粗糙积分的可加性证明

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Stochastics and Dynamics Pub Date : 2024-03-08 DOI:10.1142/s0219493724500060

YU Ito

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引用次数: 0

摘要

.在分式微积分的基础上，我们用分式导数的 Lebesgue 积分引入了沿 H(cid:127)older 粗糙路径的受控路径积分的明确表述。由于分数导数在很大程度上取决于积分区间的端点，因此积分的基本性质--关于积分区间的可加性在该表述下并不明显。在本文中，我们证明了该公式下积分的可加性。与之前的研究相比，我们的证明似乎更简单，而且适用于利用分数微积分方法进行粗略路径分析。

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A proof of the additivity of rough integral

. On the basis of fractional calculus, we introduce an explicit formulation of the integral of controlled paths along H(cid:127)older rough paths in terms of Lebesgue integrals for fractional derivatives. The additivity with respect to the interval of integration, a fundamental property of the integral, is not apparent under the formulation because the fractional derivatives depend heavily on the endpoints of the interval of integration. In this paper, we provide a proof of the additivity of the integral under the formulation. Our proof seems to be simpler than those provided in previous studies and is suitable for utilizing the fractional calculus approach to rough path analysis.

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来源期刊

Stochastics and Dynamics 数学-统计学与概率论

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： This interdisciplinary journal is devoted to publishing high quality papers in modeling, analyzing, quantifying and predicting stochastic phenomena in science and engineering from a dynamical system''s point of view. Papers can be about theory, experiments, algorithms, numerical simulation and applications. Papers studying the dynamics of stochastic phenomena by means of random or stochastic ordinary, partial or functional differential equations or random mappings are particularly welcome, and so are studies of stochasticity in deterministic systems.