שמור ב:
| Main Authors: | , |
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| פורמט: | Recurso digital |
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| יצא לאור: |
Zenodo
2025
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| גישה מקוונת: | https://doi.org/10.5281/zenodo.17806833 |
| תגים: |
הוספת תג
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תוכן הענינים:
- This paper explores the intricate relationship between stochastic entropy and martingale convergence within the framework of Lévy-Gaussian fields. We introduce a robust definition of stochastic entropy for these fields, which combine the heavy-tailed, jump characteristics of Lévy processes with the smooth, spatially correlated nature of Gaussian fields. Our primary objective is to investigate conditions under which sequences of random variables derived from such fields exhibit martingale properties and subsequently converge. We develop a theoretical framework that integrates concepts from stochastic calculus, measure theory, and information theory to analyze the evolution of uncertainty and predictability in these complex stochastic systems. The study establishes novel convergence theorems for martingales associated with Lévy-Gaussian fields, providing insights into the long-term behavior and stability of processes driven by both continuous and discontinuous noise. The implications of these findings extend to diverse applications, including financial modeling, environmental sciences, and quantum field theory, where phenomena exhibit both continuous fluctuations and abrupt changes.