On random walk simulation of one-dimensional diffusion processes with discontinuous coefficients.
Exact simulation for solutions of one-dimensional Stochastic Differential Equations with discontinuous drift
In this note we propose an exact simulation algorithm for the solution of (1)
d X t = d W t + b̅ ( X t ) d t, X 0 = x, where
A Donsker theorem to simulate one-dimensional processes with measurable coefficients
In this paper, we prove a Donsker theorem for one-dimensional processes generated by an operator with measurable coefficients. 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 these quantities by solving some suitable elliptic PDE problems.
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