Generation of The White Noise

1. Generation of The White Noise • Eui-Sun Lee • Department of Physics • Kangwon National University • Random number A random number is a number chosen from some specified distribution. Such numbers are required to be independent in order that there are no correlations between successive numbers. t1,t2 are statistically independent bounded random numbers, for any t1 and t2, and for t1t2. • Uniform distribution Usually the word “random” means “random with a uniform distribution”.

2. Box-Muller Transform • Box-Muller Transform A transformation transforms from a two-dimensional continuous uniform distribution to a two-dimensional normal distribution. If r1 ,r2 are random numbers uniformly and independently distributed in the interval (0,1), the transform : gives the normal distributed random numbers of mean zero and variance one.

3. Wiener Process and White-Noise • Wiener process • White-noise The Wiener process is white noise and also the derivative of wiener process w(t) is white-noise ,(t),

4. Summary 1. Box-muller transform transforms uniformly distributed variables to normal distributed variables of mean zero and variance one. 2. The Wiener process is white noise and also the derivative of wiener process is white-noise