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CARMA workshop in Newcastle, 2009

Tue, 08/18/2009 - 08:13 — arminstraub

On August 18, 2009, the University of Newcastle hosted a CARMA workshop on Multidimensional Numerical Integration and Special Function Evaluation. Besides enjoying very interesting talks it's been my pleasure to present, together with James Wan, on progress of our joint work with Jon Borwein, Peter Donovan and Dirk Nuyens on expectations of random walks.

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randomwalkintegrals.pdf
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A trick for playing a multivariate integral

Wed, 05/13/2009 - 14:35 — arminstraub

For suitable functions f the integral

$$ \int_0^{\infty} \int_0^{\infty} \ldots \int_0^{\infty} \frac{dx_1 dx_2 \cdots dx_n}{(f(x_1) + f(x_2) + \ldots + f (x_n))^{k+1}} $$

is equal to

$$ \frac{1}{k!} \int_0^{\infty} t^k \left( \int_0^{\infty} e^{- t f(x)} dx \right)^n dt . $$

To see why this is true, start with the last integral and write the n-th power of the inner integral as a multiple integral over variables x1, …, xn. Then change order of integration and evaluate read more »

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