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Results tagged with pr.probability
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user 69642
Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
5
votes
Accepted
Differentiability of characteristic functions and moments of the corresponding measure
A good reference regarding this type of results is the book by Eugène Lukacs "Characteristic Function". For example, chapter 2.3 "Characteristic functions and moments" provides results in this directi …
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2
votes
Connections between two constructions of infinite dimensional Gaussian measures
I think that what you are looking for is the link between the white noise measure $\mu_C$ and the isonormal process indexed by $\ell^2(\mathbb{Z}^d)$ with covariance structure given by $C$. The white …
- 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".
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2
votes
Existence of strong solution to SDEs with non-Lipschitzian drift
Another approach for this problem has been developped in "Construction of strong solutions of SDE's via Malliavin calculus" by T. Meyer-Brandis and F. Proske. It has been further developped and extend …
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1
vote
Rate of Convergence of Compound Poisson Laws to Infinitely Divisible Laws
You might want to check this recent preprint:
https://arxiv.org/abs/1712.10051
and Section 4 in particular (Theorems 4.2, 4.4 and 4.5 and Proposition 4.4).
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2
votes
0
answers
52
views
Reference Request: Dirichlet operators with singular coefficients
Let $d\geq 2$, $\delta \in (0,1)$ and let $\mathcal{L}_{d,\delta}$ be the second order differential operator defined by
\begin{align*}
\mathcal{L}_{d,\delta}(f)(x) = \Delta(f)(x)-\delta \|x\|^{\delta- …
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0
votes
Explicit constant for Carbery–Wright inequality
Have you looked at the original paper by A. Carbery and J. Wright, Distributional and $L^q$ norm inequalities for polynomials over convex bodies in $\mathbb R^n$? Theorem 8 page 244 is the famous ineq …
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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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1
vote
Multiple Wiener-Ito integral distribution
Below some references regarding distributional properties of Wiener chaoses
The book, Gaussian Hilbert spaces, by S. Janson, is a standard reference to start with. In particular, you might want to r …
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