Random variable transformation for generalized stochastic radiative transfer in finite participating slab media

El-Wakil, S.A.; Sallah, Mohammed; Elhanbaly, A.

doi:10.1016/j.physa.2015.04.033

Cited by 7 publications

(2 citation statements)

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“…via RVT method within the context of r.d.e. 's, it is worth pointing out that some significant contributions are [8][9][10][11][12][13][14]. Most of these contributions usually assume that uncertainty enters via a single r.v.…”

Section: Motivationmentioning

confidence: 99%

Solving Random Homogeneous Linear Second-Order Differential Equations: A Full Probabilistic Description

et al. 2016

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Roselló, M. (2016). Solving random homogeneous linear second-order differential equations: a full probabilistic description. Mediterranean Journal of Mathematics. 13(6): 3817-3836. doi:10.1007/s00009-016-0716-6 Solving random homogeneous linear secondorder differential equations: A full probabilistic description Abstract. In this paper a complete probabilistic description for the solution of random homogeneous linear second-order differential equations via the computation of its two first probability density functions is given. As a consequence, all unidimensional and two-dimensional statistical moments can be straightforwardly determined, in particular, mean, variance and covariance functions, as well as the first-order conditional law. With the aim of providing more generality, in a first step, all involved input parameters are assumed to be statistically dependent random variables having an arbitrary joint probability density function. Secondly, the particular case that just initial conditions are random variables is also analysed. Both problems have common and distinctive feature which are highlighted in our analysis. The study is based on Random Variable Transformation method. As a consequence of our study, the well-known deterministic results are nicely generalized. Several illustrative examples are included.Mathematics Subject Classification (2010). 60H35, 60H10, 37H10. Keywords. Random Variable Transformation method, first and second probability density functions, random homogeneous linear second-order differential equations. MotivationThe quantification of uncertainty in dynamic models is currently playing an important role in many applied areas. Classical deterministic differential equations, which have demonstrated to be powerful tools for analysing problems that appear in areas such as Physics, Engineering, Chemistry, Epidemiology, etc., need to consider randomness in their formulation in order to account for measurement errors and inherent complexity of problems underThis work was completed with the support of our T E X-pert. [4][5][6]. However, it is important to point out that in the random context besides computing the solution stochastic process (s.p.), say Z(t), it is also of great interest the determination of its main statistical properties. Most of the contributions focus on the computation of the mean, µ Z (t) = E[Z(t)], and the variance, σ 2 Z (t) = V[Z(t)], functions of the solution s.p. However, a more convenient goal is the determination of its first probability density function (1-p.d.f.), f 1 (z, t), since from it one can easily compute not just these two first statistical moments,but also the one-dimensional statistical moment of any orderThe 1-p.d.f. characterizes, from a probabilistic point of view, the solution s.p. Z(t) at every time instant t. In general, more challenging is the determination of the rest of the so-called fidis (finite dimensional distributions), i.e., the n-dimensional p.d.f.'s of the solution s.p. for n ≥ 2, because it usually involves complex developments...

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Section: Motivationmentioning

confidence: 99%

Solving Random Homogeneous Linear Second-Order Differential Equations: A Full Probabilistic Description

et al. 2016

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“…To complete a fair overview of the state of the art with respect to the general goal of computing the probability density function of the solution process to random partial differential equations, it must be said that a powerful technique that has been extensively used is the Random Variable Transformation technique [130,160]. Some relevant contributions in this regard include [64,88,89,154], for example.…”

Section: Introductionmentioning

confidence: 99%

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

Sanz¹

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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.

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An approximate probabilistic solution of a random SIR-type epidemiological model using RVT technique

Slama

Hussein

El-Bedwhey

et al. 2019

Applied Mathematics and Computation

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Random variable transformation for generalized stochastic radiative transfer in finite participating slab media

Cited by 7 publications

References 16 publications

Solving Random Homogeneous Linear Second-Order Differential Equations: A Full Probabilistic Description

Solving Random Homogeneous Linear Second-Order Differential Equations: A Full Probabilistic Description

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

An approximate probabilistic solution of a random SIR-type epidemiological model using RVT technique

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