We do consider models of the population or opinion dynamics which result in  non-linear stochastic differential equations (SDEs) exhibiting  spurious long-range memory. In this context, the correspondence between the description of  birth-death processes as  continuous-time Markov chains and  continuous SDEs is of high importance for the alternatives of modeling. We propose and generalize  Bessel-like birth-death process having clear representation by  SDEs. The new process helps to integrate  alternatives of description and to derive  equations for the probability density function (PDF) of  burst and inter-burst duration of the proposed continuous time birth-death processes . This PDF might be used to discriminate between spurious memory and true long-range memory in complex systems exhibiting continuing fluctuations .
We consider models of the population or opinion dynamics which result in the non-linear stochastic differential equations (SDEs) exhibiting the spurious long-range memory. In this context, the correspondence between the description of the birth-death processes as the continuous-time Markov chains and the continuous SDEs is of high importance for the alternatives of modeling. We propose and generalize the Bessel-like birth-death process having clear representation by the SDEs. The new process helps to integrate the alternatives of description and to derive the equations for the probability density function (PDF) of the burst and inter-burst duration of the proposed continuous time birth-death processes .
D
do
A
the
A
the
A
the
A
the
A
the
A
the
A
the
A
the
A
the
A
the
D
. This PDF might be used to discriminate between spurious memory and true long-range memory in complex systems exhibiting continuing fluctuations