A convenient Gauss᎐Laguerre quadrature formula is presented for integrands which depend on the radial coordinates r and r of two bodies as well as on 1 2 their relative distance r . This formula generalizes the analytic method by Calais and 12 w Ž .x Lowdin J. Mol. Spectrosc. 8, 203 1962 to cases w
Itô Formula for Free Stochastic Integrals
✍ Scribed by Michael Anshelevich
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 184 KB
- Volume
- 188
- Category
- Article
- ISSN
- 0022-1236
No coin nor oath required. For personal study only.
✦ Synopsis
The objects under investigation are the stochastic integrals with respect to free Lévy processes. We define such integrals for square-integrable integrands, as well as for a certain general class of bounded integrands. Using the product form of the Itô formula, we prove the full functional Itô formula in this context.
📜 SIMILAR VOLUMES
Let X = (Xt, Ft) be a continuous local martingale with quadratic variation X and X0 = 0. Define iterated stochastic integrals In(X) = (In(t, X), Ft) , n ≥ 0, inductively by In(t, X
In particular, Ž . G 2 s q y 4 Ž  2 q 2 ␥q␥ 2 .
Recently P. Lax has produced a novel approach to the proof of the change of variable formula for multiple integrals. In Section 1 we give a variant of Lax's proof, using the language of differential forms. In Sections 2 and 3 we discuss extensions involving more singular maps and integrands. 2002