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Stochastic Processes
概述
CEA CAPA Partner 机构: Universidad Carlos III de 马德里
地点: 马德里,西班牙
Primary Subject Area: 数学
指令: 英语
课程代码: 18282
Transcript Source: Partner 机构
课程详细信息: 400级
Recommended Semester Credits: 3
联系时间: 42
先决条件: Probbability (Year 2 - Semester 2)
描述
1. Introduction to Stochastic Processes.
1.1. Basic Definitions and Notations.
1.2. Examples: branching processes and queues.
1.3. Review of Conditional Expectation.
1.4. Review of Characteristic Functions and applications.
2. Discrete time Markov Chains.
2.1. Basic Definitions and Notations.
2.2 Chapman-Kolmogorov Equations and classification of states.
2.3. Asymptotic results.
2.4. First Step Analysis.
2.5. Random Walks and Success Runs.
2.6 The Geo/Geo/1 queue.
3. Renewal Theory and Poisson process.
3.1 Definition and basic notions.
3.2 The Elementary Renewal Theorem.¿
3.3 The Key Renewal Theorem.
3.4 The Delayed Renewal Theorem.
3.5 Compound Poisson Process.
4. Continuous time Markov Chains.
4.1 Definition and basic notions¿
4.2 Chapman-Kolmogorov Equations and Limit Theorems
4.3 Birth and Death Processes (M/M/m queues).
5. Continuous time Markov Processes: Brownian Motion.
5.1 Brownian Motion and Gaussian Processes.
5.2 Variations and Extensions.
5.3命中次数.¿
5.4 Relation with Martingales.
1.1. Basic Definitions and Notations.
1.2. Examples: branching processes and queues.
1.3. Review of Conditional Expectation.
1.4. Review of Characteristic Functions and applications.
2. Discrete time Markov Chains.
2.1. Basic Definitions and Notations.
2.2 Chapman-Kolmogorov Equations and classification of states.
2.3. Asymptotic results.
2.4. First Step Analysis.
2.5. Random Walks and Success Runs.
2.6 The Geo/Geo/1 queue.
3. Renewal Theory and Poisson process.
3.1 Definition and basic notions.
3.2 The Elementary Renewal Theorem.¿
3.3 The Key Renewal Theorem.
3.4 The Delayed Renewal Theorem.
3.5 Compound Poisson Process.
4. Continuous time Markov Chains.
4.1 Definition and basic notions¿
4.2 Chapman-Kolmogorov Equations and Limit Theorems
4.3 Birth and Death Processes (M/M/m queues).
5. Continuous time Markov Processes: Brownian Motion.
5.1 Brownian Motion and Gaussian Processes.
5.2 Variations and Extensions.
5.3命中次数.¿
5.4 Relation with Martingales.
