Brown and Levy Steady-State Motions
This paper introduces and explores a novel class of Brown and Levy steady-state motions. These motions generalize, respectively, the Ornstein-Uhlenbeck process (OUP) and the Levy-driven OUP. As the OUP and the Levy-driven OUP: the motions are Markov; their dynamics are Langevin; and their steady-sta...
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2025-06-01
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| author | Iddo Eliazar |
| author_facet | Iddo Eliazar |
| author_sort | Iddo Eliazar |
| collection | DOAJ |
| description | This paper introduces and explores a novel class of Brown and Levy steady-state motions. These motions generalize, respectively, the Ornstein-Uhlenbeck process (OUP) and the Levy-driven OUP. As the OUP and the Levy-driven OUP: the motions are Markov; their dynamics are Langevin; and their steady-state distributions are, respectively, Gauss and Levy. As the Levy-driven OUP: the motions can display the Noah effect (heavy-tailed amplitudal fluctuations); and their memory structure is tunable. And, as Gaussian-stationary processes: the motions can display the Joseph effect (long-ranged temporal dependencies); and their correlation structure is tunable. The motions have two parameters: a critical exponent which determines the Noah effect and the memory structure; and a clock function which determines the Joseph effect and the correlation structure. The novel class is a compelling stochastic model due to the following combination of facts: on the one hand the motions are tractable and amenable to analysis and use; on the other hand the model is versatile and the motions display a host of both regular and anomalous features. |
| format | Article |
| id | doaj-art-61bdd106cd554e758a9b675201d03a0a |
| institution | Kabale University |
| issn | 1099-4300 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj-art-61bdd106cd554e758a9b675201d03a0a2025-08-20T03:27:32ZengMDPI AGEntropy1099-43002025-06-0127664310.3390/e27060643Brown and Levy Steady-State MotionsIddo Eliazar0School of Chemistry, Tel Aviv University, Tel Aviv 6997801, IsraelThis paper introduces and explores a novel class of Brown and Levy steady-state motions. These motions generalize, respectively, the Ornstein-Uhlenbeck process (OUP) and the Levy-driven OUP. As the OUP and the Levy-driven OUP: the motions are Markov; their dynamics are Langevin; and their steady-state distributions are, respectively, Gauss and Levy. As the Levy-driven OUP: the motions can display the Noah effect (heavy-tailed amplitudal fluctuations); and their memory structure is tunable. And, as Gaussian-stationary processes: the motions can display the Joseph effect (long-ranged temporal dependencies); and their correlation structure is tunable. The motions have two parameters: a critical exponent which determines the Noah effect and the memory structure; and a clock function which determines the Joseph effect and the correlation structure. The novel class is a compelling stochastic model due to the following combination of facts: on the one hand the motions are tractable and amenable to analysis and use; on the other hand the model is versatile and the motions display a host of both regular and anomalous features.https://www.mdpi.com/1099-4300/27/6/643ornstein-uhlenbeck processeslevy-driven processesmarkov processes and Langevin dynamicsnoah effect and heavy tailsjoseph effect and long-range dependencememory and correlation |
| spellingShingle | Iddo Eliazar Brown and Levy Steady-State Motions Entropy ornstein-uhlenbeck processes levy-driven processes markov processes and Langevin dynamics noah effect and heavy tails joseph effect and long-range dependence memory and correlation |
| title | Brown and Levy Steady-State Motions |
| title_full | Brown and Levy Steady-State Motions |
| title_fullStr | Brown and Levy Steady-State Motions |
| title_full_unstemmed | Brown and Levy Steady-State Motions |
| title_short | Brown and Levy Steady-State Motions |
| title_sort | brown and levy steady state motions |
| topic | ornstein-uhlenbeck processes levy-driven processes markov processes and Langevin dynamics noah effect and heavy tails joseph effect and long-range dependence memory and correlation |
| url | https://www.mdpi.com/1099-4300/27/6/643 |
| work_keys_str_mv | AT iddoeliazar brownandlevysteadystatemotions |