On an interpolation model for the transition operator for Markov and non-Markov processes

Balakrishnan, V. (1979) On an interpolation model for the transition operator for Markov and non-Markov processes Pramana - Journal of Physics, 13 (4). pp. 337-352. ISSN 0304-4289

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Official URL: http://www.ias.ac.in/j_archive/pramana/13/4/337-35...

Related URL: http://dx.doi.org/10.1007/BF02846131


A phenomenological interpolation model for the transition operator of a stationary Markov process is shown to be equivalent to the simplest difference approximation in the master equation for the conditional density. Comparison with the formal solution of the Fokker-Planck equation yields a criterion for the choice of the correlation time in the approximate solution. The interpolation model is shown to be form-invariant under an iteration-cum-rescaling scheme. Next, we go beyond Markov processes to find the effective time-development operator (the counterpart of the conditional density) in the following very general situation: the stochastic interruption of the systematic evolution of a variable by an arbitrary stationary sequence of randomizing pulses. Continuous-time random walk theory with a distinct first-waiting-time distribution is used, along with the interpolation model for the transition operator, to obtain the solution. Convenient closed-form expressions for the 'averaged' time-development operator and the autocorrelation function are presented in various special cases. These include (i) no systematic evolution, but correlated pulses; (ii) systematic evolution interrupted by an uncorrelated (Poisson) sequence of pulses.

Item Type:Article
Source:Copyright of this article belongs to Indian Academy of Sciences.
Keywords:Markov Processes; Transition Operator; Interpolation Model; Continuous-Time Random Walk; Pulse Sequences; Non-Markov Processes
ID Code:1085
Deposited On:27 Sep 2010 04:29
Last Modified:16 May 2016 12:15

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