Syllabus

Topics in Probability, Math 8690, Fall 1998

The intention is to cover

• Properties of the Wiener process
• Stochastic Itô integral
• Itô stochastic equations
• Stationary processes and sequences:
  • Spectral analysis of second-order stationary processes
  • Ornstein-Uhlenbeck process
  • Processes with rational spectral density
  • Birkhoff-Khinchin theorem for stationary processes
• Processes with independent increments:
  • Levy-Khinchin theorem
  • Jump measures and the structure of trajectories
• Other topics can be treated upon request.

Five homeworks will be assigned and will form part of the final grade.

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