An Inverse First Passage Problem for Brownian Motion

Zaeem Burq (Department of Mathematics and Statistics, The University of Melbourne)

MSI Computational Mathematics Seminar Series

DATE: 2007-06-25
TIME: 11:00:00 - 12:00:00
LOCATION: John Dedman G35
CONTACT: JavaScript must be enabled to display this email address.

ABSTRACT:
The (direct) first passage problem is a well known problem in the theory of stochastic processes: Given a stochastic process $X_t$ and a function $c(t): [0,\infty) \to \mathbb{R}$, and defining $\tau(c) := \inf \{ t >0 : W_t \geq c(t) \}$, the direct problem is to find the probability distribution of $\tau(c)$.

The {\em inverse} first passage problem is as follows: Given a stochastic process $X_t$ and a probability measure $Q$ on $(0,\infty]$, find a function $c(t): [0,\infty) \to \mathbb{R} $ for which the first passage time $\tau(c)$ has distribution $Q$.

We will discuss a solution to the inverse first passage problem for one-dimensional Brownian motion.
BIO:
http://www.ms.unimelb.edu.au/~zab/