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Stationary increments
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Related lectures (13)
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Levy Flights and Central Limit Theorem
Covers Levy flights, Central Limit Theorem, and Mesoscopic Master Equation with transition rates in an assurance system.
Stochastic Differential Equations
Covers Stochastic Differential Equations, Wiener increment, Ito's lemma, and white noise integration in financial modeling.
Fourier Transform and Spectral Densities
Covers the Fourier transform, spectral densities, Wiener-Khinchin theorem, and stochastic processes.
Markov Chains: Homogeneous Processes and Stationary Distributions
Explores Markov chains, focusing on homogeneous processes and stationary distributions, with practical exercises.
General Linear Processes: Wold Decomposition Theorem
Explores general linear processes, the Wold decomposition theorem, and spectral analysis in time series analysis.
Poisson processes
Covers the properties and construction of Poisson processes from i.i.d. Exp(X) random variables, emphasizing the importance of the process rate and jump time distributions.
Fokker-Planck Equations
Explores Fokker-Planck equations, escape rates, and first passage time analysis in statistical physics.
Limiting Distribution and Ergodic Theorem
Explores limiting distribution in Markov chains and the implications of ergodicity and aperiodicity on stationary distributions.
Elements of Statistics: Memorylessness and Stationary Processes
Covers memorylessness, stationary processes, MLE estimation, and random walks.
Ergodic Theory: Markov Chains
Explores ergodic theory in Markov chains, discussing irreducibility and unique stationary distributions.
Spectral Analysis: Integrated Spectrum and Autocovariance
Explores spectral analysis, integrated spectrum, autocovariance, estimation, and convergence in time series models.
Stochastic Models for Communications: Markov Chains and Random Variables
Covers Markov chains, random variables, independence, characteristic functions, and queueing theory.
Stochastic Processes: Generation and Embedding
Explores the generation of stochastic processes, including Gaussian processes, Markov processes, Poisson processes, and circulant embedding.
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