An Implicit Euler Scheme with Non-uniform Time Discretization for Heat Equations with Multiplicative Noise
| dc.creator | Mueller-Gronbach, Thoms | |
| dc.creator | Ritter, Klaus | |
| dc.date | 2006-04-27 | |
| dc.date.accessioned | 2026-07-07T07:11:20Z | |
| dc.date.available | 2026-07-07T07:11:20Z | |
| dc.description | We present an algorithm for solving stochastic heat equations, whose key ingredient is a non-uniform time discretization of the driving Brownian motion $W$. For this algorithm we derive an error bound in terms of its number of evaluations of one-dimensional components of $W$. The rate of convergence depends on the spatial dimension of the heat equation and on the decay of the eigenfunctions of the covariance of $W$. According to known lower bounds, our algorithm is optimal, up to a constant, and this optimality cannot be achieved by uniform time discretizations. | |
| dc.description | 22 pages | |
| dc.identifier | https://arxiv.org/abs/math/0604600 | |
| dc.identifier | http://arxiv.org/abs/math/0604600 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/111719 | |
| dc.subject | Probability | |
| dc.title | An Implicit Euler Scheme with Non-uniform Time Discretization for Heat Equations with Multiplicative Noise | |
| dc.type | text |