In addition, we should also learn modern algebra and group theory (the most basic definitions are introduced in the following courses), functional analysis and real variable functions (the mapping and martingale convergence of probability measures in various spaces are often used, especially the introduction of measure theory), ordinary differential equations (the derivation of Poisson's forward and backward equations and the stable distribution of horse chains), and partial differential equation theory (Brownian motion and fractional Brownian motion are widely used). I think the arrangement of foreign textbooks for operational research, economics and numerical analysis (actuarial use) is better. In addition to what I just said, preparatory courses such as measure theory, probability and measure, probability theory and analytical probability have been added abroad. , let them slowly enter the 1/3 section to apply the knowledge of stochastic processes. Because the random process is preceded by the word application, which is a postgraduate course, it is very difficult. Especially the exercises, there are many unanswered things.
For domestic reference, please refer to Lin Edition and Peace Edition.
For foreign languages, please refer to Application of Stochastic Process: Introduction to Probability Model (English version 10), which is easy to understand and covers a wide range. The main contents include random variables, conditional probability and conditional expectation, discrete and continuous Markov chains, exponential distribution, Poisson process, Brownian motion and stationary process, renewal theory and queuing theory. It also includes the application of stochastic process in physics, biology, logistics, network, genetics, economy, insurance, finance, reliability and so on. Especially the content of stochastic simulation provides a powerful tool for the simulation calculation of stochastic system operation. The Application of Stochastic Process —— Introduction to Probability Model (10 Edition: English Edition) contains about 700 exercises, among which the exercises with an asterisk also provide answers.
Application of Stochastic Process: Introduction to Probability Model (English version 10) can be used as a basic course of stochastic process for the majors of probability theory and statistics, computer science, insurance, physics, social science, life science, management science and engineering.