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MEXIT: Maximal un-coupling times for stochastic processes by Ernst, P. A.; Kendall, W. S.; Roberts, G. O.; Rosenthal, J. S. is a scholarly article available to read on EtoBox.

What is MEXIT: Maximal un-coupling times for stochastic processes about?

Classical coupling constructions arrange for copies of the \emph{same} Markov process started at two \emph{different} initial states to become equal as soon as possible. In this paper, we consider an alternative coupling framework in which one seeks to arrange for two \emph{different} Markov (or other stochastic) processes to remain equal for as long as possible, when started in the \emph{same} state. We refer to this "un-coupling" or "maximal agreement" construction as \emph{MEXIT}, standing for "maximal exit". After highlighting the importance of un-coupling arguments in a few key statistical and probabilistic settings, we develop an explicit \MEXIT construction for stochastic processes in discrete time with countable state-space. This construction is generalized to random processes on general state-space running in continuous time, and then exemplified by discussion of \MEXIT for Brownian motions with two different constant drifts.

Author

Ernst, P. A.; Kendall, W. S.; Roberts, G. O.; Rosenthal, J. S.

Published

2017

Language

EN