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In an analogy from symmetric ordinary differential equation numerical integrators, we derive a three-stage, weak 2nd-order procedure for Monte-Carlo simulations of Itô stochastic differential equations. Our composite procedure splits each time step into three parts: an $$h/2$$ h / 2 -stage of trapezoidal rule, an $$h$$ h -stage martingale, followed by another $$h/2$$ h / 2...
In this paper we study numerical solutions of the Dirichlet problem in high dimensions using the Feynman–Kac representation. What is involved are Monte-Carlo simulations of stochastic differential equations and algorithms to accurately determine exit times and process values at the boundary. It is assumed that the radius of curvature of the boundary is much larger than the square root of the step...
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