Electronic Journal of Probability

A Non-Skorohod Topology on the Skorohod Space

Adam Jakubowski

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A new topology (called $S$) is defined on the space $D$ of functions $x: [0,1] \to R^1$ which are right-continuous and admit limits from the left at each $t > 0$. Although $S$ cannot be metricized, it is quite natural and shares many useful properties with the traditional Skorohod's topologies $J_1$ and $M_1$. In particular, on the space $P(D)$ of laws of stochastic processes with trajectories in $D$ the topology $S$ induces a sequential topology for which both the direct and the converse Prohorov's theorems are valid, the a.s. Skorohod representation for subsequences exists and finite dimensional convergence outside a countable set holds.

Article information

Electron. J. Probab., Volume 2 (1997), paper no. 4, 21 pp.

Accepted: 4 July 1997
First available in Project Euclid: 26 January 2016

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Mathematical Reviews number (MathSciNet)

Primary: 60F17: Functional limit theorems; invariance principles
Secondary: 60B05: Probability measures on topological spaces 60G17: Sample path properties 54D55: Sequential spaces

Skorohod space Skorohod representation convergence in distribution sequential spaces semimartingales

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Jakubowski, Adam. A Non-Skorohod Topology on the Skorohod Space. Electron. J. Probab. 2 (1997), paper no. 4, 21 pp. doi:10.1214/EJP.v2-18. https://projecteuclid.org/euclid.ejp/1453839980

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