Advances on Uncertainty Quantification: Theory and Modelling

Dear Colleagues,

Numerous physical, chemical, and biological phenomena, which are very important for scientistic and technological progress, have been traditionally formulated through mathematical models based on ordinary or partial differential equations, where the data (initial/boundary conditions, source term, and/or coefficients) are expressed by means of numerical values or deterministic functions. Nevertheless, scientists really fix these data from measurements, which are always subject to error. How satisfactory the results obtained from the model will be depends on the quality of these measurements (which can frequently take a lot of time and incur high costs). In addition to measurement errors, we must consider the random character of complex external factors that can affect the system, such as pressure, temperature, and humidity in Meteorology; the composition of the land in Seismology; investor tendency and economical policy of countries and companies in Finance; the environmental and genetical factors in Epidemiology; etc. These circumstances make it more advisable to consider the data as random magnitudes; if what is to be measured is a magnitude functionally independent of others values, it would be better to consider it as a random variable; when a dependency exists with respect to other magnitudes, such as time, space, etc., it would be more advisable to interpret it not as a function but as a stochastic process. The consideration of these facts leads to the reformulation of traditional deterministic models, which, in order to improve them, must be replaced by random models. Thus, this is the main purpose of this Special Issue: to gather contributions addressing new analytic and numerical methods and their applications to nontrivial problems to solve, simulate, and approximate random and stochastic equations in a wide sense (algebraic, difference, differential, integral, etc.). Applications of these equations in the settting of applications are particularly welcome.

Prof. Dr. Juan Carlos Cortés López
Prof. Dr. Rafael Villanueva Micó
Guest Editors

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