Electronic Communications in Probability

Skorokhod’s M1 topology for distribution-valued processes

Sean Ledger

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Abstract

Skorokhod’s M1 topology is defined for càdlàg paths taking values in the space of tempered distributions (more generally, in the dual of a countably Hilbertian nuclear space). Compactness and tightness characterisations are derived which allow us to study a collection of stochastic processes through their projections on the familiar space of real-valued càdlàg processes. It is shown how this topological space can be used in analysing the convergence of empirical process approximations to distribution-valued evolution equations with Dirichlet boundary conditions.

Article information

Source
Electron. Commun. Probab., Volume 21 (2016), paper no. 34, 11 pp.

Dates
Received: 10 December 2015
Accepted: 11 April 2016
First available in Project Euclid: 21 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1461251162

Digital Object Identifier
doi:10.1214/16-ECP4754

Mathematical Reviews number (MathSciNet)
MR3492929

Zentralblatt MATH identifier
1338.60105

Subjects
Primary: 60G07: General theory of processes 60F17: Functional limit theorems; invariance principles

Keywords
Skorokhod M1 topology compacntess and tightness characterisation tempered distribution countably Hilbertian nuclear space

Rights
Creative Commons Attribution 4.0 International License.

Citation

Ledger, Sean. Skorokhod’s M1 topology for distribution-valued processes. Electron. Commun. Probab. 21 (2016), paper no. 34, 11 pp. doi:10.1214/16-ECP4754. https://projecteuclid.org/euclid.ecp/1461251162


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