Stretched non-local Pearson diffusions

Autor(es)

Beghin, Luisa ; Leonenko, Nikolai ; Papic, Ivan ; Vaz, Jayme

• Tipo de documento: Artigo Científico
• Fonte: Stochastic Processes and their Applications; v. 195, p. 24-pg., 2026-05-01.

Resumo

We define a novel class of time-changed Pearson diffusions, termed stretched non-local Pearson diffusions, where the stochastic time-change model has the Kilbas-Saigo function as its Laplace transform. Moreover, we introduce a stretched variant of the Caputo fractional derivative and prove that its eigenfunction is, in fact, the Kilbas-Saigo function. Furthermore, we solve fractional Cauchy problems involving the generator of the Pearson diffusion and the Fokker-Planck operator, providing both analytic and stochastic solutions, which connect the newly defined process and fractional operator with the Kilbas-Saigo function. We also prove that stretched non-local Pearson diffusions share the same limiting distributions as their standard counterparts. Finally, we investigate fractional hyperbolic Cauchy problems for Pearson diffusions, which resemble time-fractional telegraph equations, and provide both analytical and stochastic solutions. As a byproduct of our analysis, we derive a novel representation and an asymptotic formula for the Kilbas-Saigo function with complex arguments, which, to the best of our knowledge, are not currently available in the existing literature. (AU)

• Processo FAPESP: 22/09201-8 - Sistemas diferenciais fracionários e estocástica
• Beneficiário: Jayme Morandi Vaz
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional
• Processo FAPESP: 24/17510-6 - Cálculo Fracionário e Processos Estocásticos
• Beneficiário: Jayme Morandi Vaz
• Modalidade de apoio: Bolsas no Exterior - Pesquisa