Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7550369 | Stochastic Processes and their Applications | 2018 | 29 Pages |
Abstract
Many dynamical phenomena display a cyclic behavior, in the sense that time can be partitioned into units within which distributional aspects of a process are homogeneous. In this paper, we introduce a class of models - called conjugate processes - allowing the sequence of marginal distributions of a cyclic, continuous-time process to evolve stochastically in time. The connection between the two processes is given by a fundamental compatibility equation. Key results include Laws of Large Numbers in the presented framework. We provide a constructive example which illustrates the theory, and give a statistical implementation to risk forecasting in financial data.
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Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Eduardo Horta, Flavio Ziegelmann,