Sharif Digital Repository

We investigate the stochasticity in temperature fluctuations in the cosmic microwave background (CMB) radiation data from the Wilkinson Microwave Anisotropy Probe. We show that the angular fluctuation of the temperature is a Markov process with a Markov angular scale, ΘMarkov = 1.01 -0.07+0.09. We characterize the complexity of the CMB fluctuations by means of a Fokker-Planck or Langevin equation and measure the associated Kramers-Moyal coefficients for the fluctuating temperature field T (n̂)and its increment, ∇ T = T(n̂2). Through this method we show that temperature fluctuations in the CMB have fat tails compared to a Gaussian distribution. © 2006 IOP Publishing Ltd and SISSA  

We use multifractal detrended fluctuation analysis (MF-DFA), to study sunspot number fluctuations. The result of the MF-DFA shows that there are three crossover timescales in the fluctuation function. We discuss how the existence of the crossover timescales is related to a sinusoidal trend. Using Fourier detrended fluctuation analysis, the sinusoidal trend is eliminated. The Hurst exponent of the time series without the sinusoidal trend is 0.12 ± 0.01. Also we find that these fluctuations have multifractal nature. Comparing the MF-DFA results for the remaining data set to those for shuffled and surrogate series, we conclude that its multifractal nature is almost entirely due to long range...