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The Generation of Correlated Non-Gaussian Random Variables with Diffusion Processes |
Hu Luo-quan; Zhu Hong-bo |
School of Communication and Information Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210003, China |
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Abstract Random variables of non-Gaussian distribution are produced by diffusion processes. Under the assumption of ergodicity, the stationary distribution of Markov diffusion processes described by a Stochastic Differential Equation (SDE) is obtained, which is determined by drift coefficient and diffusion coefficient. Let the drift coefficient be the first order power of x, and then the diffusion coefficient can be derived as a function of diffusion coefficient and aimed probability density function. As a result, the SDE is determined, and its solution by using Milstein high order method produces the aimed random variables. The correlation of the random samples can be adjusted through changing the constant of diffusion coefficient. Taking the Nakagami distribution and K-distribution as examples, simulation results are similar to the theoretical value, which validates the effectiveness of this method.
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Received: 20 July 2006
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