• Corpus ID: 9876117

Analytical computation of frequency distributions of path-dependent processes by means of a non-multinomial maximum entropy approach

@article{Hanel2015AnalyticalCO,
  title={Analytical computation of frequency distributions of path-dependent processes by means of a non-multinomial maximum entropy approach},
  author={Rudolf Hanel and Bernat Corominas-Murtra and Stefan Thurner},
  journal={ArXiv},
  year={2015},
  volume={abs/1511.00414}
}
Path-dependent stochastic processes are often non-ergodic and observables can no longer be computed within the ensemble picture. The resulting mathematical difficulties pose severe limits to the analytical understanding of path-dependent processes. Their statistics is typically non-multinomial in the sense that the multiplicities of the occurrence of states is not a multinomial factor. The maximum entropy principle is tightly related to multinomial processes, non-interacting systems, and to the… 
Matrix Multinomial Systems with Finite Syntax
TLDR
It is demonstrated that for a sufficiently well behaved class of complex processes, it is possible to derive an exact criterion for deciding whether a sequence of arbitrary length is well formed or not.
Maximum Configuration Principle for Driven Systems with Arbitrary Driving
TLDR
The maximum configuration entropy (that predicts empirical distribution functions) in the context of driven dissipative systems is developed and the corresponding framework and entropy functional that describes the distribution of observable states as a function of the details of the driving process are developed.
Extreme robustness of scaling in sample space reducing processes explains Zipf's law in diffusion on directed networks
TLDR
The result that Zipf's law emerges as a generic feature of diffusion on networks, regardless of its details, and that the exponent of visiting times is related to the amount of cycles in a network could be relevant for a series of applications in traffic-, transport- and supply chain management.

References

SHOWING 1-10 OF 31 REFERENCES
How multiplicity determines entropy and the derivation of the maximum entropy principle for complex systems
TLDR
This paper proves that a MEP indeed exists for complex systems and derive the generalized entropy, and finds that it belongs to the class of the recently proposed (c,d)-entropies, and shows that path-dependent random processes with memory naturally require specific generalized entropies.
A comprehensive classification of complex statistical systems and an ab-initio derivation of their entropy and distribution functions
To characterize strongly interacting statistical systems within a thermodynamical framework - complex systems in particular - it might be necessary to introduce generalized entropies, $S_g$. A series
When do generalized entropies apply? How phase space volume determines entropy
We show how the dependence of phase space volume Ω(N) on system size N uniquely determines the extensive entropy of a classical system. We give a concise criterion when this entropy is not of
The dynamics of correlated novelties
TLDR
A simple mathematical model is proposed that mimics the process of exploring a physical, biological, or conceptual space that enlarges whenever a novelty occurs and predicts statistical laws for the rate at which novelties happen and for the probability distribution on the space explored.
Functional limit theorems for multitype branching processes and generalized Pólya urns
A functional limit theorem is proved for multitype continuous time Markov branching processes. As consequences, we obtain limit theorems for the branching process stopped by some stopping rule, for
Partition structures, Polya urns, the Ewens sampling formula, and the ages of alleles.
  • P. Donnelly
  • Mathematics, Medicine
    Theoretical population biology
  • 1986
TLDR
A genealogical proof of this result equates the labelling of balls in the urn to the partition by age of alleles in the sample, which is seen to be equivalent to the size biased permutation of the Poisson-Dirichlet distribution.
Breaking the Path of Institutional Development? Alternatives to the New Determinism
The concept of path dependence is being used in highly deterministic ways in neo-institutionalist analysis, so that studies using this framework have dif.culty in accounting for, or predicting,
Asymptotic Normality in the Generalized Polya–Eggenberger Urn Model, with an Application to Computer Data Structures
In the generalized Polya–Eggenberger urn model, an urn initially contains a given number of white and black balls. A ball is selected at random from the urn, and the number of white and black balls
The Pólya information divergence
Extensions of Sanov's Theorem and the Conditional Limit Theorem (CoLT) are established for a multicolor Polya-Eggenberger (PE) urn sampling scheme, giving the Polya information divergence and a Polya
Martingale Functional Central Limit Theorems for a Generalized Polya Urn
In a generalized two-color Polya urn scheme, allowing negative replacements, we use martingale techniques to obtain weak invariance principles for the urn process $(W_n)$, where $W_n$ is the number
...
1
2
3
4
...