Stochastic Processes

Learning Outcomes

This course provides an introduction to stochastic processes in communications, signal processing and digital and computer systems. Topics include continuous and discrete random processes, correlation and power spectral density, Markov chains, and queuing theory.

At the end of this course, students will have acquired advanced/in depth knowledge in the field of Stochastic Processes, with particular emphasis on Probabilities, Stochastic Analysis, Stochastic Modelling and design of systems and signals with stochastic behavior.

The students will be capable of formulating and processing problems using Stochastic Analysis tools, quantitatively and qualitatively assessing stochastic properties and applying these methodologies and design principles to real world problems in telecommunication networks, taking into account critical parameters, such as spectral efficiency requirements, noise spectral density, interference, signals and waveforms.

Course Contents

• Introduction: review of probability theory, Stochastic Processes, types of stochastic processes.
• Mean and ergodicity.
• Gaussian stochastic processes.
• Multi-variable stochastic processes.
• Independent, identically distributed random sequences.
• Discrete stochastic processes.
• Continuous stochastic processes.
• Markov chains: introduction to Markov chains, discrete-time Markov chains.
• Poisson processes: theory and applications.
• Stationary processes.
• Transmission of a random process through a linear time-invariant filter.
• Power spectral density.

Recommended Readings

• Papoulis A., Unnikrishna, S. Pillai (2002): Probability, Random Variables and Stochastic Processes, McGraw-Hill Education – Europe.
• Yates R. & Goodman D. J. (2004): Probability and Stochastic Processes, John Wiley & Sons.