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A Non-Skorohod Topology on the Skorohod Space

   
@article{EJP18,
	author = {Adam Jakubowski},
	title = {A Non-Skorohod Topology on the Skorohod Space},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {2},
	year = {1997},
	keywords = {Skorohod space, Skorohod representation, convergence in distribution, sequential spaces, semimartingales.},
	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.},
	pages = {no. 4, 1-21},
	issn = {1083-6489},
	doi = {10.1214/EJP.v2-18},    
        url = {http://ejp.ejpecp.org/article/view/18}}