Kristian Debrabant

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For linear and fully non-linear diffusion equations of Bellman-Isaacs type, we introduce a class of monotone approximation schemes relying on monotone interpolation. As opposed to classical numerical methods, these schemes converge for degenerate diffusion equations having general non-diagonal dominant coefficient matrices. Such schemes have to have a wide(More)
In recent years, implicit stochastic Runge–Kutta (SRK) methods have been developed both for strong and weak approximations. For these methods, the stage values are only given implicitly. However, in practice these implicit equations are solved by iterative schemes such as simple iteration, modified Newton iteration or full Newton iteration. We employ a(More)
This paper discusses various optimization schemes for partly stochastic and bound optimization, particular with application to solve robotic optimization problems, where robustness of the solutions is crucial. The use case revolves around grasping and manipulation of deformable objects. These kinds of tasks are difficult to tune to a satisfactory extent by(More)
We present and analyze a micro/macro acceleration technique for the Monte Carlo simulation of stochastic differential equations (SDEs) in which there is a separation between the (fast) timescale on which individual trajectories of the SDE need to be simulated and the (slow) timescale on which we want to observe the (macro-scopic) function of interest. The(More)
preprint numerics no. 1/2010 norwegian university of science and technology trondheim, norway Abstract. In this article, we construct a representation formula for stochastic B–series evaluated in a B–series. This formula is used to give for the first time the order conditions of implicit Taylor methods in terms of rooted trees. Finally, as an example we(More)