COURSE SYLLABUS

Course Number: MATH 6680
Course Title: PROBABILITY AND STOCHASTIC PROCESSES II
Credit Hours: 3
Prerequisites: MATH 6670
 
I.	Course Objectives: To provide students having a good calculus background with a solid mathematical treatment of the fundamental concepts and techniques of probability theory and stochastic processes. The course will emphasize the use of probabilistic (intuitive) reasoning to create probability models for applications to queuing systems, inventory models etc. Simulation will be used to help students to develop their intuition.

	Schedule and Outline of Course Content. (Individual instructors may re-arrange the material and use different headings.)

	Multivariate distributions (6 classes)
Joint distributions, expectations of functions of random vectors, independence. Sums of independent random variables and the Central Limit Theorem (4 classes)
	Laplace transforms, convolutions, weak convergence, simulation.
	Renewal Processes (9 classes)
Renewal equations, excess, current and total life, renewal reward processes, limiting theorems, stationary and transient renewal processes, applications .
	Continuous-time Markov chains (9 -12 classes)
The Kolmogorov differential equations, the limiting probabilities, absorbing chains, phase-type distributions, reward processes, reversibility.
	Markov renewal and semi-regenerative processes (6-9 classes)
Markov renewal functions and equations, semi-Markov processes.	
Brownian motion and diffusion (6-9 classes)
An introduction emphasizing heuristics. Applications to finance and stochastic optimal control. Diffusions, Ito Calculus, Stochastic differential equations.

	3. Possible Textbooks: 
		The Essentials of Probability, Durrett (1994);
		Probability, Pitman (1993)
		An Introduction to Stochastic Processes, Kao (1997).
		An Introduction to Stochastic Modeling, 3rd edition, Karlin and Taylor (1998)	Other texts may be used by individual.

II.	Grading and Evaluation Procedures:
1. Course requirements: Typically tests, midterm exam, final exam are used with other methods of evaluation employed at the discretion of the instructor.
2. Grading system and percentages are determined by the instructor.

III. 	Policies related to the conduct of the class are set by individual instructors.