Design of high-order short-time approximations as a problem of matching the covariance of a Brownian motion
| dc.creator | Predescu, Cristian | |
| dc.date | 2005-08-08 | |
| dc.date | 2005-08-28 | |
| dc.date.accessioned | 2026-07-07T04:32:15Z | |
| dc.date.available | 2026-07-07T04:32:15Z | |
| dc.description | One of the outstanding problems in the numerical discretization of the Feynman-Kac formula calls for the design of arbitrary-order short-time approximations that are constructed in a stable way, yet only require knowledge of the potential function. In essence, the problem asks for the development of a functional analogue to the Gauss quadrature technique for one-dimensional functions. In PRE 69, 056701 (2004), it has been argued that the problem of designing an approximation of order νis equivalent to the problem of constructing discrete-time Gaussian processes that are supported on finite-dimensional probability spaces and match certain generalized moments of the Brownian motion. Since Gaussian processes are uniquely determined by their covariance matrix, it is tempting to reformulate the moment-matching problem in terms of the covariance matrix alone. Here, we show how this can be accomplished. | |
| dc.description | 15 pages; some typos removed; some slight change of notation here and there | |
| dc.identifier | https://arxiv.org/abs/math-ph/0508017 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0508017 | |
| dc.identifier | in Proceedings of the 8-th International Conference on Path Integrals: From Quantum Information to Cosmology (Prague, Czech Republic, June 6-10, 2005) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/58121 | |
| dc.subject | Mathematical Physics | |
| dc.title | Design of high-order short-time approximations as a problem of matching the covariance of a Brownian motion | |
| dc.type | text |