it is known that a stochastic dierential equation (sde) induces two probabilisticobjects, namely a diusion process and a stochastic ow. while the diusion process isdetermined by the in nitesimal mean and variance given by the coecients of the sde,this is not the case for the stochastic ow induced by the sde. in order to characterize thestochastic ow uniquely the in nitesimal covariance give...

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 d...

in this paper, we present the numerical solution of ordinary dierential equations (or sdes), from each order especially second-order with time-varying and gaussian random coecients. we indicate a complete analysis for second-order equations in special case of scalar linear second-order equations (damped harmonic oscillators with additive or multi- plicative noises). making stochastic dierent...

this paper studies a maintenance policy for a system composed of two components, which are subject to continuous deterioration and consequently stochastic failure. the failure of each component results in the failure of the system. the components are inspected periodically and their deterioration degrees are monitored. the components can be maintained using different maintenance actions (repair...

Congestion management in electricity markets is traditionally done using deterministic values of power system parameters considering a fixed network configuration. In this paper, a stochastic programming framework is proposed for congestion management considering the power system uncertainties. The uncertainty sources that are modeled in the proposed stochastic framework consist of contingencie...

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...

the edge detour index polynomials were recently introduced for computing theedge detour indices. in this paper we nd relations among edge detour polynomials for the2-dimensional graph of tuc4c8(s) in a euclidean plane and tuc4c8(s) nanotorus.

in this paper, we intend to solve special kind of ordinary differential equations which is called heun equations, by converting to a corresponding stochastic differential equation(s.d.e.). so, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this s.d.e. is solved by numerically methods. mo...

This paper studies a maintenance policy for a system composed of two components, which are subject to continuous deterioration and consequently stochastic failure. The failure of each component results in the failure of the system. The components are inspected periodically and their deterioration degrees are monitored. The components can be maintained using different maintenance actions (repair...