Aspects of Long-Range Dependence

Aspects of Long-Range Dependence

Daryl J. Daley
Centre for Mathematics and Applications
Australian National University

Thursday, November 18, 2004
4:15 PM - 5:15 PM
Terman Engineering Center, Room 498

Abstract:

Call a stationary stochastic process {Y_n} long-range dependent (LRD) when var(Y_1 + ... + Y_n) is NOT asymptotically like (const.)n. In the talk I examine various functionals Y_n = y_{X_n} of a stationary countable state space irreducible Markov chain {X_n} with this LRD property. The simplest such functional concerns visits to a particular state i of such a chain, and the LRD property is then equivalent to an infinite second moment for return times to the state. Such a property holds for either no states or all states, and a uniform rate of slow growth (of var(Y_1 + ... + Y_n)/n ) holds for each and every state. The family of such rates of growth admits a simple description.

Operations Research Colloquia: http://or.stanford.edu/oras_seminars.html