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
b̅is a smooth real function except at point 0 where
b̅(0 + ) ≠ b̅(0 −) . The main idea is to sample an exact skeleton of Xusing an algorithm deduced from the convergence of the solutions of the skew perturbed...
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.
Download Results (CSV)