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1997 A Non-Skorohod Topology on the Skorohod Space
Adam Jakubowski
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Electron. J. Probab. 2: 1-21 (1997). DOI: 10.1214/EJP.v2-18


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.


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Adam Jakubowski. "A Non-Skorohod Topology on the Skorohod Space." Electron. J. Probab. 2 1 - 21, 1997.


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

MathSciNet: MR1475862
Digital Object Identifier: 10.1214/EJP.v2-18

Primary: 60F17
Secondary: 54D55 , 60B05 , 60G17

Keywords: Convergence in distribution , Semimartingales , sequential spaces , Skorohod representation , Skorohod space

Vol.2 • 1997
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