分数布朗运动驱动的SDE梯形数值格式的收敛性分析
Convergence Analysis of Trapezoidal Numerical Scheme for SDE Driven by Fractional Brownian Motion
摘要: 分数布朗运动驱动的SDE在金融、物理和工程等领域有广泛应用，但其精确解通常难以获得，因此数值方法的研究至关重要。梯形格式作为一种经典的数值方法，其在分数布朗运动驱动SDE中的应用及收敛性分析具有一定的理论意义和实际价值。本文研究加性分数布朗运动驱动的SDE的梯形数值格式的收敛性分析，其中分数布朗运动的Hurst参数 H∈( 1 2 ,1 ) 。利用Malliavin导数和Skorohod积分等工具，得到了该数值格式的强收敛阶为1阶。
Abstract: The SDE driven by Fractional Brownian Motion (FBM) serves as a fundamental stochastic model in fields such as financial mathematics, physics, and engineering. Due to the difficulty in obtaining exact solutions for such equations, numerical methods are indispensable tools for studying them. This paper focuses on the convergence analysis of the trapezoidal numerical scheme for SDEs driven by additive Fractional Brownian Motion, where the Hurst parameter H of the Fractional Brownian Motion belongs to ( 1 2 ,1 ) . Using tools such as Malliavin derivatives and Skorohod integrals, the strong convergence order of this numerical scheme is obtained to be of first order.
文章引用：王聪淇. 分数布朗运动驱动的SDE梯形数值格式的收敛性分析[J]. 应用数学进展, 2025, 14(3): 37-44. https://doi.org/10.12677/aam.2025.143090

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