arXiv subjects

Sebastian Becker

Publications and source records attributed to Sebastian Becker.

26 records · Page 2Linked to original sources

arXiv2016

Strong convergence rates for nonlinearity-truncated Euler-type approximations of stochastic Ginzburg-Landau equations

This article proposes and analyzes explicit and easily implementable temporal numerical approximation schemes for additive noise-driven stochastic partial differential equations (SPDEs) with polynomial nonlinearities such as, e.g., stochastic Ginzburg-Landau equations. We prove essentially sharp strong convergence rates for the considered approximation schemes. Our analysis is carried out for abstract stochastic evolution equations on separable Banach and Hilbert spaces including the above mentioned SPDEs as special cases. We also illustrate our strong convergence rate results by means of a numerical simulation in Matlab.

math.PR↗

arXiv2013

An exponential Wagner-Platen type scheme for SPDEs

The strong numerical approximation of semilinear stochastic partial differential equations (SPDEs) driven by infinite dimensional Wiener processes is investigated. There are a number of results in the literature that show that Euler-type approximation methods converge strongly, under suitable assumptions, to the exact solutions of such SPDEs with strong order 1/2 or at least with strong order 1/2 - epsilon where epsilon > 0 is arbitrarily small. Recent results extend these results and show that Milstein-type approximation methods converge, under suitable assumptions, to the exact solutions of such SPDEs with strong order 1 - epsilon. It has also been shown that splitting-up approximation methods converge, under suitable assumptions, with strong order 1 to the exact solutions of such SPDEs. In this article an exponential Wagner-Platen type numerical approximation method for such SPDEs is proposed and shown to converge, under suitable assumptions, with strong order 3/2 - epsilon to the exact solutions of such SPDEs.

math.NA↗

arXiv2013

Direct numerical integration for multi-loop integrals

We present a method to construct a suitable contour deformation in loop momentum space for multi-loop integrals. This contour deformation can be used to perform the integration for multi-loop integrals numerically. The integration can be performed directly in loop momentum space without the introduction of Feynman or Schwinger parameters. The method can be applied to finite multi-loop integrals and to divergent multi-loop integrals with suitable subtraction terms. The algorithm extends techniques from the one-loop case to the multi-loop case. Examples at two and three loops are discussed explicitly.

hep-ph↗

arXiv2012

Direct contour deformation with arbitrary masses in the loop

We present a method, which constructs a suitable deformation vector in loop momentum space, when the loop integration is done numerically with the help of the subtraction method. The method presented here extends previously discussed techniques from the massless case to the general case of arbitrary masses in the loop.

hep-ph↗

arXiv2012

Efficiency improvements for the numerical computation of NLO corrections

In this paper we discuss techniques, which lead to a significant improvement of the efficiency of the Monte Carlo integration, when one-loop QCD amplitudes are calculated numerically with the help of the subtraction method and contour deformation. The techniques discussed are: holomorphic and non-holomorphic division into sub-channels, optimisation of the integration contour, improvement of the ultraviolet subtraction terms, importance sampling and antithetic variates in loop momentum space, recurrence relations.

hep-ph↗

arXiv2011

NLO results for five, six and seven jets in electron-positron annihilation

We present next-to-leading order corrections in the leading colour approximation for jet rates in electron-positron annihilation up to seven jets. The results for the two-, three-, and four-jet rates agree with known results. The NLO jet rates have been known previously only up to five jets. The results for the six- and seven-jet rate are new. The results are obtained by a new and efficient method based on subtraction and numerical integration.

hep-ph↗

arXiv2010

Numerical NLO QCD calculations

We present an algorithm for the numerical calculation of one-loop QCD amplitudes. The algorithm consists of subtraction terms, approximating the soft, collinear and ultraviolet divergences of one-loop amplitudes and a method to deform the integration contour for the loop integration into the complex space. The algorithm is formulated at the amplitude level and does not rely on Feynman graphs. Therefore all required ingredients can be calculated efficiently using recurrence relations. The algorithm applies to massless partons as well as to massive partons.

hep-ph↗

arXiv2010

A simple formula for the infrared singular part of the integrand of one-loop QCD amplitudes

We show that a well-known simple formula for the explicit infrared poles of one-loop QCD amplitudes has a corresponding simple counterpart in unintegrated form. The unintegrated formula approximates the integrand of one-loop QCD amplitudes in all soft and collinear singular regions. It thus defines a local counter-term for the infrared singularities and can be used as an ingredient for the numerical calculation of one-loop amplitudes.

hep-ph↗