On Joint Fourier-Laplace Transforms
### On Joint Fourier-Laplace Transforms

#### P. J. Fitzsimmons, T. McElroy

Weak convergence of random variables is characterized by
pointwise convergence of the Fourier transform of the respective
distributions, and in some cases can also be characterized
through the Laplace transform. For some distributions, the
Laplace transform is easier to compute and provides an
alternative approach to the method of characteristic functions
that facilitates proving weak convergence. We show that for a
bivariate distribution, a joint Fourier-Laplace transform always
characterizes the distribution when the second variate is
positive almost surely.

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August 31, 2006