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one-dimensional process

ESAIM: Probability and Statistics (1)

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A Donsker theorem to simulate one-dimensional processes with measurable coefficients
Pierre Étoré, Antoine Lejay
Journal:

ESAIM: Probability and Statistics / Volume 11 / June 2007

Published online by Cambridge University Press:

17 August 2007, pp. 301-326

Print publication:

June 2007
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In this paper, we prove a Donsker theorem for one-dimensional processes generated by an operator with measurablecoefficients. We construct a random walk on any grid on the state space, using the transition probabilities of the approximated process, and the conditional average times it spends on each cell of the grid. Indeed we can compute thesequantities by solving some suitableelliptic PDE problems.