A Discrete Construction for Gaussian Markov Processes

A Discrete Construction for Gaussian Markov Processes

\fnmsThibaud \snmTaillefumier    \fnmsAntoine \snmToussaint
Abstract

In the Lévy construction of Brownian motion, a Haar-derived basis of functions is used to form a finite-dimensional process and to define the Wiener process as the almost sure path-wise limit of when tends to infinity. We generalize such a construction to the class of centered Gaussian Markov processes which can be written with and being continuous functions. We build the finite-dimensional process so that it gives an exact representation of the conditional expectation of with respect to the filtration generated by for . Moreover, we prove that the process converges in distribution toward .

Comments 0
Request Comment
You are adding the first comment!
How to quickly get a good reply:
  • Give credit where it’s due by listing out the positive aspects of a paper before getting into which changes should be made.
  • Be specific in your critique, and provide supporting evidence with appropriate references to substantiate general statements.
  • Your comment should inspire ideas to flow and help the author improves the paper.

The better we are at sharing our knowledge with each other, the faster we move forward.
""
The feedback must be of minimum 40 characters and the title a minimum of 5 characters
   
Add comment
Cancel
Loading ...
104984
This is a comment super asjknd jkasnjk adsnkj
Upvote
Downvote
""
The feedback must be of minumum 40 characters
The feedback must be of minumum 40 characters
Submit
Cancel

You are asking your first question!
How to quickly get a good answer:
  • Keep your question short and to the point
  • Check for grammar or spelling errors.
  • Phrase it like a question
Test
Test description