The Library
Some examples of the spatial evolution of two-parameter processes with non-adapted initial conditions
Tools
Bichard, James (2009) Some examples of the spatial evolution of two-parameter processes with non-adapted initial conditions. PhD thesis, University of Warwick.
PDF
WRAP_THESIS_Bichard_2009.pdf - Requires a PDF viewer. Download (842Kb) |
Official URL: http://webcat.warwick.ac.uk/record=b2334222~S15
Abstract
The central result of this thesis is an enlargement of filtrations result for the filtration (Fx; x ≥ 0), where
Fx = σ{Bys : y ≤ x, s ∈ [0,∞)} and (Bxt; x ∈ R, t ∈ [0,∞)) is a Brownian sheet on a complete probability space. Although this is a fairly straightforward extension of a result presented in [Yor97] for Brownian filtrations, it is of use to us in a couple of applications. The first is a discussion of ‘bridged’ Brownian sheets, in which we try to describe the law of a Brownian sheet which is fixed along some curve in the parameter space. The second application is a study of the spatial evolution of solutions to the stochastic heat equation. We fix a starting point in space, and describe the spatial evolution as driven by an (Fx; x ≥ 0)-adapted noise. Unfortunately, we find that the initial condition is not in F0. If we add this initial information to (Fx; x ≥ 0), the driving noise is no longer a martingale, but our enlargement result allows us to write a semimartingale decomposition, in some sense. We are in fact able to write a system of stochastic differential equations which describe the spatial evolution of solutions, such that each equation is driven by a martingale with respect to this larger filtration.
Item Type: | Thesis (PhD) | ||||
---|---|---|---|---|---|
Subjects: | Q Science > QA Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Brownian bridges (Mathematics) -- Research, Stochastic differential equations -- Numerical solutions, Martingales (Mathematics) | ||||
Official Date: | June 2009 | ||||
Dates: |
|
||||
Institution: | University of Warwick | ||||
Theses Department: | Mathematics Institute | ||||
Thesis Type: | PhD | ||||
Publication Status: | Unpublished | ||||
Supervisor(s)/Advisor: | Assing, Sigurd, 1965- | ||||
Format of File: | |||||
Extent: | 155 leaves : charts | ||||
Language: | eng |
Request changes or add full text files to a record
Repository staff actions (login required)
View Item |
Downloads
Downloads per month over past year