Hölder具有有界和可测量增量的随机过程的规律性

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-09-02 DOI:10.4171/aihpc/41

Ángel Arroyo, P. Blanc, M. Parviainen

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引用次数: 3

摘要

．我们得到了一类相当一般的离散随机过程期望值的渐近H′old估计。这种期望也可以被描述为动态规划原理的解或离散偏微分方程的解。该结果与偏微分方程中的Krylov-Safonov正则性结果相对应，也推广到离散极值算子满足pucci型不等式的函数中。然而，与PDE设置相比，离散步长ε有一些关键的影响。这个证明结合了分析论证和概率论证。

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Hölder regularity for stochastic processes with bounded and measurable increments

. We obtain an asymptotic H¨older estimate for expectations of a quite general class of discrete stochastic processes. Such expectations can also be described as solutions to a dynamic programming principle or as solutions to discretized PDEs. The result, which is also generalized to functions satisfying Pucci-type inequalities for discrete extremal operators, is a counterpart to the Krylov-Safonov regularity result in PDEs. However, the discrete step size ε has some crucial eﬀects compared to the PDE setting. The proof combines analytic and probabilistic arguments.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.