# Matematica | STOCHASTIC PROCESSES

## Matematica STOCHASTIC PROCESSES

 0522200044 DIPARTIMENTO DI MATEMATICA EQF7 MATHEMATICS 2022/2023

 OBBLIGATORIO YEAR OF COURSE 1 YEAR OF DIDACTIC SYSTEM 2018 SPRING SEMESTER
SSD CFU HOURS ACTIVITY TYPE OF ACTIVITY MAT/06 6 48 LESSONS COMPULSORY SUBJECTS, CHARACTERISTIC OF THE CLASS
 ANTONIO DI CRESCENZO T BARBARA MARTINUCCI
ExamDate
PROCESSI STOCASTICI21/06/2023 - 09:00
PROCESSI STOCASTICI12/07/2023 - 09:00
Objectives
THIS COURSE IS FINALIZED TO ILLUSTRATE THE FUNDAMENTAL TOPICS OF STOCHASTIC PROCESSES.

KNOWLEDGE AND UNDERSTANDING

THOROUGH UNDERSTANDING OF THE BASIC TOPICS OF STOCHASTIC PROCESSES. ABILITY TO IDENTIFY A RANDOM DYNAMIC SYSTEM AND TO UNDERSTAND ITS MAIN FEATURES.

APPLYING KNOWLEDGE AND UNDERSTANDING

INDUCTIVE AND DEDUCTIVE REASONING SKILLS IN DEALING WITH PROBLEMS INVOLVING TIME-DEPENDING RANDOM PHENOMENA. ABILITY TO OUTLINE A STOCHASTIC PROCESS, TO SET UP A PROBLEM AND TO SOLVE IT USING APPROPRIATE PROBABILISTIC TOOLS.
Prerequisites
THE STUDENT MUST HAVE ACQUIRED THE BASIC NOTIONS OF PROBABILITY THEORY.
Contents
TOPICS IN MEASURE THEORY. CONDITIONAL MEANS. STOPPING TIMES. MARTINGALES. STOCHASTIC PROCESSES. MARKOV CHAINS. RANDOM WALK. POISSON PROCESS. COUNTING PROCESS. RENEWAL PROCESS. STOCHASTIC ORDERS. INTRODUCTION TO RELIABILITY THEORY. BROWNIAN NOTION. WIENER PROCESS. DIFFUSION PROCESS. TELEGRAPH PROCESS.
Teaching Methods
CLASSROOM LECTURES.
Verification of learning
ORAL EXAMINATION TO TEST THE KNOWLEDGE OF THE DISCIPLINE.

ORAL EXAMINATION TESTS TO BE PERFORMED DURING THE LESSONS MAY BE PROVIDED ON REQUEST OF THE STUDENTS.
Texts
- SCHILLING R.L. (2017) MEASURES, INTEGRALS AND MARTINGALES, 2ND EDITION, CAMBRIDGE UP.
- ROSS S.M. (1996) STOCHASTIC PROCESSES. II EDIZIONE. WILEY.
- RESNICK S. (2005) ADVENTURES IN STOCHASTIC PROCESSES. BIRKHÄUSER.
- NORRIS J.R. (1997) MARKOV CHAINS. CAMBRIDGE UNIVERSITY PRESS.
- DINEEN, S. (2013) PROBABILITY THEORY IN FINANCE. A MATHEMATICAL GUIDE TO THE BLACK-SCHOLES FORMULA. 2ND EDITION. AMERICAN MATHEMATICAL SOCIETY, PROVIDENCE.