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Hilbert Spaces. Probability Spaces, Expectation and Integration. Convergence. Conditional Expectation. Radon-nykodym Derivative, Complements in Integration and Measure Theory. Stochastic Processes, Martingales. Continucus Time Processes, Brownian Motion. Discrete Time Markov Processes# Characterization. Stability, Criteria. Continuous Time Markov Processes, Notion of Generator, Jump Processes, Semi-markov Processes.

Faculty: Electrical and Computer Engineering
|Undergraduate Studies |Graduate Studies

Pre-required courses

44202 - Random Signals

Course with no extra credit

48868

• Brownian motion and stochastic calculus - Karatzas, Ioannis
• Brownian Motion and Stochastic Calculus - Karatzas, Ioannis.
• Markov processes : characterization and convergence - Ethier, Stewart N.
• Markov processes : characterization and convergence - Ethier, Stewart N.
• Markov processes characterization and convergence - Ethier, Stewart N.,
• Probability : theory and examples - Durrett, Richard
• Probability : theory and examples - Durrett, Richard
• Probability : theory and examples - Durrett, Richard
• Probability : theory and examples - Durrett, Richard,
• Probability and random processes - Grimmett, Geoffrey R.
• Probability theory and examples - Durrett, Richard
• Probability theory and examples - Durrett, Richard,
• Random processes for engineers - Hajek, Bruce