Kouji Yano

On the Laws of First Hitting Times of Points for One-Dimensional Symmetric Stable Lévy Processes

Several aspects of the laws of first hitting times of points are investigated for one-dimensional symmetric stable Levy processes. Ito’s excursion theory plays a key role in this study.

Around Tsirelson's equation, or: The evolution process may not explain everything

We present a synthesis of a number of developments which have been made around the celebrated Tsirelsons equation (1975), conveniently modified in the framework of a Markov chain taking values in a compact group G, and indexed by negative time. To illustrate, we discuss in detail the case of the one-dimensional torus G = T.

Convergence of excursion point processes and its applications to functional limit theorems of Markov processes on a half-line

Invariance principles are obtained for a Markov process on a half-line with continuous paths on the interior. The domains of attraction of the two different types of self-similar processes are investigated. Our approach is to establish convergence of excursion point processes, which is based on It\^{o}s excursion theory and a recent result on convergence of excursion measures by Fitzsimmons and the present author.

On h-Transforms of One-Dimensional Diffusions Stopped upon Hitting Zero

For a one-dimensional diffusion on an interval for which 0 is the regular-reflecting left boundary, three kinds of conditionings to avoid zero are studied. The limit processes are h-transforms of the process stopped upon hitting zero, where h’s are the ground state, the scale function, and the renormalized zero-resolvent. Several properties of the h-transforms are investigated.

Extensions of diffusion processes on intervals and Feller's boundary conditions

For a minimal diffusion process on

On a Zero-One Law for the Norm Process of Transient Random Walk

(a,b)

Penalising symmetric stable Levy paths

, any possible extension of it to a standard process on

Excursions Away from a Regular Point for One-Dimensional Symmetric Lévy Processes without Gaussian Part

[a,b]

Stochastic equations on compact groups in discrete negative time

is characterized by the characteristic measures of excursions away from the boundary points

A density formula for the law of time spent on the positive side of one-dimensional diffusion processes

a