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This article is concerned with the joint law of an integrated Wishart bridge process and the trace of an integrated inverse Wishart bridge process over the interval $ left[0,tright] $. Its Laplace transform is obtained by studying the Wishart bridge processes and the absolute continuity property of Wishart laws.
The Hartman-Watson distribution with density $f_r(t)$ is a probability distribution defined on $t geq 0$ which appears in several problems of applied probability. The density of this distribution is expressed in terms of an integral $theta(r,t)$ whic
Let $X^{(delta)}$ be a Wishart process of dimension $delta$, with values in the set of positive matrices of size $m$. We are interested in the large deviations for a family of matrix-valued processes ${delta^{-1} X_t^{(delta)}, t leq 1 }$ as $delta$
We study survival properties of inhomogeneous Galton-Watson processes. We determine the so-called branching number (which is the reciprocal of the critical value for percolation) for these random trees (conditioned on being infinite), which turns out
This paper deals with branching processes in varying environment, namely, whose offspring distributions depend on the generations. We provide sufficient conditions for survival or extinction which rely only on the first and second moments of the offs
We establish an explicit expression for the conditional Laplace transform of the integrated Volterra Wishart process in terms of a certain resolvent of the covariance function. The core ingredient is the derivation of the conditional Laplace transfor