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.

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Mimicking and Conditional Control with Hard Killing

  • Rene Carmona,
  • Daniel Lacker

摘要

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.