Derivatives of local times for some Gaussian fields

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:484

Article

Hong, Minhao¹  Xu, Fangjun^2,3 

[1] East China Normal Univ, Sch Stat, Shanghai 200062, Peoples R China

[2] East China Normal Univ, Sch Stat, Key Lab Adv Theory & Applicat Stat & Data Sci MOE, Shanghai 200062, Peoples R China

[3] NYU Shanghai, NYU ECNU Inst Math Sci, 3663 Zhongshan Rd North, Shanghai 200062, Peoples R China

关键词: Gaussian fields;    Derivatives of local time;    Local nondeterminism property;    Holder continuity;   

DOI  :  10.1016/j.jmaa.2019.123716

来源: Elsevier

【 摘 要 】

In this article, we consider derivatives of local time for a (2, d)-Gaussian field Z = {Z(t, s) = X-t(H1) - (X) over tilde (H2)(s), s, t >= 0}, where X-H1 and (X) over tilde (H2) are two independent processes from a class of d-dimensional centered Gaussian processes satisfying certain local nondeterminism property. We first give a condition for existence of derivatives of the local time. Then, under this condition, we show that derivatives of the local time are Holder continuous in both time and space variables. Moreover, under some additional assumptions, we show that this condition is also necessary for existence of derivatives of the local time at the origin. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free