Markovian projections for functionals of Itô semimartingales with jumps
Abstract
Given an Itô semimartingale X, its Markovian projection is an Itô semimartingale X, with Markovian differential characteristics, that matches the one-dimensional marginal laws of X. One may even require certain functionals of the two processes to have the same fixed-time marginals, at the cost of enhancing the differential characteristics of X but still in a Markovian sense. In the continuous case, the definitive result on existence of Markovian projections was obtained by Brunick and Shreve~MR3098443. In this paper, we extend their result to the fully general setting of Itô semimartingales with jumps.
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