Bulletin of the American Mathematical Society

An extension of Khintchine's estimate for large deviations to a class of Markov chains converging to a singular diffusion

H. Brezis, W. Rosenkrantz, and B. Singer

Full-text: Open access

Article information

Source
Bull. Amer. Math. Soc., Volume 77, Number 6 (1971), 980-982.

Dates
First available in Project Euclid: 4 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.bams/1183533171

Mathematical Reviews number (MathSciNet)
MR0288855

Zentralblatt MATH identifier
0232.60017

Subjects
Primary: 60F10: Large deviations
Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60J25: Continuous-time Markov processes on general state spaces

Citation

Brezis, H.; Rosenkrantz, W.; Singer, B. An extension of Khintchine's estimate for large deviations to a class of Markov chains converging to a singular diffusion. Bull. Amer. Math. Soc. 77 (1971), no. 6, 980--982. https://projecteuclid.org/euclid.bams/1183533171


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References

  • 1. H. Brezis, W. Rosenkrantz and B. Singer, On a degenerate elliptic-parabolic equation occurring in the theory of probability, Comm. Pure Appl. Math. 24 (1971), 395-416.
  • 2. K. Itô and H. McKean, Diffusion processes and their sample paths, Die Grundlehren der math. Wissenschaften, Band 125, Academic Press, New York; Springer-Verlag, Berlin, 1965. MR 33 #8031.
  • 3. J. Lamperti, A new class of probability limit theorems, J. Math. Mech. 11 (1962), 749-772. MR 26 #5629.
  • 4. M. Pinsky, An elementary derivation of Khintchine's estimate for large deviations, Proc. Amer. Math. Soc. 22 (1969), 288-290. MR 39 #6390.
  • 5. W. A. Rosenkrantz, A local limit theorem for a certain class of random walks, Ann. Math. Statist. 37 (1966), 855-859. MR 34 #873.
  • 6. H. F. Trotter, Approximation of semi-groups of operators, Pacific J. Math. 8 (1958), 887-919. MR 21 #2190.