Efficient schemes for the weak approximation of reflected diffusions (Q2724993)

The author considers the problem of numerical solution of the multidimensional reflected stochastic differential equation of the form NEWLINE\[NEWLINE X_t=x+\int_0^t B(X_s) ds +\int_0^t \sigma(X_s) dW_s +\int_0^t \gamma(X_s) dk_s, NEWLINE\]NEWLINE where \(W\) is a Brownian motion in \(R^d\), \(D\) is a smooth bounded domain of \(\mathbb{R}^d\), \(k\) is a process increasing on \(\partial D\) only, and \(\gamma\) is a unit inward vector. Two new discretization schemes are presented. Their weak convergence rate is (at least) of order \(1/2\) and, in the case where \(\gamma\) is the co-normal vector, of order one. A numerical procedure for the computation of \(E\int_0^\infty f(X_t) dt\) is also presented and discussed.