Stochastic Process
Preface
1 Basic Definitions of Stochastic Process, Kolmogorov Consistency Theorem (Lecture on 01/05/2021)
2 Stationarity, Spectral Theorem, Ergodic Theorem(Lecture on 01/07/2021)
3 Markov Chain: Definition and Basic Properties (Lecture on 01/12/2021)
4 Conditions for Recurrent and Transient State (Lecture on 01/14/2021)
5 First Visit Time, Mean Recurrent Time (Lecture on 01/19/2021)
6 Period, Ergodic, Communicate (Lecture on 01/21/2021)
7 Decomposition of States, Branching Process (Lecture on 01/26/2021)
8 Branching Process (Lecture on 01/28/2021)
9 Stationary Distribution of Markov Chain (Lecture on 02/02/2021)
10 Limiting Distribution of Markov Chain (Lecture on 02/04/2021)
11 Midterm (Lecture on 02/09/2021)
12 Poisson Process, Birth and Death Process (Lecture on 02/11/2021)
13 Birth and Death Process, MCMC for Discrete Distribution(Lecture on 02/16/2021)
14 MCMC for Continuous Distribution, Gaussian Process(Lecture on 02/18/2021)
15 Bayesian Inference for Gaussian Process(Lecture on 02/23/2021)
16 Low-rank Method to Fasten the Inference of Gaussian Process(Lecture on 02/25/2021)
17 Sparse Model to Fasten the Inference of Gaussian Process, Hidden Markov Model(Lecture on 03/02/2021)
18 Examples of HMM, Non-homogeneous Poisson Process(Lecture on 03/04/2021)
19 Full Bayesian Inference of NHPP(Lecture on 03/09/2021)
20 Final Project Presentation(Lecture on 03/11/2021)
21 Homework 1: Properties of Stochastic Process: Problems and Tentative Solutions
22 Homework 2: Markov Chain: Problems and Tentative Solutions
23 Homework 3: Poisson Process, Birth and Death Process: Problems and Tentative Solutions
24 Quiz 1: Brownian Motion and Markov Process: Problems and Tentative Solutions
25 Quiz 2: Poisson Process: Problems and Tentative Solutions
Presented by Jizhou Kang

STAT 243: Stochastic Process

STAT 243: Stochastic Process

Jizhou Kang

2021-03-12

Preface

This is an E-version notes of the Stochastic Process class in UCSC by Prof. Rajarshi Guhaniyogi, Winter 2021, typed by Jizhou Kang.