
Mohammad Reza Rahimi TabarCurrent Course 




1) Stochastic Processes Part IL1 (Time and Ensemble averaging) L2 (Joint and conditional probability distribution functions) L3 (Generating functions, kurtosis, skewness, correlation functions, stationary processes) L4 (Spectral Density) L5 ( Spectral Density  Fast Fourier Transformation (FFT )) L61 (Spectral Density  Maximum Entropy Method1 ) L62 (Spectral Density  Maximum Entropy Method2, YuleWalker Equations) L7 (Cumulants, Multidimensional Gaussian distribution, Wick theorem) L8 (Classification of stochastic processes, Markov processes, ChapmanKolmogorov equation, Markov time or length scale, Langevin equation, Brownian motion) L9 (Synthesis of correlated Gaussian signal,
BoxMuller method, Generation of longrange, scaling correlated signal,
FourierFiltering Method) L10 (RandomWalk, Detrended Fluctuation Analysis(DFA), Detrended Moving Average (DMA)) L11
(RescaledRangeAnalysis (R/S), Multifractals and Singularity Spectrum) L12 (Multifractal
Detrended Fluctuation Analysis(MFDFA) and Renyi exponents (or generalized
fractal dimension D(q) ),Shuffled and Surrogate time series, Fourier
Detrended Fluctuation Analysis(FDFA), Wavelet transformation1) L13 (Windowed Fourier
Transformation (WFT), Wavelet Transformation2, Lipchitz Regularity, Wavelet
Transform Modulus Maxima Method (WTMM), Comparison of Multifractal exponents
of MFDFA and WTMM) L14 (Density Function
Estimation: {Naive, Kernel, Sample distribution function, NearestNeighbors and
Variable kernel estimators}, ChiSquare Test, Estimation
of the Markov time or length scales via ChiSquare test, KolmogorovSimrnov
Test, KullbackLeibler entropy (distance), AndersonDarling Test) L151 ,L152 ( Maximum Likelihood Function, Confidence Levels and Intervals)
Part II
L16 (KramersMoyal Forward and Backward Expansions, Formal Solution, KaramersMoyal coefficents of Brownian Motion) L17 (Pawula Theorem, Stationary Solution of the FokkerPlanck Equation, Transition Probability Density for Small Times, PathIntegral Solutions of Time Dependent PDF) L18 (Wiener Process,
NonDifferentiability of Sample Path, L19 (FirstPassageTime and Its Moments in terms of Drift and Diffusion Coefficients, Escape Over a Potential Barrier, Level Crossing ) L20 ( The Ito and Stratonovich Integrals, Nonparticipating Functions, Ito Relation, FokkerPlanck Equation of the General Langevin Equation, Kubo Oscillator, BlackScholes Stochastic Differential Equation)
Part IIIL21 ( Scaling Functions and Scaling Invariance, Discrete Scale Invariance, Scaling Invariance in Stochastic Prosseses, Fractional Brownian Motion (FBM),Fractional Gaussian noise (FGn), The realation between the DFA exponent and Hurst exponent of FBM and FGn signals, Generation of FBM signal as an optimization problem)










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