分数随机微分方程二次变化的渐近展开

IF 1.1 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications Pub Date : 2024-05-21 DOI:10.1016/j.spa.2024.104389

Hayate Yamagishi, Nakahiro Yoshida

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引用次数: 0

摘要

我们根据收敛于混合正态极限的斯科罗霍德积分渐近展开理论，推导出满足由分数布朗运动驱动的随机微分方程的随机过程的二次变化的渐近展开。为了应用一般理论，有必要在扩展二次变化和识别极限随机符号时，估计作为分数布朗运动多个积分乘积的随机加权和的函数。为了克服这一困难，我们利用了作者在 Yamagishi 和 Yoshida（2023 年）中提出的函数指数理论。

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Asymptotic expansion of the quadratic variation of fractional stochastic differential equation

We derive an asymptotic expansion for the quadratic variation of a stochastic process satisfying a stochastic differential equation driven by a fractional Brownian motion, based on the theory of asymptotic expansion of Skorohod integrals converging to a mixed normal limit. In order to apply the general theory, it is necessary to estimate functionals that are a randomly weighted sum of products of multiple integrals of the fractional Brownian motion, in expanding the quadratic variation and identifying the limit random symbols. To overcome the difficulty, we utilized the theory of exponents of functionals, which was introduced by the authors in Yamagishi and Yoshida (2023).

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来源期刊

Stochastic Processes and their Applications 数学-统计学与概率论

CiteScore

2.90

自引率

7.10%

发文量

180

审稿时长

23.6 weeks

期刊介绍： Stochastic Processes and their Applications publishes papers on the theory and applications of stochastic processes. It is concerned with concepts and techniques, and is oriented towards a broad spectrum of mathematical, scientific and engineering interests. Characterization, structural properties, inference and control of stochastic processes are covered. The journal is exacting and scholarly in its standards. Every effort is made to promote innovation, vitality, and communication between disciplines. All papers are refereed.