Extremes of Lp-norm of vector-valued Gaussian processes with trend
نویسندگان
چکیده
منابع مشابه
On the Norm Continuity of ^'-valued Gaussian Processes
Let Sf be the Schwartz space of all rapidly decreasing functions on R, Sf be the topological dual space of Sf and for each positive integer p,Sfp be the space of all elements of £f' which are continuous in the p-th norm defining the nuclear Frechet topology of Sf. The main purpose of the present paper is to show that if {Xtί t e [0, + oo)} is an ^'-valued Gaussian process and for any fixed φβ^ ...
متن کاملExtremes of Independent Gaussian Processes
For every n ∈ N, let X1n, . . . , Xnn be independent copies of a zero-mean Gaussian process Xn = {Xn(t), t ∈ T}. We describe all processes which can be obtained as limits, as n → ∞, of the process an(Mn − bn), where Mn(t) = maxi=1,...,n Xin(t) and an, bn are normalizing constants. We also provide an analogous characterization for the limits of the process anLn, where Ln(t) = mini=1,...,n |Xin(t)|.
متن کاملconstruction of vector fields with positive lyapunov exponents
in this thesis our aim is to construct vector field in r3 for which the corresponding one-dimensional maps have certain discontinuities. two kinds of vector fields are considered, the first the lorenz vector field, and the second originally introced here. the latter have chaotic behavior and motivate a class of one-parameter families of maps which have positive lyapunov exponents for an open in...
15 صفحه اولOn Extremes of Multidimensional Stationary Diffusion Processes in Euclidean Norm
Let (Xt)t≥0 be a R-valued stationary reversible diffusion process. We investigate the asymptotic behavior of MT := max0≤t≤T |Xt|, where | · | is the Euclidean norm in R. The aim of this paper is to characterize the tail asymptotics of MT for fixed T > 0 as well as the long time behavior of MT as T → ∞. This is related to spectral asymptotics of the generator of (Xt)t≥0 subject to Dirichlet boun...
متن کاملSmall ball probabilities for Gaussian Markov processes under the Lp - norm ( Wenbo
Let {X (t); 06t61} be a real-valued continuous Gaussian Markov process with mean zero and covariance (s; t)=EX (s)X (t) 6= 0 for 0¡s; t ¡ 1. It is known that we can write (s; t)= G(min(s; t))H (max(s; t)) with G¿ 0; H ¿ 0 and G=H nondecreasing on the interval (0; 1). We show that for the Lp-norm on C[0; 1], 16p6∞ lim →0 2 logP(‖X (t)‖p ¡ ) =− p (∫ 1 0 (G′H − H ′G)p=(2+p) dt )(2+p)=p and its var...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Stochastics
سال: 2018
ISSN: 1744-2508,1744-2516
DOI: 10.1080/17442508.2018.1499101