On Extremes of Multidimensional Stationary Diffusion Processes in Euclidean Norm
نویسنده
چکیده
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 boundary conditions on the ball around the origin with radius R in the limit as R→∞. We give conditions when sharp spectral asymptotics can be obtained testing with rotationally symmetric functions. Examples include not only rotationally symmetric but also highly non-symmetric processes.
منابع مشابه
A Statistical Study of two Diffusion Processes on Torus and Their Applications
Diffusion Processes such as Brownian motions and Ornstein-Uhlenbeck processes are the classes of stochastic processes that have been investigated by researchers in various disciplines including biological sciences. It is usually assumed that the outcomes of these processes are laid on the Euclidean spaces. However, some data in physical, chemical and biological phenomena indicate that they cann...
متن کاملAssessment of the Log-Euclidean Metric Performance in Diffusion Tensor Image Segmentation
Introduction: Appropriate definition of the distance measure between diffusion tensors has a deep impact on Diffusion Tensor Image (DTI) segmentation results. The geodesic metric is the best distance measure since it yields high-quality segmentation results. However, the important problem with the geodesic metric is a high computational cost of the algorithms based on it. The main goal of this ...
متن کاملA Multidimensional Filter Algorithm for Nonlinear Equations and Nonlinear Least-Squares
We introduce a new algorithm for the solution of systems of nonlinear equations and nonlinear least-squares problems that attempts to combine the efficiency of filter techniques and the robustness of trust-region methods. The algorithm is shown, under reasonable assumptions, to globally converge to zeros of the system, or to first-order stationary points of the Euclidean norm of its residual. P...
متن کاملModeling Fluid's Dynamics with Master Equations in Ultrametric Spaces Representing the Treelike Structure of Capillary Networks
We present a new conceptual approach for modeling of fluid flows in random porous media based on explicit exploration of the treelike geometry of complex capillary networks. Such patterns can be represented mathematically as ultrametric spaces and the dynamics of fluids by ultrametric diffusion. The images of p-adic fields, extracted from the real multiscale rock samples and from some reference...
متن کاملReturn level estimation from non-stationary spatial data exhibiting multidimensional covariate effects
Careful modelling of non-stationarity is critical to reliable specification of marine and coastal design criteria. We present a spline based methodology to incorporate spatial, directional, temporal and other covariate effects in extreme value models for environmental variables such as storm severity. For storm peak significant wave height events, the approach uses quantile regression to estima...
متن کامل