| 来源类型 | Article |
| 规范类型 | 其他 |
| DOI | 10.1088/1367-2630/aa611d |
| Understanding frequency distributions of path-dependent processes with non-multinomial maximum entropy approaches. | |
| Hanel R; Corominas-Murtra B; Thurner S | |
| 发表日期 | 2017 |
| 出处 | New Journal of Physics 19 (3): e033008 |
| 出版年 | 2017 |
| 语种 | 英语 |
| 摘要 | 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. |
| 主题 | Advanced Systems Analysis (ASA) |
| URL | http://pure.iiasa.ac.at/id/eprint/14521/ |
| 来源智库 | International Institute for Applied Systems Analysis (Austria) |
| 引用统计 | |
| 资源类型 | 智库出版物 |
| 条目标识符 | http://119.78.100.153/handle/2XGU8XDN/130923 |
| 推荐引用方式 GB/T 7714 | Hanel R,Corominas-Murtra B,Thurner S. Understanding frequency distributions of path-dependent processes with non-multinomial maximum entropy approaches.. 2017. |
| 条目包含的文件 | ||||||
| 文件名称/大小 | 资源类型 | 版本类型 | 开放类型 | 使用许可 | ||
| Hanel_2017_New_J._Ph（1119KB） | 智库出版物 | 限制开放 | CC BY-NC-SA | 浏览 | ||
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