Permanental sequences related to a Markov chain example of Kolmogorov

• Published in: Stochastic processes and their applications Vol. 130; no. 12; pp. 7098 - 7130
• Main Authors: Marcus, Michael B., Rosen, Jay
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.12.2020
• Subjects: Moduli of continuity at 0; Permanental sequences with non-symmetric kernels; Potential of a Markov chain with an instantaneous state; 60G99; Permanental sequences with non-symmetric kernels; Moduli of continuity at 0; Potential of a Markov chain with an instantaneous state; 60J27; 60G17; 60E07; 60G15
• ISSN: 0304-4149; 1879-209X
• DOI: 10.1016/j.spa.2020.07.008

Permanental sequences with non-symmetric kernels that are generalization of the potentials of a Markov chain with state space {0,1∕2,…,1∕n,…} and a single instantaneous state 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.