# Department of Statistics

## STAT 521

521—Applied Stochastic Processes. (3) (Prereq: STAT 511 with a grade of C or higher) An introduction to stochastic processes, including conditional probability, Markov chains, Poisson processes, and Brownian motion. Incorporates simulation and applications to actuarial science.

Sample Course Homepage: Recent Semester

Usually Offered: Alternating Spring Semesters

Learning Objectives: By the end of the term successful students should be able to do the following:

• Demonstrate a working knowledge of the basic definitions of discrete and continuous Markov chains, the Poisson process, Brownian motion and its preliminary stochastic calculus.
• Be able to effectively utilize the computer package R to perform the basic calculations required to apply the methods covered in the course, and to demonstrate the methods using simulation.
• Be able to apply the methods covered in the course to a large variety of problems one may encounter on actuarial exams.
• Appreciate how probability theory can be applied to the study of phenomena in fields as diverse as engineering, computer science, management science, the physical and social sciences, and operational research.

Current Textbook: Introduction to Probability Models (11th Ed.), Sheldon M. Ross, Academic Press, 2014.

 Topics Covered Chapters Time Review of Basic Probability: Events and random variables, permutations, combinations, simulation, conditional probability, independence, common distributions and their properties 1-2-3 2.5 weeks Discrete Markov chain theory: Chapman-Kolmogorov's equations, classification of states, equilibrium and its applications, branching processes, MCMC methods 4 3.5 weeks Exponential distribution and Poisson processes: memoryless property, counting processes, interarrival times, applications to insurance 5 2.5 weeks Continuous Markov models: Birth and Death processes, queueing models, limiting probabilities, transition functions 6 3 weeks Rudiments of Brownian motion, stochastic integration, Gaussian time series analysis 10 2.5 weeks

The above textbook and course outline should correspond to the most recent offering of the course by the Statistics Department. Please check the current course homepage or with the instructor for the course regulations, expectations, and operating procedures.

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