Stochastic Environmental Research and Risk Assessment· 2026Q1
Kumaraswamy diffusion processes
- 1citations
- Q1SCImago
- 2026year
Short summary
New bounded continuous-time diffusion models are introduced, using Kumaraswamy distributions as their invariant and limiting distributions, offering flexible alternatives for stochastic modeling.
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Key points
- Introduced bounded continuous-time diffusion models with Kumaraswamy distributions as invariant/limiting distributions.
- Models are derived from Jacobi diffusions, resulting in type I and type II variants with distinct pathwise properties.
- Derived explicit eigenfunction expansions for transition densities and conditional moments.
- Demonstrated utility through numerical examples and an application to water reservoir risk monitoring.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract This paper introduces a set of bounded continuous-time diffusion models with standard and modified Kumaraswamy distributions as their invariant and limiting distributions. Both Kumaraswamy distributions, including their reflected versions, are considered. The models are constructed through transformations of Jacobi diffusions, with two distinct construction methods giving rise to type I and type II diffusions. The resulting models have distinct pathwise properties while sharing the same invariant distribution and provide flexible and tractable alternatives for stochastic modeling of bounded processes in a range of applications. Explicit eigenfunction expansions for the transition densities and conditional moments are derived for all four model classes. Numerical examples illustrate the properties of the proposed diffusions, and an application to statistical risk monitoring in the context of water reservoir management is presented.
The authors' abstract, as published at the source. Stochastic Environmental Research and Risk Assessment, 2026 · DOI ↗
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Field: Statistics and Probability
Statistics and ProbabilityMathematics