Study with us

I.The Basic Information of the Course

Course Number:202012420037

The EnglishName of theCourse：Stochastic Analysis

The ChineseName of theCourse：随机分析

In-classHours andAllocation(total class hours:32, classroom teaching:32classhours.)

Credit(s):2

Semester:1

AppliedDiscipline(ProfessionalDegreeCategory)：Mathematics

CourseObjectOriented：Masteranddoctoral student

EvaluationMode:Closed-bookExamination

TeachingMethod:MixedTeaching

CourseOpening Department:Collegeof Mathematical Sciences

II.Prerequisite Course

Mathematical analysis,Real variable functions,Probability theory and Mathematical Statistics

III. The Objectives and Requirements of the Course

Through this course of study, make the student fully grasp measure theory, the basic knowledge of stochastic process, stochastic analysis, develop the students' ability of theoretical thinking, develop students' thinking, improve students' practical ability, for further study of statistics of each branch, engaged in professional research and application of statistics to lay a solid theoretical basis.

IV. The Content of the Course

1. Stochastic process: including discrete event Martingale, Markov process, stationary independent incremental process, General theory of Markov process.

2.stochastic analysis: including martingale and its properties, Brownian motion and square integrable martingale, stochastic integral

3. Mathematical statistics: including point estimation, hypothesis testing, interval estimation, Bayes estimation, goodness of fit test and non-parametric test, statistical measurement methods, maximum likelihood estimation

4. Nonparametric statistics: including estimation and test of nonparametric density function, nonparametric regression, and additive model

5. Regression analysis: including basic knowledge of regression analysis, model introduction, parameter estimation, hypothesis testing and interval estimation, model diagnosis, anOVA model, covariance analysis model, mixed effect model, generalized linear model.

V. Reference Books, Reference Literatures, and Reference Materials

1. Fima C Klebaner. Introduction to Variables with Applications.

2. Thomas Mikosch. Elementary Calculus with Finance View. World Scientific Publishing Company, 1999.

Outline Writer (Signature):冯国峰

Leader in charge of teaching at the College (Signature)：

Date：