灰色布朗运动的小球概率和大偏差

IF 0.5 4区数学 Q4 STATISTICS & PROBABILITY

Electronic Communications in Probability Pub Date : 2023-01-01 DOI:10.1214/23-ecp555

Stefan Gerhold

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引用次数: 0

摘要

我们证明了单位区间广义灰色布朗运动的一致范数具有解析密度，排除了分数阶布朗运动的特殊情况。我们的主要结果是广义灰色布朗运动小球概率的渐近展开式，并推广到路径空间上的其他范数。衰减率不是指数的，而是二阶多项式的。对于统一范数和Hölder范数，我们也证明了一个大偏差估计。

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Small ball probabilities and large deviations for grey Brownian motion

We show that the uniform norm of generalized grey Brownian motion over the unit interval has an analytic density, excluding the special case of fractional Brownian motion. Our main result is an asymptotic expansion for the small ball probability of generalized grey Brownian motion, which extends to other norms on path space. The decay rate is not exponential but polynomial, of degree two. For the uniform norm and the Hölder norm, we also prove a large deviations estimate.

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来源期刊

Electronic Communications in Probability 工程技术-统计学与概率论

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Electronic Communications in Probability (ECP) publishes short research articles in probability theory. Its sister journal, the Electronic Journal of Probability (EJP), publishes full-length articles in probability theory. Short papers, those less than 12 pages, should be submitted to ECP first. EJP and ECP share the same editorial board, but with different Editors in Chief.