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Kosuke Yamato

Publications and source records attributed to Kosuke Yamato.

12 recordsLinked to original sources
arXiv2026

State-dependent inverse-subordinator time changes of regenerative processes: Excursion structure and multiscale occupation-time limits

We study regenerative processes time-changed by state-dependent inverse subordinators. The construction assigns possibly different independent subordinators to measurable classes of excursions and builds a random clock from the corresponding occupation times. Although the resulting process is generally not regenerative, we prove that its transformed excursion point process is again Poisson, using an excursion-wise marking-and-mapping procedure. We apply this to study occupation-time asymptotics. Under regular variation assumptions on the transformed excursion lifetime tails, we prove a multiscale joint occupation-time limit theorem, including generalized arcsine laws and Darling--Kac type limits.

math.PR↗
arXiv2024

Entrance boundary for standard processes with no negative jumps and its application to exponential convergence to the Yaglom limit

We study standard processes with no negative jumps under the entrance boundary condition. Similarly to one-dimensional diffusions, we show that the process can be made into a Feller process by attaching the boundary point to the state space. We investigate the spectrum of the infinitesimal generator in detail via the scale function, characterizing it as the zeros of an entire function. As an application, we prove that under the strong Feller property, the convergence to the Yaglom limit of the process killed on hitting the boundary is exponentially fast.

math.PR↗
arXiv2024

Conditioning to avoid zero via a class of concave functions for one-dimensional diffusions

For one-dimensional diffusions on the half-line, we study a specific type of conditioning to avoid zero. We introduce supermartingales defined via concave functions with respect to the scale function. A conditioning is formulated through the exit times of the supermartingale, and its existence is shown. We also investigate the absolute continuity relations of the limit laws at time infinity.

math.PR↗
arXiv2023

Analytic property of generalized scale functions for standard processes with no negative jumps and its application to quasi-stationary distributions

For a generalized scale function of standard processes, we characterize it as a unique solution to a Volterra type integral equation. This allows us to extend it to an entire function and to derive a useful identity that we call the resolvent identity. We apply this result to study the existence of a quasi-stationary distribution for the processes killed at hitting boundaries. A new classification of the boundary, which is a natural extension of Feller's for one-dimensional diffusions, is introduced and plays a central role to characterize the existence.

math.PR↗
arXiv2023

Existence of quasi-stationary distributions for downward skip-free Markov chains

For downward skip-free continuous-time Markov chains on non-negative integers stopped at zero, existence of a quasi-stationary distribution is studied. The scale function for these processes is introduced and the boundary is classified by a certain integrability condition on the scale function, which gives an extension of Feller's classification of the boundary for birth-and-death processes. The existence and the set of quasi-stationary distributions are characterized by the scale function and the new classification of the boundary.

math.PR↗
arXiv2022

Existence of quasi-stationary distributions for spectrally positive Lévy processes on the half-line

For spectrally positive Lévy processes killed on exiting the half-line, existence of a quasi-stationary distribution is characterized by the exponential integrability of the exit time, the Laplace exponent and the non-negativity of the scale functions. It is proven that if there is a quasi-stationary distribution, there are necessarily infinitely many ones and the set of quasi-stationary distributions is characterized. A sufficient condition for the minimal quasi-stationary distribution to be the Yaglom limit is given.

math.PR↗
arXiv2022

Reproduction of initial distributions from the first hitting time distribution for birth-and-death processes

For birth-and-death processes, we show that every initial distribution is reproduced from the first hitting time distribution. The reproduction is done by applying to the distribution function a differential operator defined through the eigenfunction of the generator. Using the spectral theory for generalized second-order differential operators, we study asymmetric random walks.

math.PR↗
arXiv2020

A unifying approach to non-minimal quasi-stationary distributions for one-dimensional diffusions

Convergence to non-minimal quasi-stationary distributions for one-dimensional diffusions is studied. We give a method of reducing the convergence to the tail behavior of the lifetime via a property which we call the first hitting uniqueness. We apply the results to Kummer diffusions with negative drifts and give a class of initial distributions converging to each non-minimal quasi-stationary distribution.

math.PR↗
arXiv2020

Aging arcsine law in Brownian motion and its generalization

Classical arcsine law states that fraction of occupation time on the positive or the negative side in Brownian motion does not converge to a constant but converges in distribution to the arcsine distribution. Here, we consider how a preparation of the system affects the arcsine law, i.e., aging of the arcsine law. We derive aging distributional theorem for occupation time statistics in Brownian motion, where the ratio of time when measurements start to the measurement time plays an important role in determining the shape of the distribution. Furthermore, we show that this result can be generalized as aging distributional limit theorem in renewal processes.

math.PR↗