On the representation of certain classes of stochastic Itô integrals in the form of pathwise Lebesgue integrals (Q2711131)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On the representation of certain classes of stochastic Itô integrals in the form of pathwise Lebesgue integrals |
scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the representation of certain classes of stochastic Itô integrals in the form of pathwise Lebesgue integrals |
scientific article |
Statements
2 May 2001
0 references
Itô integral
0 references
local time
0 references
Itô formula
0 references
Brownian motion
0 references
0.9216649
0 references
0.90459114
0 references
0.8945621
0 references
0.89233315
0 references
0.89208376
0 references
On the representation of certain classes of stochastic Itô integrals in the form of pathwise Lebesgue integrals (English)
0 references
The main result of this paper is a representation theorem for quite a general stochastic integral along some Brownian path \(B\), in terms of the difference of two Lebesgue integrals along time involving the Brownian local time and the truncated Brownian motion above any level set. This yields, of course, a generalized Itô formula. More interestingly, this entails that the right-continuous inverse of the increasing function \(\int_0^1 {\mathbf Un}_{B_s < u} ds\) is actually an absolutely continuous process a.s.
0 references
