Kristian Debrabant

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For linear and fully non-linear diffusion equations of BellmanIsaacs 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 nondiagonal dominant coefficient matrices. Such schemes have to have a wide(More)
In the present paper, a class of stochastic Runge–Kutta methods containing the second order stochastic Runge–Kutta scheme due to E. Platen for the weak approximation of Itô stochastic differential equation systems with a multi-dimensional Wiener process is considered. Order 1 and order 2 conditions for the coefficients of explicit stochastic Runge–Kutta(More)
The author’s presentation of multilevel Monte Carlo path simulation at the MCQMC 2006 conference stimulated a lot of research into multilevel Monte Carlo methods. This paper reviews the progress since then, emphasising the simplicity, flexibility and generality of the multilevel Monte Carlo approach. It also offers a few original ideas and suggests areas(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)
The multi-level Monte Carlo method proposed by Giles (2008) approximates the expectation of some functionals applied to a stochastic process with optimal order of convergence for the mean-square error. In this paper a modified multi-level Monte Carlo estimator is proposed with significantly reduced computational costs. As the main result, it is proved that(More)
preprint numerics no. 4/2007 norwegian university of science and technology trondheim, norway Abstract. In the last years, implicit SRK methods have been developed both for strong and weak approximation. For these methods, the stage values are only given implicitly. However, in practice these implicit equations are solved by iterative schemes like simple(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)
s at ICCAM 2012 Multi-Step Skipping Methods with Modified Search Direction for Unconstrained Optimization Nudrat Aamir Department of Mathematical Sciences, University of Essex Wivenhoe Park, Colchester, Essex, CO4 3SQ United Kingdom naamir@essex.ac.uk Joint work with: John A. Ford When dealing with unconstrained non-linear optimization problems using(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)