Persistence and ball exponents for Gaussian stationary processes

IF 3.1 1区 数学 Q1 MATHEMATICS
Naomi D. Feldheim, Ohad N. Feldheim, Sumit Mukherjee
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引用次数: 0

Abstract

Consider a real Gaussian stationary process , indexed on either or and admitting a spectral measure . We study , the persistence exponent of . We show that, if has a positive density at the origin, then the persistence exponent exists; moreover, if has an absolutely continuous component, then if and only if this spectral density at the origin is finite. We further establish continuity of in , in (under a suitable metric) and, if is compactly supported, also in dense sampling. Analogous continuity properties are shown for , the ball exponent of , and it is shown to be positive if and only if has an absolutely continuous component.
高斯平稳过程的持续性和球指数
考虑一个真实的高斯平稳过程,在或上索引,并承认一个谱测度。我们研究,持久性指数。我们证明,如果在原点处密度为正,则持久性指数存在;此外,如果有一个绝对连续的分量,那么当且仅当这个谱密度在原点是有限的。我们进一步建立了in, in(在合适的度量下)的连续性,并且,如果是紧支持的,也在密集采样中。的球指数具有类似的连续性,且当且仅当其具有绝对连续分量时,其为正。
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来源期刊
CiteScore
6.70
自引率
3.30%
发文量
59
审稿时长
>12 weeks
期刊介绍: Communications on Pure and Applied Mathematics (ISSN 0010-3640) is published monthly, one volume per year, by John Wiley & Sons, Inc. © 2019. The journal primarily publishes papers originating at or solicited by the Courant Institute of Mathematical Sciences. It features recent developments in applied mathematics, mathematical physics, and mathematical analysis. The topics include partial differential equations, computer science, and applied mathematics. CPAM is devoted to mathematical contributions to the sciences; both theoretical and applied papers, of original or expository type, are included.
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