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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Research Article| March 02 2020
Fat tails and black swans: Exact results for multiplicative processes with resets
Special Collection: Dynamics of Social Systems
D. H. Zanette ;
D. H. Zanette a)
Centro Atómico Bariloche and Instituto Balseiro, Comisión Nacional de Energía Atómica and Universidad Nacional de Cuyo, Consejo Nacional de Investigaciones Científicas y Técnicas, Av. E. Bustillo 9500, R8402AGP San Carlos de Bariloche, Río Negro,
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D. H. Zanette, S. Manrubia; Fat tails and black swans: Exact results for multiplicative processes with resets. Chaos 1 March 2020; 30 (3): 033104. https://doi.org/10.1063/1.5141837
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