Fundamental properties of process distances

Julio Backhoff Veraguas, Mathias Beiglböck (Korresp. Autor*in), Manuel Eder, Alois Pichler

Veröffentlichungen: Beitrag in FachzeitschriftArtikelPeer Reviewed

Abstract

To quantify the difference of distinct stochastic processes it is not sufficient to consider the distance of their states and corresponding probabilities. Instead, the information, which evolves and accumulates over time and which is mathematically encoded by filtrations, has to be accounted for as well. The nested distance, also known as bicausal Wasserstein distance, recognizes this component and involves the filtration properly. This distance is of emerging importance due to its applications in stochastic analysis, stochastic programming, mathematical economics and other disciplines.

This paper investigates the basic metric and topological properties of the nested distance on the space of discrete-time processes. In particular we prove that the nested distance generates a Polish topology, although the genuine space is not complete. Moreover we identify its completion to be the space of nested distributions, a space of generalized stochastic processes.
OriginalspracheEnglisch
Seiten (von - bis)5575-5591
Seitenumfang17
FachzeitschriftStochastic Processes and their Applications
Jahrgang130
Ausgabenummer9
DOIs
PublikationsstatusVeröffentlicht - Sep. 2020

ÖFOS 2012

  • 101024 Wahrscheinlichkeitstheorie
  • 101019 Stochastik

Zitationsweisen