A branched chain approach to fractal time

Marcel Ovidiu Vlad

Physica A: Statistical Mechanics and its Applications, 1992, vol. 184, issue 3, 325-341

Abstract: A branched chain description of fractal time is suggested. Within its framework the long time tails are the result of a stochastic renormalization procedure. The jumps are grouped into blocks of random size, the blocks of blocks, etc., the size of a block being described by a branching chain process. The block formation ends up after a random number of steps, according to a scale invariant probability law. The general scaled form of a multi-state waiting time density function is derived. As expected, this function has a long tail for large times. The Shlesinger-Hughes time scaling (Physica A 109 (1981) 597) is recovered as a particular case of our approach. The fluctuation analysis outlines an essential feature of the theory: due to jump clustering, the correlation functions have also long tails; however, unlike the case of true chain reactions the system has the tendency to smooth the fluctuations.

Date: 1992
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:184:y:1992:i:3:p:325-341

DOI: 10.1016/0378-4371(92)90309-E

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