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Stochastic processes

 

• Discrete-time and continuous-time models, Time averages and ergodic principle
• Sampling principle and interpolation, Simulation of random processes

MATH 645. Advanced Stochastic Processes

• Weak convergence, Random walks , Brownian motion, Martingales
• Stochastic integration , Ito Formula, Stochastic differential equations, applications

Topics for Stochastic process

• Probability theory, limit theorems, conditional distributions, Moredimensional Gauss distribution, generating functions, characteristic functions, convergence in quadratic mean , convergence in distribution, probability on systems of fuzzy sets, Markov chains, Kolmogorov equation, classification , applications, Markov processes, exponential distribution , Poisson process, convolution of exponential distributions.
• models of queueing systems , Basic classification of stochastic processes, stationarity, Wiener process, Conditional probability, basic definition of stochastic processes, Discrete time Markov chains, Modelling of real life systems as Markov chains, transient behaviour, limiting behaviour , classification of states, first passage , recurrence times, absorption problems, ergodic theorems, Markov chains with costs , rewards, reversibility, Poisson processes.