FRACTIONAL STOCHASTIC PARTIAL DIFFERENTIAL EQUATION FOR RANDOM TANGENT FIELDS ON THE SPHERE

被引：6

作者：

Anh, V. V. ^{[1
]}

Olenko, A. ^{[2
]}

Wang, Y. G. ^{[3
,4
,5
]}

机构：

[1] Swinburne Univ Technol, Fac Sci Engn & Technol, POB 218, Hawthorn, Vic 3122, Australia

[2] La Trobe Univ, Dept Math & Stat, Melbourne, Vic 3086, Australia

[3] Max Planck Inst Math Sci, Inselstr 22, D-04103 Leipzig, Germany

[4] Shanghai Jiao Tong Univ, Sch Math Sci, Inst Nat Sci, Shanghai 200240, Peoples R China

[5] Shanghai Jiao Tong Univ, Key Lab Sci & Engn Comp, Minist Educ MOE LSC, Shanghai 200240, Peoples R China

来源：

THEORY OF PROBABILITY AND MATHEMATICAL STATISTICS | 2021年 / 104卷

基金：

欧洲研究理事会; 澳大利亚研究理事会;

关键词：

Fractional stochastic partial differential equation; random tangent field; vector spherical harmonics; fractional Brownian motion; BROWNIAN-MOTION; APPROXIMATION; MODELS; DRIVEN; OZONE; TIME;

D O I：

10.1090/tpms/1142

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

This paper develops a fractional stochastic partial differential equation (SPDE) to model the evolution of a random tangent vector field on the unit sphere. The SPDE is governed by a fractional diffusion operator to model the Levy-type behaviour of the spatial solution, a fractional derivative in time to depict the intermittency of its temporal solution, and is driven by vector-valued fractional Brownian motion on the unit sphere to characterize its temporal long-range dependence. The solution to the SPDE is presented in the form of the Karhunen-Loeve expansion in terms of vector spherical harmonics. Its covariance matrix function is established as a tensor field on the unit sphere that is an expansion of Legendre tensor kernels. The variance of the increments and approximations to the solutions are studied and convergence rates of the approximation errors are given. It is demonstrated how these convergence rates depend on the decay of the power spectrum and variances of the fractional Brownian motion.

引用

页码：3 / 22

页数：20

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