Mean Square Analytic Solutions of Random Linear Models

Sanjuan, Gemma Calbo

doi:10.4995/thesis/10251/8721

Cited by 3 publications

(5 citation statements)

References 42 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, it would be interesting to prove the existence of mean square solution under a more general assumption than boundedness. We take as main reference here the works [11][12][13]. Reference [11] studies random first-order linear differential equations, [12] is devoted to a specific random second-order linear differential equation to introduce some random trigonometric functions, and [13] is a doctoral dissertation on the application of the Fröbenius method to solve random differential equations.…”

Section: Introduction Goals and Assumptionsmentioning

confidence: 99%

Beyond the hypothesis of boundedness for the random coefficient of Airy, Hermite and Laguerre differential equations with uncertainties

Gregori

Cortés

Sanz

2020

Stochastic Analysis and Applications

View full text Add to dashboard Cite

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.

show abstract

Section: Introduction Goals and Assumptionsmentioning

confidence: 99%

Beyond the hypothesis of boundedness for the random coefficient of Airy, Hermite and Laguerre differential equations with uncertainties

Gregori

Cortés

Sanz

2020

Stochastic Analysis and Applications

View full text Add to dashboard Cite

show abstract

“…This is the extension of the deterministic Fröbenius method to the random setting, which shows important applications for solving second-order linear differential equations [33]. Several differential equations from Mathematical Physics have been randomized and rigorously solved using the random Fröbenius method [27,29,43].…”

Section: Introductionmentioning

confidence: 99%

“…However, it would be interesting to prove the existence of mean square solution under a more general assumption than boundedness. We take as main reference here the works [28,30,27]. Reference [28] studies random first-order linear differential equations, [30] is devoted to a specific random second-order linear differential equation to introduce some random trigonometric functions, and [27] is a doctoral dissertation on the application of the Fröbenius method to solve random differential equations.…”

Section: Introductionmentioning

confidence: 99%

“…We take as main reference here the works [28,30,27]. Reference [28] studies random first-order linear differential equations, [30] is devoted to a specific random second-order linear differential equation to introduce some random trigonometric functions, and [27] is a doctoral dissertation on the application of the Fröbenius method to solve random differential equations. Following these works, we will assume that Y 0 and Y 1 are fourth-order random variables and that…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Mean square solutions of random linear models and computation of their probability density function

Sanz¹

View full text Add to dashboard Cite

This thesis concerns the analysis of differential equations with uncertain input parameters, in the form of random variables or stochastic processes with any type of probability distributions. In modeling, the input coefficients are set from experimental data, which often involve uncertainties from measurement errors. Moreover, the behavior of the physical phenomenon under study does not follow strict deterministic laws. It is thus more realistic to consider mathematical models with randomness in their formulation. The solution, considered in the sample-path or the mean square sense, is a smooth stochastic process, whose uncertainty has to be quantified. Uncertainty quantification is usually performed by computing the main statistics (expectation and variance) and, if possible, the probability density function.

show abstract

“…On the one hand, Section 2.1 is addressed to give the fundamental principles and results in probability, Random Variables (RVs) and Stochastic Processes (SPs). Notice that Section 2.1 is based on the preliminaries of thesis [79] given that the mathematical tools explained in this section are common in both dissertations. On the other hand, the main results that will be required in next chapters, are summarized in Section 2.2.…”

Section: Preliminariesmentioning

confidence: 99%

Computational Methods for Random Differential Equations: Theory and Applications

Quiles¹

View full text Add to dashboard Cite

Mean Square Analytic Solutions of Random Linear Models

Cited by 3 publications

References 42 publications

Beyond the hypothesis of boundedness for the random coefficient of Airy, Hermite and Laguerre differential equations with uncertainties

Beyond the hypothesis of boundedness for the random coefficient of Airy, Hermite and Laguerre differential equations with uncertainties

Mean square solutions of random linear models and computation of their probability density function

Computational Methods for Random Differential Equations: Theory and Applications

Contact Info

Product

Resources

About