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Weak convergence to a Markov process: The martingale approach
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  • Published: September 1993

Weak convergence to a Markov process: The martingale approach

  • Abhay G. Bhatt1 &
  • Rajeeva L. Karandikar1 

Probability Theory and Related Fields volume 96, pages 335–351 (1993)Cite this article

  • 193 Accesses

  • 6 Citations

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Summary

In this article, we obtain some sufficient conditions for weak convergence of a sequence of processes {X n } toX, whenX arises as a solution to a well posed martingale problem. These conditions are tailored for application to the case when the state space for the processesX n ,X is infinite dimensional. The usefulness of these conditions is illustrated by deriving Donsker's invariance principle for Hilbert space valued random variables. Also, continuous dependence of Hilbert space valued diffusions on diffusion and drift coefficients is proved.

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References

  1. Bhatt, A.G., Karandikar, R.L.: Invariant measures and evolution equations for Markov processes characterised via martingale problems. Ann. Probab. (to appear)

  2. Ethier, S.N., Kurtz, T.G.: Markov processes: Characterization and convergence. New York: Wiley 1986

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  5. Stroock, D.W., Varadhan, S.R.S.: Multidimensional diffusion processes. Berlin Heidelberg New York: Springer 1979

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Author information

Authors and Affiliations

  1. Indian Statistical Institute, 7, S.J.S. Sansanwal Marg, 110016, New Delhi, India

    Abhay G. Bhatt & Rajeeva L. Karandikar

Authors
  1. Abhay G. Bhatt
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  2. Rajeeva L. Karandikar
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Additional information

Research supported by National Board for Higher Mathematics, Bombay, India

Part of the work was done at University of California, Santa Barbara, USA

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Cite this article

Bhatt, A.G., Karandikar, R.L. Weak convergence to a Markov process: The martingale approach. Probab. Th. Rel. Fields 96, 335–351 (1993). https://doi.org/10.1007/BF01292676

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  • Received: 03 December 1991

  • Revised: 03 November 1992

  • Issue Date: September 1993

  • DOI: https://doi.org/10.1007/BF01292676

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Mathematics Subject Classification (1980)

  • 60J25
  • 60J35
  • 60G44
  • 60G05
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