This is the 8th day of my participation in the August More Text Challenge
Random Process
Stochastic processes provide a lot of great ideas for learning artificial intelligence algorithms. Let’s think about these problems from the perspective of probability. I spent three days reviewing this course. Finally, I grasped the key points and wrote this note to share with you. Please forgive the scrawl.
Chapter I Stochastic process and its classification
1. Differences between random process and sample function and random variable:
Random process refers to X(t, w) with uncertain time and parameters, that is, the sum of sample functions under all parameters
Sample function X(·, w), with uncertain time and definite parameter, that is, events occurring at a series of time under certain parameter
Random variable X(t, ·), time is determined and parameter is uncertain, that is, different events under a series of parameters at a certain time
2. Typical distribution
Exponential distribution, Poisson distribution, normal distribution, uniform distribution
Chapter two: Markov process
Markov process is a very typical stochastic process
1. The definition of markov
The general idea of Markov process is that the future is only about the present, not the past. * * :
1 represents one-step transition probability, 2 represents initial state, and 3 represents state transition rate matrix
2. C – k equation
Conditional probability multiplicative relation:
Two kinds of relationships:
3. First arrival time
4. Status classification
Example 1: Gambler runs out
Their thinking
5. Finite state and limit distribution of Markov chains
6. Analysis of very recurrent state
7. Markov chains with continuous parameters and discrete states
Pure discontinuous Markov chains
Limiting properties of purely discontinuous Markov processes
Chapter 3 Poisson Process (Poisson Signal Flow)
Poisson process is a special pure discontinuous Markov process.
A concept.
1. Independent incremental process
The increments of x (t) are independent of each other. If x (0) of x (t) is a definite value, it is a Markov process
2. Counting process
3. Homogeneous Poisson process
Poisson process and exponential distribution process
5. Non-synchronous process
Compound poisson
Ix. Update process
Chapter 4 second – moment process, stationary process and stochastic analysis
Chapter 5: Spectral analysis of stationary processes
Chapter 6 Gauss Process (Wiener Process)
Code word is not easy, all see here as well as a point of praise oh ~ I also wrote a lot of articles, welcome to pay attention to me oh ~
