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A Non-Skorohod Topology on the Skorohod Space


 
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1. Title Title of document A Non-Skorohod Topology on the Skorohod Space
 
2. Creator Author's name, affiliation, country Adam Jakubowski; Nicholas Copernicus University
 
3. Subject Discipline(s) Mathematics
 
3. Subject Keyword(s) Skorohod space, Skorohod representation, convergence in distribution, sequential spaces, semimartingales.
 
3. Subject Subject classification 60F17, 60B05, 60G17, 54D55.
 
4. Description Abstract 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.
 
5. Publisher Organizing agency, location
 
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7. Date (YYYY-MM-DD) 1997-07-04
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/18
 
10. Identifier Digital Object Identifier 10.1214/EJP.v2-18
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 2
 
12. Language English=en en
 
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