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We consider an extension of the Gompertz homogeneous diffusion process by introducing time functions (exogenous factors) that affect its trend. After obtaining its transition probability density function, the inference on the parameters of the process is obtained by considering discrete sampling of the sample paths. Finally, we apply this stochastic process(More)
In this paper, we consider a Stochastic System modelling by the Stochastic Rayleigh Diffusion Process and we discuss theoretical aspects of the latter and establish a statistical methodology to adjust it to real cases, particulary, in the field of biometry and related areas. of Applied Probability 23 (1986) 398–408], is examined from the perspective of the(More)
This paper proposes a means of using stochastic diffusion processes to model the total consumption of electrical power (including distribution and transport losses) in Morocco, as recorded by the official data for total sales published by Office Nationale de l'E ´ lectricité (ONE), the Moroccan electricity authority. Two models of univariate stochastic(More)
SUMMARY In this paper we propose a bivariate stochastic Gompertz diffusion model as the solution for a system of two Itô stochastic differential equations (SDE) that are similar as regards the drift and diffusion coefficients to those considered in the univariate Gompertz diffusion model, which has been the object of much study in recent years. We establish(More)
—Stochastic modeling concerns the use of probability to model real-world situations in which uncertainty is present. Therefore, the purpose of stochastic modeling is to estimate the probability of outcomes within a forecast, i.e. to be able to predict what conditions or decisions might happen under different situations. In the present study, we present a(More)
In this paper we consider a new model of multivariate lognormal diffusion process with a vector of exogenous factors such that each component exclusively affects the respective endogenous variable of the process. Starting from the Kolmogorov differential equations and Ito's stochastics equation of this model, its transition probability density is obtained.(More)
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