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Results tagged with reference-request
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user 69642
This tag is used if a reference is needed in a paper or textbook on a specific result.
4
votes
Accepted
Reference for LIL for fractional Brownian motion
This has been proved by S. Orey in this article:
Steven Orey. Growth rate of certain Gaussian processes. Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, Vol. I …
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3
votes
0
answers
88
views
Error rate implying regularity
My question is a bit general/vague.
It is well known that the regularity of certain functions can be measured through the rate of decay of certain error quantity based on an approximation procedure (s …
- 778
1
vote
0
answers
74
views
Dimension dependence: boundedness result of the fractional Riesz integral
I am looking for the best known constant in the boundedness result of the fractional Riesz integral. In particular, I am interested in the dependence on the dimension $d$ and on the parameter $\alpha< …
- 778
4
votes
Accepted
Reference request: The transform of a bounded random variable has a zero in the complex plane
It is the content of Theorem 7.2.3 page 202 of Eugene Lukacs book "Characteristic Function".
- 778
13
votes
2
answers
558
views
A conjecture of De Giorgi on weighted Sobolev spaces
Let $\mu$ be a probability measure on $\mathbb{R}^d$ which is absolutely continuous with respect to the Lebesgue measure with density $\rho$. Assume that, for all $t>0$,
\begin{align*}
\exp \left(t \ …
- 778
6
votes
Accepted
A conjecture of De Giorgi on weighted Sobolev spaces
I did some diggings and some readings and found out that the conjecture has been solved here
https://link.springer.com/article/10.1134/S1064562413060173
and extended recently to a wider context in …
- 778
3
votes
1
answer
391
views
Riesz transform of fractional operators
I am interested in Riesz transforms linked to the fractional Laplacian and other fractional operators. I have been hunting down in the literature to find related results but I have not been able to fi …
- 778
7
votes
1
answer
682
views
Reference request: Constant Hölder estimates
I am reading the book "Elliptic partial differential equations of second order" by D. Gilbarg and N. S. Trudinger.
Specifically, I am interested in Hölder regularity estimates for solution of ellipti …
- 778
2
votes
Isometry for the stochastic integral wrt fractional Brownian motion for random processes
Regarding the link between stochastic integral wrt fractional Brownian motion and stochastic integral wrt Brownian motion, this is the content of Proposition 5.2.2 of the book "The Malliavin calculus …
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3
votes
PDE-oriented textbook on probability and random processes?
Maybe, you can have a look at this book:
Second order PDE’s in finite and infinite dimensions. A probabilistic approach, S. Cerrai
In many classical text books in probability, there are one or two c …
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