首页|MULTIPLE INTERSECTIONS OF SPACE-TIME ANISOTROPIC GAUSSIAN FIELDS

MULTIPLE INTERSECTIONS OF SPACE-TIME ANISOTROPIC GAUSSIAN FIELDS

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Let X={X(t)∈ Rd,t ∈ RN} be a centered space-time anisotropic Gaussian field with indices H=(H1,…,HN)∈(0,1)N,where the components Xi(i=1,…,d)of X are independent,and the canonical metric √E(Xi(t)-Xi(s))2(i=1,…,d)is commensurate with γαi(ΣNj=1|tj-sj|Hj)for s=(s1,…,sN),t=(t1,…,tN)∈ RN,αi ∈(0,1],and with the continuous function γ(·)satisfying certain conditions.First,the upper and lower bounds of the hitting probabilities of X can be derived from the corresponding generalized Hausdorff measure and capacity,which are based on the kernel functions depending explicitly on γ(·).Furthermore,the multiple intersections of the sample paths of two independent centered space-time anisotropic Gaussian fields with different distributions are considered.Our results extend the corresponding results for anisotropic Gaussian fields to a large class of space-time anisotropic Gaussian fields.

anisotropic Gaussian fieldmultiple intersectionsHausdorff measurecapacity

陈振龙、苑伟杰

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School of Statistics and Mathematics,Zhejiang Gongshang University,Hangzhou 310018,China

国家自然科学基金国家自然科学基金浙江省自然科学基金Management Project of"Digital+"Discipline Construction of Zhejiang Gongshang UniversityManagement Project of"Digital+"Discipline Construction of Zhejiang Gongshang UniversityCharacteristic & Preponderant Discipline of Key Construction Universities in Zhejiang Province(Zhejiang Gongshang UniversityScientific Research Projects of Universities in Anhui Province

1237115011971432LY21G010003SZJ2022A012SZJ2022B0172022AH050955

2024

10.1007/s10473-024-0115-1

数学物理学报(英文版)
中科院武汉物理与数学研究所

数学物理学报(英文版)

CSTPCD
影响因子：0.256
ISSN：0252-9602
年,卷(期)：2024.44(1)
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