Jump processes with deterministic and stochastic controls

Mark S. Bartlett, Amilcare Porporato, Lamberto Rondoni

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.

Original languageEnglish (US)
Article number042133
JournalPhysical Review E
Issue number4
StatePublished - Oct 25 2019

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability


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