Open Access
2016 Skorokhod’s M1 topology for distribution-valued processes
Sean Ledger
Electron. Commun. Probab. 21: 1-11 (2016). DOI: 10.1214/16-ECP4754


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.


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Sean Ledger. "Skorokhod’s M1 topology for distribution-valued processes." Electron. Commun. Probab. 21 1 - 11, 2016.


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

zbMATH: 1338.60105
MathSciNet: MR3492929
Digital Object Identifier: 10.1214/16-ECP4754

Primary: 60F17 , 60G07

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

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