104 citations · 382 across the 27 of their papers we have counts for
27 papers
Derivation of optimal stochastic Runge-Kutta methods with exotic and decorated Butcher series for the weak integration of stochastic dynamics
Adrien Busnot Laurent, Kristian Debrabant, Anne Kværnø
The design of numerical integrators for solving stochastic dynamics with high weak order relies on tedious calculations and is subject to a high number of order conditions. The ori…
B-series for SDEs with application to exponential integrators for non-autonomous semi-linear problems
Alemayehu Adugna Arara, Kristian Debrabant, Anne Kværnø
In this paper a set of previous general results for the development of B--series for a broad class of stochastic differential equations has been collected. The applicability of the…
A Comparison of Different Approaches to Dynamic Origin-Destination Matrix Estimation in Urban Traffic
Nicklas Sindlev Andersen, Marco Chiarandini, Kristian Debrabant
Given the counters of vehicles that traverse the roads of a traffic network, we reconstruct the travel demand that generated them expressed in terms of the number of origin-destina…
High order numerical integrators for single integrand Stratonovich SDEs
David Cohen, Kristian Debrabant, Andreas Rößler
We show that applying any deterministic B-series method of order with a random step size to single integrand SDEs gives a numerical method converging in the mean-square and w…
Lawson schemes for highly oscillatory stochastic differential equations and conservation of invariants
Kristian Debrabant, Anne Kværnø, Nicky Cordua Mattsson
In this paper, we consider a class of stochastic midpoint and trapezoidal Lawson schemes for the numerical discretization of highly oscillatory stochastic differential equations. T…
Weak Antithetic MLMC Estimation of SDEs with the Milstein scheme for Low-Dimensional Wiener Processes
Kristian Debrabant, Azadeh Ghasemifard, Nicky C. Mattsson
In this paper, we implement a weak Milstein Scheme to simulate low-dimensional stochastic differential equations (SDEs). We prove that combining the antithetic multilevel Monte-Car…
Study of micro-macro acceleration schemes for linear slow-fast stochastic differential equations with additive noise
Kristian Debrabant, Giovanni Samaey, Przemysław Zieliński
Computational multi-scale methods capitalize on a large time-scale separation to efficiently simulate slow dynamics over long time intervals. For stochastic systems, one often aims…
Backward Differentiation Formula finite difference schemes for diffusion equations with an obstacle term
Olivier Bokanowski, Kristian Debrabant
Finite difference schemes, using Backward Differentiation Formula (BDF), are studied for the approximation of one-dimensional diffusion equations with an obstacle term, of the form…
Stochastic B-series and order conditions for exponential integrators
Alemayehu Adugna Arara, Kristian Debrabant, Anne Kværnø
We discuss stochastic differential equations with a stiff linear part and their approximation by stochastic exponential integrators. Representing the exact and approximate solution…
General order conditions for stochastic partitioned Runge-Kutta methods
Sverre Anmarkrud, Kristian Debrabant, Anne Kværnø
In this paper stochastic partitioned Runge-Kutta (SPRK) methods are considered. A general order theory for SPRK methods based on stochastic B-series and multicolored, multishaped r…
Cheap arbitrary high order methods for single integrand SDEs
Kristian Debrabant, Anne Kværnø
For a particular class of Stratonovich SDE problems, here denoted as single integrand SDEs, we prove that by applying a deterministic Runge-Kutta method of order we obtain me…
A micro-macro acceleration method for the Monte Carlo simulation of stochastic differential equations
Kristian Debrabant, Giovanni Samaey, Przemysław Zieliński
We present and analyse a micro-macro acceleration method for the Monte Carlo simulation of stochastic differential equations with separation between the (fast) time-scale of indivi…
Semi-Lagrangian schemes for linear and fully non-linear Hamilton-Jacobi-Bellman equations
Kristian Debrabant, Espen R. Jakobsen
We consider the numerical solution of Hamilton-Jacobi-Bellman equations arising in stochastic control theory. We introduce a class of monotone approximation schemes relying on mono…
Families of efficient second order Runge-Kutta methods for the weak approximation of Itô stochastic differential equations
Kristian Debrabant, Andreas Rößler
Recently, a new class of second order Runge-Kutta methods for Itô stochastic differential equations with a multidimensional Wiener process was introduced by Rößler. In contrast to…
Classification of Stochastic Runge-Kutta Methods for the Weak Approximation of Stochastic Differential Equations
Kristian Debrabant, Andreas Rößler
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 stochas…
Continuous Weak Approximation for Stochastic Differential Equations
Kristian Debrabant, Andreas Rößler
A convergence theorem for the continuous weak approximation of the solution of stochastic differential equations by general one step methods is proved, which is an extension of a t…
Convergence of Runge-Kutta Methods Applied to Linear Partial Differential-Algebraic Equations
Kristian Debrabant, Karl Strehmel
We apply Runge-Kutta methods to linear partial differential-algebraic equations of the form , where and th…
On quasi-linear PDAEs with convection: applications, indices, numerical solution
Wenfried Lucht, Kristian Debrabant
For a class of partial differential algebraic equations (PDAEs) of quasi-linear type which include nonlinear terms of convection type a possibility to determine a time and spatial…
Diagonally drift-implicit Runge-Kutta methods of weak order one and two for Itô SDEs and stability analysis
Kristian Debrabant, Andreas Rößler
The class of stochastic Runge-Kutta methods for stochastic differential equations due to Rößler is considered. Coefficient families of diagonally drift-implicit stochastic Runge-Ku…
Analysis of multilevel Monte Carlo path simulation using the Milstein discretisation
Michael B. Giles, Kristian Debrabant, Andreas Rößler
The multilevel Monte Carlo path simulation method introduced by Giles ({\it Operations Research}, 56(3):607-617, 2008) exploits strong convergence properties to improve the computa…
On the Acceleration of the Multi-Level Monte Carlo Method
Kristian Debrabant, Andreas Rößler
The multi-level Monte Carlo method proposed by M. Giles (2008) approximates the expectation of some functionals applied to a stochastic process with optimal order of convergence fo…
A micro/macro algorithm to accelerate Monte Carlo simulation of stochastic differential equations
Kristian Debrabant, Giovanni Samaey
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 (f…
Stochastic B-series analysis of iterated Taylor methods
Kristian Debrabant, Anne Kværnø
For stochastic implicit Taylor methods that use an iterative scheme to compute their numerical solution, stochastic B--series and corresponding growth functions are constructed. Fr…
Composition of stochastic B-series with applications to implicit Taylor methods
Kristian Debrabant, Anne Kværnø
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 impl…