67 citations · 296 across the 28 of their papers we have counts for
12 papers · 1 filter
Tractability of -approximation and integration in weighted Hermite spaces of finite smoothness
Gunther Leobacher, Friedrich Pillichshammer, Adrian Ebert
In this paper we consider integration and -approximation for functions over $\RR^s$ from weighted Hermite spaces. The first part of the paper is devoted to a comparison of sev…
Numerical methods for SDEs with drift discontinuous on a set of positive reach
Gunther Leobacher, Michaela Szölgyenyi
For time-homogeneous stochastic differential equations (SDEs) it is enough to know that the coefficients are Lipschitz to conclude existence and uniqueness of a solution, as well a…
Convergence of the Euler-Maruyama method for multidimensional SDEs with discontinuous drift and degenerate diffusion coefficient
Gunther Leobacher, Michaela Szölgyenyi
We prove strong convergence of order for arbitrarily small of the Euler-Maruyama method for multidimensional stochastic differential equations (SDEs) with discontinuo…
On the optimal order of integration in Hermite spaces with finite smoothness
Josef Dick, Christian Irrgeher, Gunther Leobacher +1
We study the numerical approximation of integrals over with respect to the standard Gaussian measure for integrands which lie in certain Hermite spaces of functions.…
A Strong Order 1/2 Method for Multidimensional SDEs with Discontinuous Drift
Gunther Leobacher, Michaela Szölgyenyi
In this paper we consider multidimensional stochastic differential equations (SDEs) with discontinuous drift and possibly degenerate diffusion coefficient. We prove an existence an…
Fast orthogonal transforms for multi-level quasi-Monte Carlo integration
Christian Irrgeher, Gunther Leobacher
We combine a generic method for finding fast orthogonal transforms for a given quasi-Monte Carlo integration problem with the multilevel Monte Carlo method. It is shown by example…
Fast Orthogonal transforms for pricing derivatives with quasi-Monte Carlo
Christian Irrgeher, Gunther Leobacher
There are a number of situations where, when computing prices of financial derivatives using quasi-Monte Carlo (QMC), it turns out to be beneficial to apply an orthogonal transform…
Numerical integration in -Korobov and -cosine spaces
Josef Dick, Peter Kritzer, Gunther Leobacher +1
QMC rules are equal weight quadrature rules for approximating integrals over . One line of research studies the integration error of functions in the unit ball of so-calle…
High-dimensional integration on , weighted Hermite spaces, and orthogonal transforms
Christian Irrgeher, Gunther Leobacher
It has been found empirically that quasi-Monte Carlo methods are often efficient for very high-dimensional problems, that is, with dimension in the hundreds or even thousands. The…
A reduced fast component-by-component construction of lattice points for integration in weighted spaces with fast decreasing weights
Josef Dick, Peter Kritzer, Gunther Leobacher +1
Lattice rules and polynomial lattice rules are quadrature rules for approximating integrals over the -dimensional unit cube. Since no explicit constructions of such quadrature m…
Integration in Hermite spaces of analytic functions
Christian Irrgeher, Peter Kritzer, Gunther Leobacher +1
We study integration in a class of Hilbert spaces of analytic functions defined on the . The functions are characterized by the property that their Hermite coefficien…
Efficient calculation of the worst-case error and (fast) component-by-component construction of higher order polynomial lattice rules
Jan Baldeaux, Josef Dick, Gunther Leobacher +2
We show how to obtain a fast component-by-component construction algorithm for higher order polynomial lattice rules. Such rules are useful for multivariate quadrature of high-dime…