Students who pass the course satisfactorily will be able to
- determine the state descriptions, state spaces and index sets of the stochastic processes,
- formulate stochastic processes to study systems that evolve mostly over time randomly,
- identify the Markovian stochastic processes,
- completely characterize a CTMC with stable states by determining the corresponding embedded Discrete-Time Markov Chain and the exponential transition rates dependent on the current state,
- determine the time-dependent transition function,
- analyze the limiting behaviour of an irreducible recurrent CTMC,
- study real-life (queueing) applications of CTMCs,
- identify renewal cycles to formulate renewal processes,
- determine the ergodic structure of a renewal process,
- investigate the lifetime of a transient renewal process,
- investigate the limiting behaviour of a recurrent renewal process,
- study the real life problems by using alternating renewal processes, renewal reward processes and regenerative processes n the current state,
- identify the Martingale and Brownian Motion processes,
- use martingales to analyze Brownian Motion,
- work with the stopped processes by referring to the Martingale Stopping Theorem,
- analyze the hitting times of Brownian Motion.