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Results tagged with pr.probability
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user 46773
Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
1
vote
Smoothness of $g(t,x)=\mathbb{E}[f(X_T)|\mathcal{F}_t]$
I assume here the $x$ variable is the initial condition of you process? Here is a partial answer: if $(\mathcal F_t)$ is the brownian filtration, then by Itô's martingale representation theorem for an …
- 630
7
votes
4
answers
1k
views
Is the space of tempered distribution second countable?
Let $\mathcal S '(\mathbb R^d)$ be the space of Schwartz tempered distributions equipped with the weak-* topology. I need to know if this space is second countable, i.e. if this topology has a countab …
- 630
0
votes
0
answers
57
views
Where can I find this article of Doléans-Dade?
I need to find the article "Intégrales stochastiques dépendant d’un paramètre" by Doléans-Dade.
I could not find a pdf version online, and my university library does not have a printed version.
Thank …
- 630
3
votes
0
answers
111
views
Orlicz spaces and $\phi$-functions
A $\phi$-function $f$ is usually defined as a continuous function $f=\mathbb R_+ \to \mathbb R_+$ such that:
(1) $f$ is nondecreasing.
(2) $f(0)=0$ and $f(x)>0$ for all $x>0$.
(3) $\lim_{x\to +\inf …
- 630
2
votes
Accepted
Running supremmum of a Levy process
See Theorem 25.18 p168 in "Lévy Processes and Infinitely Divisible Distributions" by K-I Sato
- 630