具有超线性增长和片断连续漂移、超线性增长和局部赫尔德连续扩散的 SDE 的驯服-自适应欧拉-马鲁山近似法

IF 1.8 2区数学 Q1 MATHEMATICS

Journal of Complexity Pub Date : 2024-01-18 DOI:10.1016/j.jco.2024.101833

Minh-Thang Do , Hoang-Long Ngo , Nhat-An Pho

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引用次数: 0

摘要

在本文中，我们考虑了漂移系数为超线性增长且片断连续的随机微分方程，以及扩散系数为超线性增长且局部荷尔德连续的随机微分方程。我们首先证明了这类随机微分方程解的存在性和唯一性，然后提出了一种驯服自适应的 Euler-Maruyama 近似方案。我们研究了该方案在有限和无限时间间隔内的 L1 值收敛速率。

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Tamed-adaptive Euler-Maruyama approximation for SDEs with superlinearly growing and piecewise continuous drift, superlinearly growing and locally Hölder continuous diffusion

In this paper, we consider stochastic differential equations whose drift coefficient is superlinearly growing and piecewise continuous, and whose diffusion coefficient is superlinearly growing and locally Hölder continuous. We first prove the existence and uniqueness of solution to such stochastic differential equations and then propose a tamed-adaptive Euler-Maruyama approximation scheme. We study the rate of convergence in $L^{1}$ -norm of the scheme in both finite and infinite time intervals.

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来源期刊

Journal of Complexity 工程技术-计算机：理论方法

CiteScore

3.10

自引率

17.60%

发文量

审稿时长

>12 weeks

期刊介绍： The multidisciplinary Journal of Complexity publishes original research papers that contain substantial mathematical results on complexity as broadly conceived. Outstanding review papers will also be published. In the area of computational complexity, the focus is on complexity over the reals, with the emphasis on lower bounds and optimal algorithms. The Journal of Complexity also publishes articles that provide major new algorithms or make important progress on upper bounds. Other models of computation, such as the Turing machine model, are also of interest. Computational complexity results in a wide variety of areas are solicited. Areas Include: • Approximation theory • Biomedical computing • Compressed computing and sensing • Computational finance • Computational number theory • Computational stochastics • Control theory • Cryptography • Design of experiments • Differential equations • Discrete problems • Distributed and parallel computation • High and infinite-dimensional problems • Information-based complexity • Inverse and ill-posed problems • Machine learning • Markov chain Monte Carlo • Monte Carlo and quasi-Monte Carlo • Multivariate integration and approximation • Noisy data • Nonlinear and algebraic equations • Numerical analysis • Operator equations • Optimization • Quantum computing • Scientific computation • Tractability of multivariate problems • Vision and image understanding.