arXiv subjects
Publications and source records attributed to Kouji Yano.
Quasi-invariance under translation is established for the $ σ$-finite measure unifying Brownian penalisations, which has been introduced by Najnudel, Roynette and Yor. For this purpose, the theory of Wiener integrals for centered Bessel processes, due to Funaki, Hariya and Yor, plays a key role.
A zero-one law of Engelbert--Schmidt type is proven for the norm process of a transient random walk. An invariance principle for random walk local times and a limit version of Jeulin's lemma play key roles.
The characteristic measure of excursions away from a regular point is studied for a class of symmetric Lévy processes without Gaussian part. It is proved that the harmonic transform of the killed process enjoys Feller property. The result is applied to prove extremeness of the excursion measure and to prove several sample path behaviors of the excursion and the $ h $-path processes.
It is proven that the eigenvalue process of Dyson's random matrix process of size two becomes non-Markov if the common coefficient $1/\sqrt{2}$ in the non-diagonal entries is replaced by a different positive number.
Two kinds of conditionings for one-dimensional stable Lévy processes are discussed via $ h $-transforms of excursion measures: One is to stay positive, and the other is to avoid the origin.
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 Itô's excursion theory and a recent result on convergence of excursion measures by Fitzsimmons and the present author.
Several aspects of the laws of first hitting times of points are investigated for one-dimensional symmetric stable Lévy processes. Itô's excursion theory plays a key role in this study.
Limit theorems for the normalized laws with respect to two kinds of weight functionals are studied for any symmetric stable Lévy process of index $ 1 < α\le 2 $. The first kind is a function of the local time at the origin, and the second kind is the exponential of an occupation time integral. Special emphasis is put on the role played by a stable Lévy counterpart of the universal $ σ$-finite measure, found in [9] and [10], which unifies the corresponding limit theorems in the Brownian setup for which $ α=2 $.
Smoothness and asymptotic behaviors are studied for the densities of the law of the occupation time on the positive line for Bessel bridges and the normalized excursion of strictly stable processes. The key role is played by these properties for functions defined by Riemann--Liouville fractional integrals.
In this paper a stochastic equation on compact groups in discrete negative time is studied. This is closely related to Tsirelson's stochastic differential equation, of which any solution is non-strong. How the group action reflects on the set of solutions is investigated. It is applied to generalize Yor's result and give a necessary and sufficient condition for existence of a strong solution and for uniqueness in law.