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Mimicking and Conditional Control with Hard Killing

In: Stochastic Analysis and Applications 2025

Author

Listed:
  • Rene Carmona

    (Princeton University, Department of Operations Research and Financial Engineering)

  • Daniel Lacker

    (Columbia University, Department of Industrial Engineering and Operations Research)

Abstract

We first prove a mimicking theorem (also known as a Markovian projection theorem) for the marginal distributions of an Itô process conditioned to not have exited a given domain. We then apply this new result to the proof of a conjecture of P.L. Lions for the optimal control of conditioned processes.

Suggested Citation

  • Rene Carmona & Daniel Lacker, 2026. "Mimicking and Conditional Control with Hard Killing," Springer Books, in: Dan Crisan & Ilya Chevyrev & Thomas Cass & James Foster & Christian Litterer & Cristopher Salvi (ed.), Stochastic Analysis and Applications 2025, pages 311-320, Springer.
    • Handle: RePEc:spr:sprchp:978-3-032-03914-9_11
    DOI: 10.1007/978-3-032-03914-9_11
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