## Electronic Communications in Probability

### Skorokhod’s M1 topology for distribution-valued processes

Sean Ledger

#### 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
Accepted: 11 April 2016
First available in Project Euclid: 21 April 2016

https://projecteuclid.org/euclid.ecp/1461251162

Digital Object Identifier
doi:10.1214/16-ECP4754

Mathematical Reviews number (MathSciNet)
MR3492929

Zentralblatt MATH identifier
1338.60105

#### 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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