Optimal Control of Infinite-Dimensional Piecewise Deterministic Markov Processes: A BSDE Approach. Application to the Control of an Excitable Cell Membrane.
- Resource Type
- Article
- Authors
- Bandini, Elena; Thieullen, Michèle
- Source
- Applied Mathematics & Optimization. Oct2021, Vol. 84 Issue 2, p1549-1603. 55p.
- Subject
- *MARKOV processes
*DETERMINISTIC processes
*STOCHASTIC differential equations
*INTEGRO-differential equations
*VISCOSITY solutions
*HAMILTON-Jacobi equations
*HAMILTON-Jacobi-Bellman equation
- Language
- ISSN
- 0095-4616
In this paper we consider the optimal control of Hilbert space-valued infinite-dimensional Piecewise Deterministic Markov Processes (PDMP) and we prove that the corresponding value function can be represented via a Feynman–Kac type formula through the solution of a constrained Backward Stochastic Differential Equation. A fundamental step consists in showing that the corresponding integro-differential Hamilton–Jacobi–Bellman equation has a unique viscosity solution, by proving a suitable comparison theorem. We apply our results to the control of a PDMP Hodgkin-Huxley model with spatial component. [ABSTRACT FROM AUTHOR]