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A sufficient condition for the continuity of permanental processes with applications to local times of Markov processes
We provide a sufficient condition for the continuity of real valued
permanental processes. When applied to the subclass of permanental processes
which consists of squares of Gaussian processes, we obtain the sufficient
condition for continuity which is also known to be necessary. Using an
isomorphism theorem of Eisenbaum and Kaspi which relates Markov local times and
permanental processes, we obtain a general sufficient condition for the joint
continuity of local times.Comment: Published in at http://dx.doi.org/10.1214/12-AOP744 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Permanental Vectors
A permanental vector is a generalization of a vector with components that are
squares of the components of a Gaussian vector, in the sense that the matrix
that appears in the Laplace transform of the vector of Gaussian squares is not
required to be either symmetric or positive definite. In addition the power of
the determinant in the Laplace transform of the vector of Gaussian squares,
which is -1/2, is allowed to be any number less than zero.
It was not at all clear what vectors are permanental vectors. In this paper
we characterize all permanental vectors in and give applications to
permanental vectors in and to the study of permanental processes
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