On the semi-group of a scaled skew Bessel process

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.

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The relativistic semi-group, Lorentz group, and tachyons. II

Soviet Physics Journal ◽

10.1007/bf00952564 ◽

1976 ◽

Vol 19 (5) ◽

pp. 616-619

Author(s):

V. V. Yudin

Keyword(s):

Lorentz Group ◽

Semi Group

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Expansion of an hypoelliptic heat-kernel outside the cut-locus in semi-group theory

2013 International Conference on Control, Decision and Information Technologies (CoDIT) ◽

10.1109/codit.2013.6689524 ◽

2013 ◽

Author(s):

Remi Leandre

Keyword(s):

Group Theory ◽

Heat Kernel ◽

Cut Locus ◽

Semi Group ◽

Hypoelliptic Heat Kernel

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Perturbation theory and finite Markov chains

Journal of Applied Probability ◽

10.2307/3212261 ◽

1968 ◽

Vol 5 (2) ◽

pp. 401-413 ◽

Cited By ~ 211

Author(s):

Paul J. Schweitzer

Keyword(s):

Perturbation Theory ◽

Markov Chain ◽

Markov Chains ◽

Stationary Distribution ◽

Fundamental Matrix ◽

Transition Probabilities ◽

Semi Group ◽

Partial Derivatives ◽

Finite Markov Chains ◽

Derivatives Of

A perturbation formalism is presented which shows how the stationary distribution and fundamental matrix of a Markov chain containing a single irreducible set of states change as the transition probabilities vary. Expressions are given for the partial derivatives of the stationary distribution and fundamental matrix with respect to the transition probabilities. Semi-group properties of the generators of transformations from one Markov chain to another are investigated. It is shown that a perturbation formalism exists in the multiple subchain case if and only if the change in the transition probabilities does not alter the number of, or intermix the various subchains. The formalism is presented when this condition is satisfied.

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Left semi-perfect abundant semi-groups of type W

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210500004029 ◽

2005 ◽

Vol 135 (3) ◽

pp. 603-614 ◽

Cited By ~ 5

Author(s):

Xiaojiang Guo ◽

K. P. Shum

Keyword(s):

Normal Band ◽

Semi Group ◽

Characterization Theorems

We call a quasi-adequate semi-group whose set of idempotents forms a left [right] quasi-normal band a left [right] semi-perfect abundant semi-group. After obtaining some characterization theorems of such quasi-adequate semi-groups, we establish a structure for left [right] semi-perfect abundant semi-groups of type W. Our results generalize and strengthen the results of El-Qallali and Fountain on quasi-adequate semi-groups.

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