𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Worst case complexity of multivariate Feynman–Kac path integration

✍ Scribed by Marek Kwas; Youming Li

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
184 KB
Volume
19
Category
Article
ISSN
0885-064X

No coin nor oath required. For personal study only.

✦ Synopsis

We study the multivariate Feynman-Kac path integration problem. This problem was studied in Plaskota et al. (J. Comp. Phys. 164 (2000) 335) for the univariate case. We describe an algorithm based on uniform approximation, instead of the L 2 -approximation used in Plaskota et al. (2000). Similarly to Plaskota et al. (2000), our algorithm requires extensive precomputing. We also present bounds on the complexity of our problem. The lower bound is provided by the complexity of a certain integration problem, and the upper bound by the complexity of the uniform approximation problem. The algorithm presented in this paper is almost optimal for the classes of functions for which uniform approximation and integration have roughly the same complexities.

📜 SIMILAR VOLUMES

A New Algorithm and Worst Case Complexit
A New Algorithm and Worst Case Complexity for Feynman–Kac Path Integration
✍ Leszek Plaskota; Grzegorz W. Wasilkowski; Henryk Woźniakowski 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 121 KB

We study algorithms for approximation of Feynman-Kac path integrals in the worst case setting. The algorithms use a finite number of samples of the initial condition and potential functions. We present a new algorithm and an explicit bound on its cost to compute an ε-approximation to the Feynman-Kac