Singular perturbations in ergodic control of diffusions

Vivek S. Borkar, Vladimir Gaitsgory

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


Ergodic control of a nondegenerate diffusion with two time-scales is studied in the limiting case as the time-scale separation increases to infinity. It is shown that the limit problem is another ergodic control problem for the slow time-scale component alone, with its dynamics averaged over the (controlled) invariant probability measures for the fast component. These measures in turn can be treated as the "effective control variable."

Original languageEnglish
Pages (from-to)1562-1577
Number of pages16
JournalSIAM Journal on Control and Optimization
Issue number5
Publication statusPublished - 2007
Externally publishedYes


  • Controlled diffusions
  • Ergodic control
  • Invariant probability measures
  • Singular perturbations
  • Two time-scales


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