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.
References
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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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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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DOI: https://doi.org/10.1007/BF01292676
Mathematics Subject Classification (1980)
- 60J25
- 60J35
- 60G44
- 60G05