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


Authors: H. Brezis, W. Rosenkrantz and B. Singer
Journal: Bull. Amer. Math. Soc. 77 (1971), 980-982
MSC (1970): Primary 60F10; Secondary 60J10, 60J25
DOI: https://doi.org/10.1090/S0002-9904-1971-12825-2
MathSciNet review: 0288855
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  • 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. MR 199891
  • 3. J. Lamperti, A new class of probability limit theorems, J. Math. Mech. 11 (1962), 749-772. MR 26 #5629. MR 148120
  • 4. M. Pinsky, An elementary derivation of Khintchine's estimate for large deviations, Proc. Amer. Math. Soc. 22 (1969), 288-290. MR 39 #6390. MR 245078
  • 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. MR 200988
  • 6. H. F. Trotter, Approximation of semi-groups of operators, Pacific J. Math. 8 (1958), 887-919. MR 21 #2190. MR 103420

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DOI: https://doi.org/10.1090/S0002-9904-1971-12825-2

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