Step count number versus interaction time in jump Markovian dynamics

Marcel Ovidiu Vlad and Amalia Pop

Physica A: Statistical Mechanics and its Applications, 1989, vol. 159, issue 2, 256-272

Abstract: The stochastic analysis of jump Markovian models may be performed in terms either of the number of transition events q (the step count number) or in terms of the interaction time τ (the time interval that elapsed from the first occurence of a jump event). In order to describe the stochastic behavior of q and τ, a new stochastic formalism is suggested. The state probabilities attached to q and τ as well as the corresponding moments may be expressed in terms of the Green function attached to the phenomenological master equation. For time-homogeneous Markov processes with a constant overall jump frequency a detailed analysis is possible. The main results are the following. For large time, t → ∞, the second moments of q and τ have a different behavior. Whereas 〈Δτ2(t)〉 and 〈Δq(t) Δτ(t)〉 evolve towards constant values, the dispersion 〈Δq2(t)〉 increases linearly in time. For large times the random variables q and τ are practically uncorrelated.

Date: 1989
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:159:y:1989:i:2:p:256-272

DOI: 10.1016/0378-4371(89)90569-4

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