scholarly journals Zonal polynomials and a multidimensional quantum Bessel process

2015 ◽  
Vol 125 (9) ◽  
pp. 3430-3457 ◽  
Author(s):  
Wojciech Matysiak ◽  
Marcin Świeca
Keyword(s):  
Bessel Process ◽  
Zonal Polynomials

A boundary crossing probability for the Bessel process

1998 ◽  
Vol 30 (3) ◽  
pp. 807-830 ◽  
Author(s):  
Rebecca A. Betensky
Keyword(s):  
Nonparametric Test ◽  
Bessel Process ◽  
Boundary Crossing ◽  
Test Statistic ◽  
Boundary Crossing Probability ◽  
Significance Level ◽  
Straight Line ◽  
Crossing Probability ◽  
Nonparametric Test Statistic ◽  
First Crossing Time

Analytic approximations are derived for the distribution of the first crossing time of a straight-line boundary by a d-dimensional Bessel process and its discrete time analogue. The main ingredient for the approximations is the conditional probability that the process crossed the boundary before time m, given its location beneath the boundary at time m. The boundary crossing probability is of interest as the significance level and power of a sequential test comparing d+1 treatments using an O'Brien-Fleming (1979) stopping boundary (see Betensky 1996). Also, it is shown by DeLong (1980) to be the limiting distribution of a nonparametric test statistic for multiple regression. The approximations are compared with exact values from the literature and with values from a Monte Carlo simulation.

scholarly journals Calculation and Properties of Zonal Polynomials

2020 ◽  
Vol 14 (3) ◽  
pp. 623-640
Author(s):  
Lin Jiu ◽  
Christoph Koutschan
Keyword(s):  
Zonal Polynomials

scholarly journals Fractionally integrated Bessel process

2021 ◽  
Vol 477 (2250) ◽  
pp. 20200934
Author(s):  
Georgiy Shevchenko ◽  
Dmytro Zatula
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Hölder Continuity ◽  
Bessel Process ◽  
Holder Continuity ◽  
Basic Properties

We consider a fractionally integrated Bessel process defined by Y s δ , H = ∫ 0 ∞ ( u H − ( 1 / 2 ) − ( u − s ) + H − ( 1 / 2 ) ) d X u δ , where X δ is the Bessel process of dimension δ  > 2. We discuss the relation of this process to the fractional Brownian motion at its maximum, study the basic properties of the process and prove its Hölder continuity.

Invariance formulas for stopping times of squared Bessel process

2018 ◽  
Vol 36 (4) ◽  
pp. 671-699
Author(s):  
Jacek Jakubowski ◽  
Maciej Wiśniewolski
Keyword(s):  
Bessel Process ◽  
Stopping Times ◽  
Squared Bessel Process

Bilinear Forms and Zonal Polynomials

1995 ◽  
Author(s):  
A. M. Mathai ◽  
Serge B. Provost ◽  
Takesi Hayakawa
Keyword(s):  
Bilinear Forms ◽  
Zonal Polynomials
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