Quantifying and Managing Uncertainty in Piecewise-Deterministic Markov Processes

In piecewise-deterministic Markov processes (PDMPs) the state of a finite-dimensional system evolves continuously, but evolutive equation may change randomly as result discrete switches. A running cost is integrated along corresponding trajectory up to termination produce cumulative process. We address three natural questions related uncertainty in PDMP models: (1) how compute distribution function (CDF) when switching rates are fully known; (2) accurately bound CDF uncertain; and (3) assuming controlled, select control optimize that CDF. all cases, our approach requires posing suitable hyperbolic partial differential equations, which then solved numerically on an augmented space. illustrate method using simple examples planning under for several one-dimensional two-dimensional first-exit time problems. appendix, we also apply this model fish harvesting environment with random switches carrying capacity.