1. Center for Information Technology
2. National Institute of Child Health and human Development
National Institutes of Health
Bethesda, Md. 20892
January 28, 2000
3. Permanent address: Karpov Institute of Physical Chemistry, 10 Vorontsovo Pole Street, 103064 Moscow K-64, Russia.
We study dynamical system which makes transitions between two states at random times. We analyze properties of the cumulative time t spent by the system in a given state up to time T. When the probability density for the residenve time in a single sojourn in th given state differs from a negative exponential the system will be non-Markovian. Simple analytical expressions are derived for the Laplace transform with respect to T of moments of the cumulative residence time. An exact Fourier-Laplace transform of the probability densities for t at a fixed T are also found. It can be inferred from this expression, that at sufficiently large T the probability densities tend towards a Gaussian. The parameters that define the Gaussian are also given.