Sharpenings and Generalizations

  • M. I. Freidlin
  • A. D. Wentzell
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 260)


In Chapters 3, 4, 5 and 7 we established limit theorems on large deviations, involving the rough asymptotics of probabilities of the type PXhA. There arises the following question: Is it possible to obtain subtler results for families of random processes (similar to those obtained for sums of independent random variables)—local limit theorems on large deviations and theorems on sharp asymptotics? There is some work in this direction; we give a survey of the results in this section.


Invariant Measure Wiener Process Mathematical Expectation Random Measure Random Perturbation 
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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • M. I. Freidlin
    • 1
  • A. D. Wentzell
    • 2
  1. 1.Department of MathematicsUniversity of MarylandCollege ParkUSA
  2. 2.Department of MathematicsTulane UniversityNew OrleansUSA

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