Tail Measures And Regular Variation
Year:
2022Published in:
Electronic Journal of ProbabilityA general framework for the study of regular variation (RV) is that of Polish star-shaped metric spaces, while recent developments in [41] have discussed RV withrespect to a properly localised boundednessB. Along the lines of the latter approach,we discuss the RV of Borel measures and random processes on a general Polish metricspaces(D, dD). Tail measures introduced in [47] appear naturally as limiting measuresof regularly varying time series. We define tail measures on the measurable space(D,D)indexed byH(D), a countable family of 1-homogeneous coordinate maps, andshow some tractable instances for the investigation of RV whenBis determined byH(D). This allows us to study the regular variation of càdlàg processes onD(Rl,Rd)retrieving in particular results obtained in [59] for RV of stationary càdlàg processeson the real line removingl= 1therein. Further, we discuss potential applications andopen questions.
Related by author
67 publications found
Real Harmonizable Multifractional Stable Process And Its Local Properties
Publisher: Stochastic Processes and their Applications
Authors: Georgiy Shevchenko, Marco Dozzi, Yulia Mishura, Kostiantyn Ral’chenko
The Rate Of Convergence For Euler Approximations Of Solutions Of Stochastic Differential Equations Driven By Fractional Brownian Motion
Publisher: Stochastics
Authors: Georgiy Shevchenko, Yulia Mishura
Asymptotic Behavior Of Mixed Power Variations And Statistical Estimation In Mixed Models
Publisher: Statistical Inference for Stochastic Processes
Authors: Georgiy Shevchenko, Yulia Mishura, Marco Dozzi
Rate Of Convergence Of Euler Approximations Of Solution To Mixed Stochastic Differential Equation Involving Brownian Motion And Fractional Brownian Motion
Publisher: Random Operators and Stochastic Equations
Authors: Georgiy Shevchenko, Yulia Mishura
Malliavin Regularity Of Solutions To Mixed Stochastic Differential Equations
Publisher: Statistics & Probability Letters
Authors: Georgiy Shevchenko, Taras Shalaiko
Boundary Non‑Crossing Probabilities Of Gaussian Processes: Sharp Bounds And Asymptotics
Publisher: Journal of Theoretical Probability
Authors: Georgiy Shevchenko, Enkelejd Hashorva, Yulia Mishura
Fractional Brownian Motion In A Nutshell
Publisher: arxiv
Authors: Georgiy Shevchenko
Approximation Schemes For Stochastic Differential Equations In Hilbert Space
Publisher: Theory of Probability & Its Applications
Authors: Georgiy Shevchenko, Yulia Mishura
Existence And Uniqueness Of Mild Solution To Stochastic Heat Equation With White And Fractional Noises
Publisher: arxiv
Authors: Georgiy Shevchenko, Kostiantyn Prontenko, Yulia Mishura
Stochastic Wave Equation In A Plane Driven By Spatial Stable Noise
Publisher: Modern Stochastics: Theory and Applications
Authors: Georgiy Shevchenko, Larysa Pryhara