A method for the WSN channel modeling via stochastic differential equations and its applications

Exponential correlated random variables are generated by stochastic differential equations (SDEs), which are described by Markov diffusion processes. Under the assumption of ergodicity of stochastic process, the stationary distribution of Markov diffusion process is introduced, which is determined by drift and diffusion coefficient. We choose the drift coefficient as a linear function. The drift coefficient can be derived directly from diffusion coefficient and aimed probability density function (pdf). As a result, a generalized method for the generation of exponential correlated random variables is determined. We compare the different diffusion coefficients of Markov model. The new diffusion coefficient model can be used in Milstein high order method and the corresponding algorithm is more robust. The correlation of the random samples can be adjusted through changing a single parameter of diffusion coefficient. The generation of approximately uniformly distributed random variables with exponential correlation is introduced as an example of generating random variables with a specified pdf and correlation function, where there is no determined closed form expression of the pdf. Simulation results validate the accuracy and the effectiveness of this method.