Math
450, Applied Probability Models
Textbook
An Introduction to Probability Models,
by S. M. Ross. Seventh edition.
List of material to be covered
This list is not absolutely fixed.
The material from the book can be suplemented and/or
complemented to provide the Applied Probability Models
requirements in the Third
Exam of the actuarial societies.
Chapter 4: Markov Chains
Introduction to Markov chains. Chapman-Kolmorogov equations.
Communicating classes.
Transient, positive recurrent and null recurrent states. Limiting
probabilities.
Hitting probabilities.
Mean hitting times. Mean time spent on transient states.
Transit probabilities. Branching processes. Gambler's ruin problem.
Random walks.
Sections 4.1-4.7 from the textbook, completed with hitting
probabilities and mean time
probabilities.
Chapter 5: Poisson process
Exponential and gamma distribution. Poisson process.
Interarrival and waiting time distributions.
Nonhomogeneous Poisson process. Compound Poisson process.
All sections from the textbook.
Chapter 10: Brownian motion and stationary processes
Brownian motion. Hitting times, Maximum variables. Brownian motion with
a drift.
Geometric Brownian motion.
Sections 10.1-10.3 from the textbook.
Chapter 6: Continuous-time Markov chains
Continuous-time Markov chains. Birth and death processes. Transition
probabilities.
Limiting probabilities.
Sections 6.1-6.5 from the textbook.
Chapter 7: Renewal theory and its applications
Sections to be covered at the discretion of the instructor.
Chapter 8: Queueing Theory
Sections to be covered at the discretion of the instructor.
Chapter 9: Reliability Theory
Sections to be covered at the discretion of the instructor.