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Local limit theorems for transition densities of Markov chains converging to diffusions
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  • Published: August 2000

Local limit theorems for transition densities of Markov chains converging to diffusions

  • Valentin Konakov1 &
  • Enno Mammen2 

Probability Theory and Related Fields volume 117, pages 551–587 (2000)Cite this article

  • 217 Accesses

  • 29 Citations

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Abstract.

We consider triangular arrays of Markov chains that converge weakly to a diffusion process. Local limit theorems for transition densities are proved.

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Authors and Affiliations

  1. Central Economics Mathematical Institute, Academy of Sciences Nahimovskii av. 47, 117418 Moscow, Russia, , , , , , RU

    Valentin Konakov

  2. Institut für Angewandte Mathematik, Ruprecht-Karls-Universität Heidelberg Im Neuenheimer Feld 294, 69120 Heidelberg, Germany. e-mail: mammen@statlab.uni-heidelberg.de, , , , , , DE

    Enno Mammen

Authors
  1. Valentin Konakov
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  2. Enno Mammen
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Additional information

Received: 28 August 1998 / Revised version: 6 September 1999 / Published online: 14 June 2000

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Konakov, V., Mammen, E. Local limit theorems for transition densities of Markov chains converging to diffusions. Probab Theory Relat Fields 117, 551–587 (2000). https://doi.org/10.1007/PL00008735

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  • Issue Date: August 2000

  • DOI: https://doi.org/10.1007/PL00008735

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  • Key words and phrases: Markov chains – Diffusion processes – Transition densities
  • Mathematics Subject Classification (1991): Primary 62G07; Secondary 60G60
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