Search results for "long range correlation"

THE ROLE OF UNBOUNDED TIME-SCALES IN GENERATING LONG-RANGE MEMORY IN ADDITIVE MARKOVIAN PROCESSES

2013

Any additive stationary and continuous Markovian process described by a Fokker–Planck equation can also be described in terms of a Schrödinger equation with an appropriate quantum potential. By using such analogy, it has been proved that a power-law correlated stationary Markovian process can stem from a quantum potential that (i) shows an x-2 decay for large x values and (ii) whose eigenvalue spectrum admits a null eigenvalue and a continuum part of positive eigenvalues attached to it. In this paper we show that such two features are both necessary. Specifically, we show that a potential with tails decaying like x-μ with μ < 2 gives rise to a stationary Markovian process which is not p…