School of Statistics
Jiangxi University of Finance and Economics
Nanchang, Jiangxi 333000, China
email: zmb1982zqz@hotmail.com
Mingbo Zhang
Abstract:
This article concerns reflected stochastic differential equations with reflecting
boundary conditions that were introduced by Lions and Sznitman [5].
We establish a theorem on the existence and uniqueness of
the strong solution when the coefficients satisfy non-Lipschitz conditions.
We further show that the solutions depend continuously on the initial data.
Also we construct a measurable flow of the solution, and prove
that the solution is a Markov process.
The analytical solution of stochastic differential equations is generally
very difficult to obtain, so numerical approximations are important in
applications. Their convergence rates are very important for improving efficiency
and for designing algorithms. So we characterize the convergence rate of
Euler's approximations under some restrictions on the coefficients.
Submitted April 10, 2025. Published December 2, 2025.
Math Subject Classifications: 60F25, 60H20, 60G17.
Key Words: Reflected stochastic differential equations; Euler-Peano's method; non-Lipschitz continuous coefficients.
DOI: 10.58997/ejde.2025.113
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Mingbo Zhang School of Statistics Jiangxi University of Finance and Economics Nanchang, Jiangxi 333000, China email: zmb1982zqz@hotmail.com |
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