31,787 research outputs found
Change of measure in the lookdown particle system
We perform various changes of measure in the lookdown particle system of
Donnelly and Kurtz. The first example is a product type h-transform related to
conditioning a Generalized Fleming Viot process without mutation on coexistence
of some genetic types in remote time. We give a pathwise construction of this
h-transform by just "forgetting" some reproduction events in the lookdown
particle system. We also provide an intertwining relationship for the Wright
Fisher diffusion and explicit the associated pathwise decomposition. The second
example, called the linear or additive h-transform, concerns a wider class of
measure valued processes with spatial motion. Applications include: -a simple
description of the additive h-transform of the Generalized Fleming Viot
process, which confirms a suggestion of Overbeck for the usual Fleming Viot
process -an immortal particle representation for the additive h-transform of
the Dawson Watanabe process.Comment: 24 page
A Constructive Method for Approximate Solution to Scalar Wiener-Hopf Equations
This paper presents a novel method of approximating the scalar Wiener-Hopf
equation; and therefore constructing an approximate solution. The advantages of
this method over the existing methods are reliability and explicit error
bounds. Additionally the degrees of the polynomials in the rational
approximation are considerably smaller than in other approaches.
The need for a numerical solution is motivated by difficulties in computation
of the exact solution. The approximation developed in this paper is with a view
of generalisation to matrix Wiener-Hopf for which the exact solution, in
general, is not known.
The first part of the paper develops error bounds in Lp for 1<p<\infty. These
indicate how accurately the solution is approximated in terms of how accurate
the equation is approximated.
The second part of the paper describes the approach of approximately solving
the Wiener-Hopf equation that employs the Rational Caratheodory-Fejer
Approximation. The method is adapted by constructing a mapping of the real line
to the unit interval. Numerical examples to demonstrate the use of the proposed
technique are included (performed on Chebfun), yielding error as small as
10^{-12} on the whole real line.Comment: AMS-LaTeX, 19 pages, 10 figures in EPS fil
- …