Markovian projections for functionals of Itô semimartingales with jumps

2025/06/01 by Larsson, Martin, Long, Shukun
#FOS: Economics and business #FOS: Mathematics #Mathematical Finance (q-fin.MF) #Probability (math.PR)

paper · doi:10.48550/arxiv.2506.00762

Abstract

Given an Itô semimartingale X, its Markovian projection is an Itô semimartingale \widehatX, 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 \widehatX but still in a Markovian sense. In the continuous case, the definitive result on existence of Markovian projections was obtained by Brunick and Shreve~\citeMR3098443. In this paper, we extend their result to the fully general setting of Itô semimartingales with jumps.

Citations

• Inverting the Markovian projection for pure jump processes
• Markovian projections for Itô semimartingales with jumps
• Superposition and mimicking theorems for conditional McKean-Vlasov equations
• Mimicking the marginal distributions of a semimartingale

Related

• Markovian projections for Itô semimartingales with jumps
• On Itô formulas for jump processes
• Mimicking the marginal distributions of a semimartingale
• From Markov Processes to Semimartingales
• A Family of non-Gaussian Martingales with Gaussian Marginals