In this paper, a stochastic two-stage model is offered for optimization of the day-ahead scheduling of the microgrid. System uncertainties including dispatchable distributed generation and energy storage contingencies are considered in the stochastic model. For handling uncertainties, Monte Carlo simulation is employed for generation several scenarios and then a reduction method is used to decr...

In this paper, we consider learning of spatio-temporal processes by formulating a Gaussian process model as a solution to an evolution type stochastic partial differential equation. Our approach is based on converting the stochastic infinite-dimensional differential equation into a finite dimensional linear time invariant (LTI) stochastic differential equation (SDE) by discretizing the process ...

Emerging diseases in animals and plants have led to much research on questions of evolution and persistence of pathogens. In particular, there have been numerous investigations on the evolution of virulence and the dynamics of epidemic models with multiple pathogens. Multiple pathogens are involved in the spread of many human diseases including influenza, HIV-AIDS, malaria, dengue fever, and ha...

In this article we present the modeling of bi-stability view problems described by the activity or firing rates of two interacting population of neurons. Starting from the study of a complex system, the system of stochastic differential equations describing the time evolution of the activity of the two populations of neurons, we point out the strength and weakness of this model and consider its...

This paper demonstrates the use and value of stochastic differential equations for modeling space-time data in two common settings. The first consists of point-referenced or geostatistical data where observations are collected at fixed locations and times. The second considers random point pattern data where the emergence of locations and times is random. For both cases, we employ stochastic di...

Continuous approximations that are ordinary differential equations (ODEs) or stochastic differential equations (SDEs) are often used to study the properties of discrete stochastic processes. We show that different ways of taking the continuous limit of the same model may result in either an ODE or a SDE and study the manner in which each approximates the discrete model. We compare the asymptoti...