1,254 research outputs found
Explicit Evaluations of Matrix-variate Gamma and Beta Integrals in the Real and Complex Cases
Matrix transformations in terms of triangular matrices is the easiest method
of evaluating matrix-variate gamma and beta integrals in the real and complex
cases. Here we give several procedures of explicit evaluation of gamma and beta
integrals in the general real and complex situations. The procedure also
reveals the structure of these matrix-variate integrals. Apart from the
evaluation of matrix-variate gamma and beta integrals, the procedure can also
be applied to evaluate such integrals explicitly in similar situations. Various
methods described here will be useful to those who are working on integrals
involving real-valued scalar functions of matrix argument in general and gamma
and beta integrals in particular.Comment: 17 pages, LaTe
Stochastic processes via the pathway model
After collecting data from observations or experiments, the next step is to
build an appropriate mathematical or stochastic model to describe the data so
that further studies can be done with the help of the models. In this article,
the input-output type mechanism is considered first, where reaction, diffusion,
reaction-diffusion, and production-destruction type physical situations can fit
in. Then techniques are described to produce thicker or thinner tails (power
law behavior) in stochastic models. Then the pathway idea is described where
one can switch to different functional forms of the probability density
function) through a parameter called the pathway parameter.Comment: 15 pages, 7 figures, LaTe
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