STATS 526 - Discrete State Stochastic Processes
Section: 001
Term: FA 2017
Subject: Statistics (STATS)
Department: LSA Statistics
Credits:
3
Requirements & Distribution:
BS
Waitlist Capacity:
45
Advisory Prerequisites:
MATH 525 or STATS 525 or EECS 501.
BS:
This course counts toward the 60 credits of math/science required for a Bachelor of Science degree.
Repeatability:
May not be repeated for credit.
Primary Instructor:

The material is divided between discrete and continuous time processes. In both, a general theory is developed and detailed study is made of some special classes of processes and their applications. Some specific topics include: Markov chains (Markov property, recurrence and transience, stationarity, ergodicity, exit probabilities and expected exit times); exponential distribution and Poisson processes (memoryless property, thinning and superposition, compound Poisson processes); Markov processes in continuous time (generators and Kolmogorov equations, embedded Markov chains, stationary distributions and limit theorems, exit probabilities and expected exit times, Markov queues); martingales (conditional expectations, gambling (trading) with martingales, optional sampling, applications to the computation of exit probabilities and expected exit times, martingale convergence); Brownian motion (Gaussian distributions and processes, equivalent definitions of Brownian motion, invariance principle and Monte Carlo, scaling and time inversion, properties of paths, Markov property and reflection principle, applications to pricing, hedging and risk management, Brownian martingales). Significant applications will be an important feature of the course.

STATS 526 - Discrete State Stochastic Processes
Schedule Listing
001 (LEC)
P
18976
Closed
0
 
-
TuTh 10:00AM - 11:30AM
002 (LEC)
P
25429
Closed
0
 
-
TuTh 8:30AM - 10:00AM
NOTE: Data maintained by department in Wolverine Access. If no textbooks are listed below, check with the department.


ISBN: 9781461436140
Essentials of stochastic processes, Author: Richard Durrett., Publisher: Springer 2nd ed. 2012
Required
ISBN: 9781118122372
Probability and measure : anniversary edition, Author: Patrick Billingsley., Publisher: Wiley 3. ed., an
Optional
ISBN: 9780471120629
Stochastic processes., Author: Sheldon M. Ross., Publisher: Routledge. 2nd ed. 1999
Optional
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