Matematica | STOCHASTIC PROCESSES
Matematica STOCHASTIC PROCESSES
cod. 0522200044
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 | |
|---|---|---|---|---|
| MAT/06 | 6 | 48 | LESSONS |
| Exam | Date | Session | |
|---|---|---|---|
| PROCESSI STOCASTICI | 21/06/2023 - 09:00 | SESSIONE ORDINARIA | |
| PROCESSI STOCASTICI | 12/07/2023 - 09:00 | SESSIONE ORDINARIA |
| 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. |
| More Information | |
|---|---|
| SOME UTILITIES AND EDUCATIONAL AIDS ARE AVAILABLE BY COURSE TEACHERS, ALSO THROUGH E-LEARNING PLATFORMS EMAIL: ADICRESCENZO@UNISA.IT, BMARTINUCCI@UNISA.IT CLASS ATTENDANCE IS RECOMMENDED. |
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