English
 
User Manual Privacy Policy Disclaimer Contact us
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT
  Extreme value statistics of ergodic Markov processes from first passage times in the large deviation limit

Hartich, D., & Godec, A. (2019). Extreme value statistics of ergodic Markov processes from first passage times in the large deviation limit. Journal of Physics A: Mathematical and Theoretical, 52: 244001. doi:10.1088/1751-8121/ab1eca.

Item is

Basic

show hide
Item Permalink: http://hdl.handle.net/21.11116/0000-0003-ADCC-5 Version Permalink: http://hdl.handle.net/21.11116/0000-0003-ADD3-C
Genre: Journal Article

Files

show Files
hide Files
:
3060011.pdf (Publisher version), 2MB
Name:
3060011.pdf
Description:
-
Visibility:
Public
MIME-Type / Checksum:
application/pdf / [MD5]
Technical Metadata:
Copyright Date:
-
Copyright Info:
-

Locators

show

Creators

show
hide
 Creators:
Hartich, D.1, Author              
Godec, A.1, Author              
Affiliations:
1Research Group of Mathematical Biophysics, MPI for Biophysical Chemistry, Max Planck Society, ou_2396692              

Content

show
hide
Free keywords: -
 Abstract: Extreme value functionals of stochastic processes are inverse functionals of the first passage time—a connection that renders their probability distribution functions equivalent. Here, we deepen this link and establish a framework for analyzing extreme value statistics of ergodic reversible Markov processes in confining potentials on the hand of the underlying relaxation eigenspectra. We derive a chain of inequalities, which bounds the long-time asymptotics of first passage densities, and thereby extrema, from above and from below. The bounds involve a time integral of the transition probability density describing the relaxation towards equilibrium. We apply our general results to the analysis of extreme value statistics at long times in the case of Ornstein–Uhlenbeck process and a 3D Brownian motion confined to a sphere, also known as Bessel process. We find that even on time-scales that are shorter than the equilibration time, the large deviation limit characterizing long-time asymptotics can approximate the statistics of extreme values remarkably well. Our findings provide a novel perspective on the study of extrema beyond the established limit theorems for sequences of independent random variables and for asymmetric diffusion processes beyond a constant drift.

Details

show
hide
Language(s): eng - English
 Dates: 2019-05-212019-06-14
 Publication Status: Published in print
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Method: Peer
 Identifiers: DOI: 10.1088/1751-8121/ab1eca
 Degree: -

Event

show

Legal Case

show

Project information

show

Source 1

show
hide
Title: Journal of Physics A: Mathematical and Theoretical
Source Genre: Journal
 Creator(s):
Affiliations:
Publ. Info: -
Pages: 17 Volume / Issue: 52 Sequence Number: 244001 Start / End Page: - Identifier: -