Jump processes with deterministic and stochastic controls.

Phys Rev E

Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy.

Published: October 2019

We consider the dynamics of a one-dimensional system evolving according to a deterministic drift and randomly forced by two types of jump processes, one representing an external, uncontrolled forcing and the other one a control that instantaneously resets the system according to specified protocols (either deterministic or stochastic). We develop a general theory, which includes a different formulation of the master equation using antecedent and posterior jump states, and obtain an analytical solution for steady state. The relevance of the theory is illustrated with reference to stochastic irrigation to assess crop-failure risk, a problem of interest for environmental geophysics.

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http://dx.doi.org/10.1103/PhysRevE.100.042133DOI Listing

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