The Hitting Time of an Inverse Gaussian Process

Details The Hitting Time of an Inverse Gaussian Process The Hitting Time of an Inverse Gaussian Process

2011-05-07

arxiv.org/abs/1105.1468v1

Mathematics

Probability

21 pages, 1 figure

Scientific paper

The first hitting time process of an inverse Gaussian process is considered. It is shown that this process is not Levy and has monotonically increasing continuous sample paths. The density functions of one-dimensional distributions of the process are obtained. Its distribution functions are not infinitely divisible and their tail probability decay exponentially. It is also shown that the hitting time process of a stable process with index 0 < $\beta$ < 1 is not infinitely divisible. The density function is shown to solve a fractional partial differential equation. Subordination of the hitting time process to Brownian motion is considered and the underlying PDE of the subordinated process is derived.

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