On a method of solving of possibilistic-probabilistic programming problems

В статье исследуется задача возможностно-вероятностной оптимизации, основанная на принципе ожидаемой возможности, и метод решения ее стохастического аналога в случае слабейшей t-нормы, описывающей взаимодействие нечетких параметров. Получены более простые для проверки условия, обеспечивающие сходимость метода стохастических квазиградиентов решения эквивалентного стохастического аналога. The paper studies possibilistic-probabilistic optimization problems, based on the principle of expected possibility, and a method for solving its stochastic analogue in the case of the weakest t-norm describing the interaction of fuzzy parameters. The conditions that are easier to verify and ensure the convergence of the method of stochastic quasigradients of the solution of an equivalent stochastic analog are obtained.

On the Construction of Some Deterministic and Stochastic Non-Local SIR Models

Fractional-order epidemic models have become widely studied in the literature. Here, we consider the generalization of a simple SIR model in the context of generalized fractional calculus and we study the main features of such model. Moreover, we construct semi-Markov stochastic epidemic models by using time changed continuous time Markov chains, where the parent process is the stochastic analog of a simple SIR epidemic. In particular, we show that, differently from what happens in the classic case, the deterministic model does not coincide with the large population limit of the stochastic one. This loss of fluid limit is then stressed in terms of numerical examples.

Stochastic resonance as the averaged response to random broadband excitation and its possible applications

Within the framework of vibrational mechanics, a stochastic analog of the Stephenson–Kapitza pendulum with random two-dimensional oscillations of the suspension point was considered and the dynamic properties of its averaged motion were studied. It is shown that, unlike the ordinary Stephenson–Kapitsa pendulum with deterministic vertical oscillations of the suspension point, both an increase and a decrease in the effective natural frequency are possible under the influence of high-frequency stochastic oscillations. A formula is derived for the amplitude of low-frequency oscillations as a function of the intensity of high-frequency stochastic oscillations and the possibility of a stochastic resonance in this system is shown. The dependence of the stochastic resonance on the mass and the damping coefficient is analyzed. It is shown that the points of the stochastic resonance lie in the plane of parameters “intensity of stochastic excitation” and “amplitude of low-frequency oscillation” on a universal curve that is independent of the mass of the pendulum. Peculiar self-oscillations in a system for which stochastic oscillations are produced by a technological load and, therefore, depend monotonically on the amplitude of low-frequency oscillations are discussed. A schematic diagram of these phenomena is proposed. The motion of the machine is described by the same equations as the stochastic analog of the Stephenson–Kapitza pendulum with random two-dimensional oscillations of the suspension point. A strategy of control for such a vibro-machine is proposed with the aim of maintaining it at resonance and providing an energetically efficient mode of operation.

Development and comparative evaluation of a stochastic analog method to downscale daily GCM precipitation

There are a number of statistical techniques that downscale coarse climate information from general circulation models (GCMs). However, many of them do not reproduce the small-scale spatial variability of precipitation exhibited by the observed meteorological data, which is an important factor for predicting hydrologic response to climatic forcing. In this study a new downscaling technique (Bias-Correction and Stochastic Analog method; BCSA) was developed to produce stochastic realizations of bias-corrected daily GCM precipitation fields that preserve both the spatial autocorrelation structure of observed daily precipitation sequences and the observed temporal frequency distribution of daily rainfall over space. We used the BCSA method to downscale 4 different daily GCM precipitation predictions from 1961 to 1999 over the state of Florida, and compared the skill of the method to results obtained with the commonly used bias-correction and spatial disaggregation (BCSD) approach, a modified version of BCSD which reverses the order of spatial disaggregation and bias-correction (SDBC), and the bias-correction and constructed analog (BCCA) method. Spatial and temporal statistics, transition probabilities, wet/dry spell lengths, spatial correlation indices, and variograms for wet (June through September) and dry (October through May) seasons were calculated for each method. Results showed that (1) BCCA underestimated mean daily precipitation for both wet and dry seasons while the BCSD, SDBC and BCSA methods accurately reproduced these characteristics, (2) the BCSD and BCCA methods underestimated temporal variability of daily precipitation and thus did not reproduce daily precipitation standard deviations, transition probabilities or wet/dry spell lengths as well as the SDBC and BCSA methods, and (3) the BCSD, BCCA and SDBC methods underestimated spatial variability in daily precipitation resulting in underprediction of spatial variance and overprediction of spatial correlation, whereas the new stochastic technique (BCSA) replicated observed spatial statistics for both the wet and dry seasons. This study underscores the need to carefully select a downscaling method that reproduces all precipitation characteristics important for the hydrologic system under consideration if local hydrologic impacts of climate variability and change are going to be reasonably predicted. For low-relief, rainfall-dominated watersheds, where reproducing small-scale spatiotemporal precipitation variability is important, the BCSA method is recommended for use over the BCSD, BCCA, or SDBC methods.