Solution of the finite Milne problem in stochastic media with RVT Technique

Analysis of random non-autonomous logistic-type differential equations via the Karhunen–Loève expansion and the Random Variable Transformation technique

“…It is worthy highlighting that in the context of RDEs, the RVT technique has been successfully applied to determine the 1-PDF of the solution stochastic process of relevant problems, formulated via RDEs, that appear in different areas [28,29,30,31].…”

Uncertainty quantification analysis of the biological Gompertz model subject to random fluctuations in all its parameters

“…When a closed-form solution of the RDE is available, the RVT technique is often useful to obtain an exact expression of the 1-PDF of the solution stochastic process [32,33]. This method has also been successfully applied to determine the 1-PDF of other random equations (see [34,35] for its application to solve random difference equations, and [36,37] to deal with random partial differential equations). The RVT method has demonstrated to be very useful to compute approximations of the 1-PDF of the aforementioned type of random equations in combination with other techniques such as Karhunen-Loève expansions [38,39], Fröbenius expansions [40], differential transform method [41], the homotopy method [42], numerical schemes [43,44], etc.…”

Random differential equations with discrete delay

“…However, the study of RDED needs further analysis. Indeed, while the theory and applications for random ordinary differential equations have been extensively studied in the extant literature [10][11][12][13], there is still a lack of analysis for important variations of RDE, like the ones formulated via delays. We must point out that one exception is the generalization to the random context of the classical theory of fractional differential equations performed in [14,15].…”