What is a diffusion process? Wikipedia says "In probability theory, a branch of mathematics, a diffusion process is a solution to a stochastic differential equation. It is a continuous-time Markov process with almost surely continuous sample paths. Brownian motion, reflected Brownian motion and Ornstein–Uhlenbeck processes are examples of diffusion processes." What is continuous sample path?

If so, then

1- is a Brownian motion with drift a diffusion process? Why? I know it is a Markov process and I can prove it but I'm not sure if it has continuous sample path.

2- In fact, I am not quite sure if I got the meaning of "continuous sample path" right. Is it the same as continuous state space or continuous index set (i.e. parameter set)?

Another question:

3- If a process is diffusion process then it can not be a Jump Process, right? (Perhaps I can answer this question by myself if I know what continuous sample time mean).


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.