Second order Runge–Kutta methods for Itô stochastic differential equations
A Rößler - SIAM Journal on Numerical Analysis, 2009 - SIAM
A new class of stochastic Runge–Kutta methods for the weak approximation of the solution
of Itô stochastic differential equation systems with a multidimensional Wiener process is …
of Itô stochastic differential equation systems with a multidimensional Wiener process is …
Optimization of mesh hierarchies in multilevel Monte Carlo samplers
We perform a general optimization of the parameters in the multilevel Monte Carlo (MLMC)
discretization hierarchy based on uniform discretization methods with general approximation …
discretization hierarchy based on uniform discretization methods with general approximation …
Goal-oriented adaptive finite element multilevel Monte Carlo with convergence rates
In this study, we present an adaptive multilevel Monte Carlo (AMLMC) algorithm for
approximating deterministic, real-valued, bounded linear functionals that depend on the …
approximating deterministic, real-valued, bounded linear functionals that depend on the …
Adaptive multilevel monte carlo simulation
This work generalizes a multilevel forward Euler Monte Carlo method introduced in Michael
B. Giles.(Michael Giles. Oper. Res. 56 (3): 607–617, 2008.) for the approximation of …
B. Giles.(Michael Giles. Oper. Res. 56 (3): 607–617, 2008.) for the approximation of …
A posteriori error analysis and adaptivity for high-dimensional elliptic and parabolic boundary value problems
F Merle, A Prohl - Numerische Mathematik, 2023 - Springer
We derive a posteriori error estimates for the (stopped) weak Euler method to discretize SDE
systems which emerge from the probabilistic reformulation of elliptic and parabolic (initial) …
systems which emerge from the probabilistic reformulation of elliptic and parabolic (initial) …
Implementation and analysis of an adaptive multilevel Monte Carlo algorithm
We present an adaptive multilevel Monte Carlo (MLMC) method for weak approximations of
solutions to Itô stochastic differential equations (SDE). The work [Oper. Res. 56 (2008), 607 …
solutions to Itô stochastic differential equations (SDE). The work [Oper. Res. 56 (2008), 607 …
Lower error bounds for strong approximation of scalar SDEs with non-Lipschitzian coefficients
We study pathwise approximation of scalar stochastic differential equations at a single time
point or globally in time by means of methods that are based on finitely many observations of …
point or globally in time by means of methods that are based on finitely many observations of …
Basic tracking using nonlinear continuous-time dynamic models [tutorial]
D Crouse - IEEE Aerospace and Electronic Systems Magazine, 2015 - ieeexplore.ieee.org
Physicists generally express the motion of objects in continuous time using differential
equations, whereas the majority of target tracking algorithms use discrete-time models. This …
equations, whereas the majority of target tracking algorithms use discrete-time models. This …
[HTML][HTML] On non-polynomial lower error bounds for adaptive strong approximation of SDEs
L Yaroslavtseva - Journal of Complexity, 2017 - Elsevier
Recently, it has been shown in Hairer et al.(2015) that there exists a system of stochastic
differential equations (SDE) on the time interval [0, T] with infinitely often differentiable and …
differential equations (SDE) on the time interval [0, T] with infinitely often differentiable and …
Second order Runge–Kutta methods for Stratonovich stochastic differential equations
A Rößler - BIT Numerical Mathematics, 2007 - Springer
The weak approximation of the solution of a system of Stratonovich stochastic differential
equations with am–dimensional Wiener process is studied. Therefore, a new class of …
equations with am–dimensional Wiener process is studied. Therefore, a new class of …