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Asymptotic expansions for the first hitting times of bessel processes

Hamana Yuji, Kaikura Ryo, Shinozaki Kosuke

Opuscula Mathematica

2021

Vol. 41, no. 4

509--537

We study a precise asymptotic behavior of the tail probability of the first hitting time of the Bessel process. We deduce the order of the third term and decide the explicit form of its coefficient.

Exact solution of flow in a composite porous channel

Singh Sanjeeva Kumar, Verma Vineet Kumar

Archive of Mechanical Engineering

2020

LXVII, nr 1

97--110

This article concerns fully developed laminar flow of a viscous incompressible fluid in a long composite cylindrical channel. Channel consist of three regions. Outer and inner regions are of uniform permeability and mid region is a clear region. Brinkman equation is used as a governing equation of motion in the porous region and Stokes equation is used for the clear fluid region. Analytical expressions for velocity profiles, rate of volume flow and shear stress on the boundaries surface are obtained and exhibited graphically. Effect of permeability variation parameter on the flow characteristics has been discussed.

A note on speed of convergence to the quasi-stationary distribution

Polak M., Rolski T.

Demonstratio Mathematica

2012

Vol. 45, nr 2

385-397

In this note we show that for Z being a birth and death process on Z or Brownian motion with drift and (…), the speed of convergence to the quasi-stationary distribution is of order 1/t. The corresponding version that X is the number of calls in M/M/1 queue or the reflected Brownian motion is also considered. The result is obtained by asymptotic expansions of some transition functions. For this we use some new asymptotic expansion of the Bessel function.

A radial version of the Kontorovich-Lebedev transform in the unit ball

Yakubovich S. B., Vieira N.

Opuscula Mathematica

2011

Vol. 31, no. 1

137-146

In this paper we introduce a radial version of the Kontorovich-Lebedev transform in the unit ball. Mapping properties and an inversion formula are proved in Lp.

Layering of the Poisson process in the quadrant

Levikson B., Rolski T., Weiss G.

Probability and Mathematical Statistics

2001

Vol. 21, Fasc. 2

417--440

We consider the increasing sequence of non-intersecting monotone decreasing step processes Y*n(t), n = 1, 2,...(t > 0), whose jump points cover all the points of the homogeneous rate 1 Poisson process on the quadrant R2+. We deriveproperties of these processes, in particular the marginal distributions P(Y*n(t) > x), in terms of a Toeplitz determinant of some modified Bessel functions. Our system provides a new view of the Hammersley interacting particle system discussed by Aldousand Diaconis, and the distributions we derive are related tothe distribution of the length of the longest ascending sequence in a random permutation.