Convergence of the stochastic Euler scheme for locally Lipschitz coefficients. (arXiv:0912.2609v1 [math.NA])

Stochastic differential equations are often simulated with the Monte Carlo
Euler method. Convergence of this method is well understood in the case of
globally Lipschitz continuous coefficients of the stochastic differential
equation. The important case of superlinearly growing coefficients, however,
remained an open question for a long time now. The main difficulty is that
numerically weak convergence fails to hold in many cases of superlinearly
growing coefficients. In this paper we overcome this difficulty and establish
convergence of the Monte Carlo Euler method for a large class of
one-dimensional stochastic differential equations whose drift functions have at
most polynomial growth.

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Original source : http://arxiv.org/abs/0912.2609...