30515  APPLIED STOCHASTIC PROCESSES
Department of Decision Sciences
GIACOMO ZANELLA
Suggested background knowledge
Mission & Content Summary
MISSION
CONTENT SUMMARY
 Conditional probabilities and conditional expectations.
 Introduction to stochastic processes and Markov chains.
 Discretetime Markov chains: ChapmanKolmogorov equation, Classification of states, Limiting properties, Applications (e.g. stochastic models, sequential testing, website ranking).
 Introduction to Stochastic Simulation, Simulation techniques and Monte Carlo methods.
 Markov Chain Monte Carlo algorithms, Computational applications.
 Counting processes and the Poisson process, Continuoustime stochastic processes, Examples and modeling applications.
Intended Learning Outcomes (ILO)
KNOWLEDGE AND UNDERSTANDING
 Understand the connection between simple random variables and more elaborate and realistic stochastic processes.
 Formulate and analyse probabilistic models based on Markov chains and counting processes.
 Understand the principles of stochastic simulation and Monte Carlo algorithms.
APPLYING KNOWLEDGE AND UNDERSTANDING
 Translate realworld situations involving randomness and uncertainty into probabilistic models.
 Exploit the tools of probability theory to answer relevant questions, such as: what is the equilibrium distribution of a specific stochastic system? What is the probability of a certain outcome?
 Use software to simulate the evolution of probabilistic systems. Design simple Monte Carlo algorithms for computational purposes.
 Apply stochastic processes to model and solve realworld problems commonly occurring in diverse fields, such as business, industry, economics, finance and data science.
Teaching methods
 Facetoface lectures
 Exercises (exercises, database, software etc.)
DETAILS
The main learning activity of this course consists in facetoface lectures. Lectures integrate discussions of theoretical notions, such as mathematical definitions, with examples and inclass solution of exercises. The aim of the examples and exercises shown in class is two folded:
 First to illustrate and visualize the theoretical notions with simple examples.
 Secondly to describe realworld applications (both modeling and computational) of the probabilistic tools.
In addition, the R statistical software is used in class to display computer simulations of the stochastic models under consideration. A set of exercises are provided for students to practice and get familiar with the lectures’ content.
Assessment methods
Continuous assessment  Partial exams  General exam  


x 
ATTENDING AND NOT ATTENDING STUDENTS
The assessment for all students, both attending and nonattending, consists in a written exam. The aim of the exam is to verify both the students’ understanding of the theoretical material (e.g. ability to provide definitions and characterizations of some noteworthy stochastic process), and their capacity to apply the theory for modeling or computational purposes (e.g. ability to identify appropriate models for a given situation and use them to answer specific questions).
Teaching materials
ATTENDING AND NOT ATTENDING STUDENTS
S.M. ROSS, Introduction to probability models, Academic Press, 2014.