Abstract
A Skorohod representation type theorem is proved for the weak convergence of stochastic processes in the Skorohod topology. This allows the “time changes” arising from the Skorohod topology to be considered as stochastic processes. While thenth time change processA n t is not adapted to thenth filtration (ℱ n t ) t⩾0, it is possible to choose the processesA n such that they are adapted to
, where
, where γ n is a sequence of constants decreasing to 0 asn tends to ∞.
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Supported in part by NSF Grant No. DMS-9103454.
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Jacod, J., Protter, P. A remark on the weak convergence of processes in the Skorohod topology. J Theor Probab 6, 463–472 (1993). https://doi.org/10.1007/BF01066712
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DOI: https://doi.org/10.1007/BF01066712