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Kouji Yano

Publications and source records attributed to Kouji Yano.

At least 37 records · Page 2Linked to original sources
arXiv2018

Multiray generalization of the arcsine laws for occupation times of infinite ergodic transformations

We prove that the joint distribution of the occupation time ratios for ergodic transformations preserving an infinite measure converges to a multidimensional version of Lamperti's generalized arcsine distribution, in the sense of strong distributional convergence. Our results can be applied to interval maps and Markov chains. We adopt the double Laplace transform method, which has been utilized in the study of occupation times of diffusions on multiray. We also discuss the inverse problem.

math.PR↗
arXiv2018

On optimal periodic dividend strategies for Lévy risk processes

In this paper, we revisit the optimal periodic dividend problem, in which dividend payments can only be made at the jump times of an independent Poisson process. In the dual (spectrally positive Lévy) model, recent results have shown the optimality of a periodic barrier strategy, which pays dividends at Poissonian dividend-decision times, if and only if the surplus is above some level. In this paper, we show the optimality of this strategy for a spectrally negative Lévy process whose dual has a completely monotone Lévy density. The optimal strategies and value functions are concisely written in terms of the scale functions. Numerical results are also provided.

math.OC↗
arXiv2018

Local time penalizations with various clocks for one-dimensional diffusions

We study some limit theorems for the law of a generalized one-dimensional diffusion weighted and normalized by a non-negative function of the local time evaluated at a parametrized family of random times (which we will call a clock). As the clock tends to infinity, we show that the initial process converges towards a new penalized process, which generally depends on the chosen clock. However, unlike with deterministic clocks, no specific assumptions are needed on the resolvent of the diffusion. We then give a path interpretation of these penalized processes via some universal $ σ$-finite measures.

math.PR↗
arXiv2017

On optimal periodic dividend and capital injection strategies for spectrally negative Lévy models

De Finetti's optimal dividend problem has recently been extended to the case dividend payments can only be made at Poisson arrival times. This paper considers the version with bail-outs where the surplus must be nonnegative uniformly in time. For a general spectrally negative Lévy model, we show the optimality of a Parisian-classical reflection strategy that pays the excess above a given barrier at each Poisson arrival times and also reflects from below at zero in the classical sense.

math.PR↗
arXiv2017

Evolutionary model of a population of DNA sequences through the interaction with an environment and its application to speciation analysis

In this study, we construct an evolutionary model of a population of DNA sequences interacting with the surrounding environment on the topological monoid A* of strings on the alphabet A = { a, c, g, t }. A partial differential equation governing the evolution of the DNA population is derived as a kind of diffusion equation on A*. Analyzing the constructed model in a theoretical manner, we present conditions for sympatric speciation, the possibility of which continues to be discussed. It is shown that under other same conditions one condition determines whether sympatric speciation occurs or the DNA population continues to move around randomly in a subset of A*. We next demonstrate that the population maintains a kind of equlibrium state under certain conditions. In this situation, the population remains nearly unchanged and does not differentiate even if it can differentiate into others. Furthermore, we calculate the probability of sympatric speciation and the time expected to elapse before it.

q-bio.PE↗
arXiv2014

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.

math.PR↗
arXiv2014

Functional limit theorems for processes pieced together from excursions

A notion of convergence of excursion measures is introduced. It is proved that convergence of excursion measures implies convergence in law of the processes pieced together from excursions. This result is applied to obtain homogenization theorems of jumping-in extensions for positive self-similar Markov processes, for Walsh diffusions and for the Brownian motion on the Sierpiński gasket.

math.PR↗
arXiv2012

Entropy of random chaotic interval map with noise which causes coarse-graining

A random chaotic interval map with noise which causes coarse-graining induces a finite-state Markov chain. For a map topologically conjugate to a piecewise-linear map with the Lebesgue measure being ergodic, we prove that the Shannon entropy for the induced Markov chain possesses a finite limit as the noise level tends to zero. In most cases, the limit turns out to be strictly greater than the Lyapunov exponent of the original map without noise.

math.PR↗
arXiv2010

Scaling limit of d-inverse of Brownian motion with functional drift

The d-inverse is a generalized notion of inverse of a stochastic process having a certain tendency of increasing expectations. Scaling limit of the d-inverse of Brownian motion with functional drift is studied. Except for degenerate case, the class of possible scaling limits is proved to consist of the d-inverses of Brownian motion without drift, one with explosion in finite time, and one with power drift.

math.PR↗
arXiv2010

Random walk in a finite directed graph subject to a road coloring

A necessary and sufficient condition for a random walk in a finite directed graph subject to a road coloring to be measurable with respect to the driving random road colors is proved to be that the road coloring is synchronizing. For this, the random walk subject to a non-synchronizing road coloring is proved to have uniform law on a certain partition of the state space.

math.PR↗
arXiv2010

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 Tsirelson's 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=\bT $.

math.PR↗