Stochastic control for a class of random evolution models

Max Olivier Hongler, Halil Mete Soner, Ludwig Streit

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We construct the explicit connection existing between a solvable model of the discrete velocities non-linear Boltzmann equation and the Hamilton-Bellman-Jacobi equation associated with a simple optimal control of a piecewise deterministic process. This study extends the known relation that exists between the Burgers equation and a simple controlled diffusion problem. In both cases the resulting partial differential equations can be linearized via a logarithmic transformation and hence offer the possibility to solve physically relevant non-linear field models in full generality.

Original languageEnglish (US)
Pages (from-to)113-121
Number of pages9
JournalApplied Mathematics and Optimization
Issue number2
StatePublished - Mar 2004
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Applied Mathematics


  • Logarithmic transformation
  • Nonlinear field equations
  • Piecewise deterministic evolutions
  • Stochastic optimal control


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