# 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…

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## References

SHOWING 1-10 OF 31 REFERENCES

How multiplicity determines entropy and the derivation of the maximum entropy principle for complex systems

- Medicine, PhysicsProceedings of the National Academy of Sciences
- 2014

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

- Mathematics, Physics
- 2010

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

- Physics
- 2011

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

- Computer Science, MedicineScientific reports
- 2014

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

- Mathematics
- 2004

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.

- Mathematics, MedicineTheoretical population biology
- 1986

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

- Sociology
- 2004

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

- Mathematics
- 1985

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

- Mathematics, Computer ScienceInf. Sci.
- 2010

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

- Mathematics
- 1993

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…