Limit theorems for stationary random evolutions

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9 Scopus citations


On a separable Banach space, let A(ξ1),A(ξ2),... be a strictly stationary sequence of infinitesimal operators, centered so that EA(ξi) = 0, i = 1,2,.... This paper characterizes the limit of the random evolutions Yn(t)=exp 1 nA(ξ[n2t])⋯exp 1 nA(ξ2)exp 1 nA(ξ1)Yn(0)as the solution to a martingale problem. This work is a direct extension of previous work on i.i.d. random evolutions.

Original languageEnglish (US)
Pages (from-to)189-224
Number of pages36
JournalStochastic Processes and their Applications
Issue number2
StatePublished - Apr 1985


  • central limit theorem
  • law of large numbers
  • martingale problem
  • mixing
  • random evolution
  • stationary process

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics


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