Asymptotic Properties of Permanental Sequences

Professor Marcus is Professor Emeritus at The City College, CUNY and the CUNY Graduate Center and Professor Rosen is Distinguished Professor at The College of Staten Island, CUNY and the CUNY Graduate Center. Together they have published more than two hundred papers of which thirty six were written jointly and five books three of which were written jointly. Together they have delivered more than three hundred invited talks. Their research is on sample path properties of stochastic processes, specializing in Gaussian processes, random Fourier series, Gaussian chaos, Levy processes, Markov processes, local times, intersection local times, loop soups and permanental processes.

• 1.Introduction, General Results and Applications.- 2.Birth and death processes.- 3.Birth and death processes with emigration.- 4.Birth and death processes with emigration related to first order Gaussian autoregressive sequences.- 5.Markov chains with potentials that are the covariances of higher order Gaussian autoregressive sequences.- 6.Relating permanental sequences to  Gaussian sequences.- 7. Permanental sequences with kernels that have uniformly bounded row sums.- 8.Uniform Markov chains.- References.- Index.