Event Type:

Probability Seminar

Date/Time:

Tuesday, June 3, 2014 - 09:00

Location:

Kidder 350

Abstract:

The connection between Bessel process and the integral of geometric Brownian motion (IGBM) has been well-established. The key to this approach is the Lamperti relation. However, a common difficulty is that arguments constructed for Bessel processes with positive index generally do not carry over to the ones with negative index. In this talk, we use a differential equation approach to study the hitting times of IGBM. We discuss the paper by Metzler (2013) in which the Laplace transform of hitting times is expressed in terms of the gamma and confluent hypergeometric functions. The transform satisfies Kummer's equation which is obtained using Ito's formula and standard results on hitting times of diffusion processes.