Book [Pins]

R.G.Pinsky, Positive harmonic functions and diffusions

* Keyword : SDE
= definition of stochastic integral + Ito processes + Ito's formula + solution of SDE
= Sect 1.5 -- Sect 1.7
* Keyword : martingale problem
* Keyword : Feynman Kac formula

Book [Jac1]

N.Jacob, Pseudo differential operator, volume I.

* Sect. 4.5 -- finished
* Sect. 4.8 -- finished

* Keyword : negative definite symbol
* Keyword : resolvents
* Keyword : spectrum
* Keyword : Levy - Khinchin formula

Hankel Function

Hankel function -- Wolfram mathworld
Bessel function -- wikipedia
Properties of Hankel and Bessel functions

Some useful exercises

You can easily find some exercise made by LaTeX. For example, if you would like to see some exercises of the theory of stochastic processes, search by

exercise stochastic process filetype:pdf

Try it later!

Durrett has published the forth edition of a his book.

Professor R.Durrett announces that he has published the beta version of forth edition of "Probability : Theory and Examples" in his website.

He corrects many parts and adds to the third version, the stories of multi-dimensional Brownian motions and the recurrency and transiency of them.

New references

Stanislav A. Molchanov, Donald Andrew Dawson, Vojkan Jakšić, Boris Rufimovich Vaĭnberg, Probability and mathematical physics, CRM proceedings and lecture notes, volume 42, published by AMS.

Keywords

Large deviation principle
Feynman-Kac formula
Levy system
symmetric stable processes
regular Dirichlet forms
(sub-)critical
Hunt processes
Davies' conjecture
minimum Green function

I've read through Chap.3 of Jacob's book (copy)

I've read through chapter 3 of "pseudo differential operators and Markov processes (volume III)". I have to write a report about this part.

(The original update was at 11/08/2008 06:22:00 PM.)

I updated website (copy)

Please see mathematical memorandum later if you like. I updated some memorandums of Durrett's textbook and Jacob's textbook.

(The original update was done at 10/26/2008 01:42:00 PM.)

XEmacs (copy)

We can search a paticular word from the current position forward or backward.

1. [M-x] (or [Esc-x])
2. type "search-forward" or "search-backward"
3. input "(keyword)"

But we can find only one word.

Another way

(The original update was done at 10/22/2008 11:44:00 AM.)