<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this paper the randomized Cauchy-Euler differential equation is studied. With this aim, from a statistical point of view, both the first and second probability density functions of the solution stochastic process are computed. Then, the main statistical functions, namely, the mean, the variance and the covariance functions are determined as well. The study includes the computation of the first and second probability density functions of the regular-singular infinite point via an adequate mapping transforming the problem about the origin. The study is strongly based upon the Random Variable Transformation technique along with some results that have been recently published by some of authors to the random homogeneous linear second-order differential equation. Finally, an illustrative example is shown.</p></abstract>

In this paper the randomized Cauchy-Euler differential equation is studied. With this aim, from a statistical point of view, both the first and second probability density functions of the solution stochastic process are computed. Then, the main statistical functions, namely, the mean, the variance and the covariance functions are determined as well. The study includes the computation of the first and second probability density functions of the regular-singular infinite point via an adequate mapping transforming the problem about the origin. The study is strongly based upon the Random Variable Transformation technique along with some results that have been recently published by some of authors to the random homogeneous linear second-order differential equation. Finally, an illustrative example is shown.

Computing the two first probability density functions of the random Cauchy-Euler differential equation: Study about regular-singular points

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

In this paper the randomized Cauchy-Euler differential equation is studied. With this aim, from a statistical point of view, both the first and second...

Cases	p₁	p₂	p_s
I	0.978524	0.021476	0.966055
II	0.530394	0.469606	0.966054
III	0.045171	0.954829	0.999866

Computing the two first probability density functions of the random Cauchy-Euler differential equation: Study about regular-singular points

Pubblicato online: 23 giu 2017

Pagine: 213 - 224

Ricevuto: 22 feb 2017

Accettato: 23 giu 2017

DOI: https://doi.org/10.21042/AMNS.2017.1.00018

Parole chiave
random Cauchy-Euler differential equation, Random Variable Transformation technique, first and second probability density functions

© 2017 J.-C. Cortés, A. Navarro-Quiles, J.-V. Romero, M.-D. Roselló, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Fig. 1

Fig. 2

Fig. 3

Columns p1 and p2 = 1 − p1 collect the values of the probabilities given by (25) corresponding to Cases I–III, when Ji ~ N(μi,Σ), being μi and Σ specified in (24). Values of ps represent the probabilities associated with asymptotic stability according to (26).

Computing the two first probability density functions of the random Cauchy-Euler differential equation: Study about regular-singular points

Pubblicato online: 23 giu 2017

Pagine: 213 - 224

Ricevuto: 22 feb 2017

Accettato: 23 giu 2017

DOI: https://doi.org/10.21042/AMNS.2017.1.00018

Parole chiaverandom Cauchy-Euler differential equation, Random Variable Transformation technique, first and second probability density functions

© 2017 J.-C. Cortés, A. Navarro-Quiles, J.-V. Romero, M.-D. Roselló, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Fig. 1

Fig. 2

Fig. 3

Columns p1 and p2 = 1 − p1 collect the values of the probabilities given by (25) corresponding to Cases I–III, when Ji ~ N(μi,Σ), being μi and Σ specified in (24). Values of ps represent the probabilities associated with asymptotic stability according to (26).

Parole chiave
random Cauchy-Euler differential equation, Random Variable Transformation technique, first and second probability density functions