Permanental sequences that are related to a Markov chain example of Kolmogorov

2019/11/30 by Marcus, Michael B., Rosen, Jay
#60E07 #60G15 #60G17 #60G99 #60J27 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1912.00285

Abstract

Permanental sequences with non-symmetric kernels that are generalization of the potentials of a Markov chain with state space \0,1/2, …, 1/n,…\ that was introduced by Kolmogorov, are studied. Depending on a parameter in the kernels we obtain an exact rate of divergence of the sequence at 0, an exact local modulus of continuity of the sequence at 0, or a precise bounded discontinuity for the sequence at 0.

Related

• Asymptotic properties of permanental sequences
• Local moduli of continuity for permanental processes that are zero at zero
• Conditions for permanental processes to be unbounded
• Sample path properties of permanental processes
• Heat kernels, intrinsic contractivity and ergodicity of discrete-time Markov chains killed by potentials