Fat tails and black swans: Exact results for multiplicative processes with resets
We consider a class of multiplicative processes which, added with stochastic reset events, give origin to stationary distributions with power-law tails?ubiquitous in the statistics of social, economic, and ecological systems. Our main goal is to provide a series of exact results on the dynamics and...
| Authors: | , |
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| Format: | article |
| Status: | Published version |
| Publication Date: | 2020 |
| Country: | Argentina |
| Institution: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repository: | CONICET Digital (CONICET) |
| Language: | English |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/142455 |
| Online Access: | http://hdl.handle.net/11336/142455 |
| Access Level: | Open access |
| Keyword: | MUTIPLICATIVE PROCESSES STOCHASTIC PROCESSES RESETTING https://purl.org/becyt/ford/1.3 https://purl.org/becyt/ford/1 |
| Summary: | We consider a class of multiplicative processes which, added with stochastic reset events, give origin to stationary distributions with power-law tails?ubiquitous in the statistics of social, economic, and ecological systems. Our main goal is to provide a series of exact results on the dynamics and asymptotic behavior of increasingly complex versions of a basic multiplicative process with resets, including discrete and continuous-time variants and several degrees of randomness in the parameters that control the process. In particular, we show how the power-law distributions are built up as time elapses, how their moments behave with time, and how their stationary profiles become quantitatively determined by those parameters. Our discussion emphasizes the connection with financial systems, but these stochastic processes are also expected to be fruitful in modeling a wide variety of social and biological phenomena. |
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