EE 531 - Probability and Stochastic Processes

Weekly outline

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  General

  EE 531

  Probability and Stochastic Processes

  Instructor: Prof. Dr. Elif Uysal

  
  

  Course Content

  Review of probability theory. Sequence of random variables, stochastic convergence. Discrete stochastic processes: The Poisson process, Counting processes, Renewal processes. Finite State Markov Chains, Countable state Markov Chains. Gaussian processes, Brownian motion.

  
  
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  Course Materials

  • Lecture 1: MEASURABLE SPACES File
  • Lecture 2: PROBABILITY SPACES File
  • Lecture 3: CONTINUITY OF PROBABILITY, BAYES' S RULE, INDEPENDENCE File
  • Lecture 4: BOREL CANTELLI LEMMAS File
  • Lecture 5: PROOF OF THE BOREL CANTELLI LEMMAS File
  • Lecture 6: RANDOM VARIABLES File
  • Lecture 7: CUMULATIVE DISTRIBUTION FUNCTION (CDF) File
  • Lecture 8: DISCRETE RANDOM VARIABLES File
  • Lecture 9: CONTINUOUS RANDOM VARIABLES File
  • Lecture 10: INTRODUCTION TO STOCHASTIC PROCESSES File
  • Lecture 11: DISCRETE STOCHASTIC PROCESSES File
  • Lecture 12: EXPECTATION File
  • Lecture 13: VARIANCE File
  • Lecture 14: COVARIANCE File
  • Lecture 15: CONDITIONAL EXPECTATION File
  • Lecture 16: ITERATED EXPECTATION File
  • Lecture 17: MARKOV & CHEBYCHEV INEQUALITIES File
  • Lecture 18: CONVERGENCE IN PROBABILITY File
  • Lecture 19: CONVERGENCE IN DISTRIBUTION File
  • Lecture 20: MEAN SQUARE SENSE AND ALMOST SURE CONVERGENCE File
  • Lecture 21: EXAMPLE: ALMOST SURE CONVERGENCE File
  • Lecture 22: EXAMPLE: IN PROBABILITY vs MSE CONVERGENCE File
  • Lecture 23: EXAMPLE: MSE CONVERGENCE DOES NOT IMPLY ALMOST SURE CONVERGENCE File
  • Lecture 24: COUNTING PROCESSES File
  • Lecture 25: THE POISSON PROCESS (DEFINITION 1) File
  • Lecture 26: THE POISSON PROCESS (DEFINITION 2) File
  • Lecture 27: THE POISSON PROCESS (DEFINITION 3) File
  • Lecture 28: MERGING AND SPLITTING POISSON PROCESSES File
  • Lecture 29: POISSON PROCESS EXAMPLE File
  • Lecture 30- MARKOV CHAINS File
  • Lecture 31: CONVERGENCE IN MARKOV CHAINS File
  • Lecture 32: MARKOV CHAINS: CLASSIFICATION OF STATES PART 1 File
  • Lecture 33: MARKOV CHAINS: CLASSIFICATION OF STATES PART 2 File
  • Lecture 34: CLASSIFICATION OF MARKOV CHAINS File
  • Lecture 35: MARKOV CHAINS: CONVERGENCE File
  • Lecture 36: STATIONARY DISTRIBUTIONS IN A MARKOV CHAIN File
  • Lecture 37: EXPECTED FIRST PASSAGE TIME File
  • Lecture 38: MARKOV CHAINS WITH REWARDS File
  • Lecture 39: STRONG LAW FOR RENEWAL PROCESSES File
  • Lecture 40: RENEWAL REWARD PROCESSES TIME AVERAGE REWARD File
  • Lecture 41: EXAMPLES RENEWAL REWARD PROCESSES TIME AVERAGE REWARD File
  • Lecture 42: MARTINGALES File
  • Lecture 43: MARTINGALES - 2 File
  • Lecture 44: STOPPING TIMES File
  • Lecture 45: STOPPED MARTINGALES AND WALD'S EQUALITY File
  • Lecture 46: APPLICATION OF WALD'S EQUALITY File