Antonio DI CRESCENZO | STOCHASTIC PROCESSES
Antonio DI CRESCENZO STOCHASTIC PROCESSES
cod. 0522200044
STOCHASTIC PROCESSES
| 0522200044 | |
| DEPARTMENT OF MATHEMATICS | |
| EQF7 | |
| MATHEMATICS | |
| 2024/2025 |
| 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 | 14/01/2025 - 09:00 | SESSIONE DI RECUPERO | |
| PROCESSI STOCASTICI | 04/02/2025 - 09:00 | SESSIONE DI RECUPERO | |
| PROCESSI STOCASTICI | 25/02/2025 - 09:00 | SESSIONE DI RECUPERO |
| Objectives | |
|---|---|
| LEARNING OUTCOMES: THE COURSE HAS THE PRIMARY AIM OF PROVIDING THE ESSENTIAL NOTIONS INHERENT TO STOCHASTIC PROCESSES. KNOWLEDGE AND UNDERSTANDING: THE STUDENT WILL ACQUIRE IN-DEPTH KNOWLEDGE OF THE ESSENTIAL TOPICS OF THE THEORY OF STOCHASTIC PROCESSES, AND WILL ALSO DEVELOP THE ABILITY TO IDENTIFY A TIME-VARYING STOCHASTIC MODEL AND UNDERSTAND ITS MAIN CHARACTERISTICS. ABILITY TO APPLY KNOWLEDGE AND UNDERSTANDING: THE STUDENT WILL ACQUIRE INDUCTIVE AND DEDUCTIVE REASONING SKILLS IN DEALING WITH PROBLEMS INVOLVING RANDOM PHENOMENA THAT EVOLVE OVER TIME, AND WILL ALSO DEVELOP THE ABILITY TO SCHEMATIZE A RANDOM PROCESS IN RIGOROUS TERMS, TO SET UP PROBLEMS CONNECTED TO THEM AND TO SOLVE THEM USING APPROPRIATE PROBABILITY TOOLS. MAKING JUDGEMENTS: THE STUDENT WILL BE ABLE - TO BUILD A MATHEMATICAL MODEL FOR THE REPRESENTATION OF A COMPLEX REAL PHENOMENON THAT EVOLVES UNDER CONDITIONS OF UNCERTAINTY, - TO DESCRIBE ITS MAIN CHARACTERISTICS AND PREDICT ITS EVOLUTION OVER TIME, - TO ADAPT THE FORMAL STRATEGIES EXAMINED DURING THE COURSE TO NEW CONTEXTS. COMMUNICATION SKILLS: WITH REFERENCE TO PHENOMENA THAT EVOLVE OVER TIME IN RANDOM CONDITIONS, THE STUDENT WILL BE ABLE - TO FORMALLY DESCRIBE COMPLEX CONCEPTS REFERRING TO THESE PHENOMENA, - TO FULLY ILLUSTRATE THEIR FUNDAMENTAL PROPERTIES, - TO RIGOROUSLY ARGUE THE STRATEGIES FOR SOLVING RELATED PROBLEMS. LEARNING ABILITY: THE STUDENT WILL BE ABLE - TO USE TRADITIONAL BIBLIOGRAPHIC TOOLS AND IT RESOURCES FOR INDEPENDENT STUDY, - TO UNDERSTAND AND INTERPRET COMPLEX TEXTS, - TO PROCEED WITH THE CONTINUOUS UPDATING OF ONE'S KNOWLEDGE, USING TECHNICAL AND SCIENTIFIC LITERATURE. |
| 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. |
| 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 EDUCATIONAL AIDS ARE AVAILABLE THROUGH THE TEAMS E-LEARNING PLATFORM EMAIL: ADICRESCENZO@UNISA.IT, BMARTINUCCI@UNISA.IT CLASS ATTENDANCE IS RECOMMENDED. |
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