Weak approximation of SDEs by discrete-time processes
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Date
2008-04-15T11:56:56Z
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Abstract
We consider the martingale problem related to the solution of an SDE on the line. It is
shown that the solution of this martingale problem can be approximated by solutions of the
corresponding time-discrete martingale problems under some conditions. This criterion
is especially expedient for establishing the convergence of population processes to SDEs.
We also show that the criterion yields a weak Euler scheme approximation of SDEs under
fairly weak assumptions on the driving force of the approximating processes.
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Keywords
stochastic differential equation, martingale problem, Doob-Meyer decomposition, discrete-time process, weak convergence, Galton-Watson process, Euler scheme