TY  - JOUR
ID  - iiasa14521
UR  - https://pure.iiasa.ac.at/id/eprint/14521/
IS  - 3
A1  - Hanel, R.
A1  - Corominas-Murtra, B.
A1  - Thurner, S.
Y1  - 2017/03/06/
N2  - 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 ensemble picture; it loses its meaning for path-dependent processes. Here we show that an equivalent to the ensemble picture exists for path-dependent processes, such that the non-multinomial statistics of the underlying dynamical process, by construction, is captured correctly in a functional that plays the role of a relative entropy. We demonstrate this for self-reinforcing Pólya urn processes, which explicitly generalize multinomial statistics. We demonstrate the adequacy of this constructive approach towards non-multinomial entropies by computing frequency and rank distributions of Pólya urn processes. We show how microscopic update rules of a path-dependent process allow us to explicitly construct a non-multinomial entropy functional, that, when maximized, predicts the time-dependent distribution function.
PB  - IOP
JF  - New Journal of Physics
VL  - 19
SN  - 1367-2630
TI  - Understanding frequency distributions of path-dependent processes with non-multinomial maximum entropy approaches
AV  - public
ER  -