Beyond the hypothesis of boundedness for the random coefficient of Airy, Hermite and Laguerre differential equations with uncertainties. Issue 5 (2nd September 2020)

• Record Type: Journal Article
• Authors: Calatayud Gregori, Julia; Cortés, Juan-Carlos; Jornet Sanz, Marc
• Is Part Of: Stochastic analysis and applications. Volume 38:Issue 5(2020)
• Page Start: 875
• Page End: 885
• Publication Date: 2020-09-02
• Subjects: Random differential equation -- second-order linear differential equation -- Fröbenius method -- mean square calculus -- mean fourth calculus; 34A30 -- 34F05 -- 60H10; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2020.1733017
• Languages: English
• ISSNs: 0736-2994

Abstract

Abstract: In this work, we study the full randomized versions of Airy, Hermite and Laguerre differential equations, which depend on a random variable appearing as an equation coefficient as well as two random initial conditions. In previous contributions, the mean square stochastic solutions to the aforementioned random differential equations were constructed via the Fröbenius method, under the assumption of exponential growth of the absolute moments of the equation coefficient, which is equivalent to its essential boundedness. In this paper we aim at relaxing the boundedness hypothesis to allow more general probability distributions for the equation coefficient. We prove that the equations are solvable in the mean square sense when the equation coefficient has finite moment-generating function in a neighborhood of the origin. A thorough discussion of the new hypotheses is included.