strong solutions to the Cauchy problem of stochastic equations of the form dXt=αXtdt+σXtγdBt,X0=x>0.
Farai Julius Mhlanga, Lazarus Rundora
doaj   +1 more source

Weak observability estimates for 1-D wave equations with rough coefficients [PDF]

, 2013
In this paper we prove observability estimates for 1-dimensional wave equations with non-Lipschitz coefficients. For coefficients in the Zygmund class we prove a "classical" observability estimate, which extends the well-known observability results in ...
Fanelli, Francesco, Zuazua, Enrique
core   +4 more sources

ON STOCHASTIC EVOLUTION EQUATIONS WITH NON-LIPSCHITZ COEFFICIENTS [PDF]

Stochastics and Dynamics, 2009
In this paper, we study the existence and uniqueness of solutions for several classes of stochastic evolution equations with non-Lipschitz coefficients, that contains backward stochastic evolution equations, stochastic Volterra type evolution equations and stochastic functional evolution equations.
openaire   +3 more sources

Nonexplosion and Pathwise Uniqueness of Stochastic Differential Equation Driven by Continuous Semimartingale with Non-Lipschitz Coefficients

Journal of Mathematics, 2015
We study a class of stochastic differential equations driven by semimartingale with non-Lipschitz coefficients. New sufficient conditions on the strong uniqueness and the nonexplosion are derived for d-dimensional stochastic differential equations on Rd (
Jinxia Wang
doaj   +1 more source

Approximate solutions for a class of doubly perturbed stochastic differential equations

Advances in Difference Equations, 2018
In this paper, we study the Carathéodory approximate solution for a class of doubly perturbed stochastic differential equations (DPSDEs). Based on the Carathéodory approximation procedure, we prove that DPSDEs have a unique solution and show that the ...
Wei Mao, Liangjian Hu, Xuerong Mao
doaj   +1 more source

Stochastic flows for SDEs with non-Lipschitz coefficients

Bulletin des Sciences Mathématiques, 2003
A stochastic differential equation \[ dX_t=\sum_{n=1}^\infty\sigma_n(X_t)dW_t^n+b(X_t)dt,\quad X_0=x\in{\mathbb R}, \] is considered, where \(W^n\) are Brownian motions, \(n=1,2,\dots\), and none of the \(\sigma_n\)'s or \(b\) are Lipschitz. Conditions on coefficients are given which imply that the solution is a.s.\ continuous in \(x\) and \(t\) for ...
Ren, Jiagang, Zhang, Xicheng
openaire   +1 more source