Search results for "probability"
showing 10 items of 3417 documents
Noncommutative Davis type decompositions and applications
2018
We prove the noncommutative Davis decomposition for the column Hardy space $\H_p^c$ for all $0<p\leq 1$. A new feature of our Davis decomposition is a simultaneous control of $\H_1^c$ and $\H_q^c$ norms for any noncommutative martingale in $\H_1^c \cap \H_q^c$ when $q\geq 2$. As applications, we show that the Burkholder/Rosenthal inequality holds for bounded martingales in a noncommutative symmetric space associated with a function space $E$ that is either an interpolation of the couple $(L_p, L_2)$ for some $1<p<2$ or is an interpolation of the couple $(L_2, L_q)$ for some $2<q<\infty$. We also obtain the corresponding $\Phi$-moment Burkholder/Rosenthal inequality for Orlicz functions that…
Spatial Besov regularity for stochastic partial differential equations on Lipschitz domains
2010
We use the scale of Besov spaces B^\alpha_{\tau,\tau}(O), \alpha>0, 1/\tau=\alpha/d+1/p, p fixed, to study the spatial regularity of the solutions of linear parabolic stochastic partial differential equations on bounded Lipschitz domains O\subset R^d. The Besov smoothness determines the order of convergence that can be achieved by nonlinear approximation schemes. The proofs are based on a combination of weighted Sobolev estimates and characterizations of Besov spaces by wavelet expansions.
Blow-up of the non-equivariant 2+1 dimensional wave map
2014
It has been known for a long time that the equivariant 2+1 wave map into the 2-sphere blows up if the initial data are chosen appropriately. Here, we present numerical evidence for the stability of the blow-up phenomenon under explicit violations of equivariance.
Conjunction of Conditional Events and T-norms
2019
We study the relationship between a notion of conjunction among conditional events, introduced in recent papers, and the notion of Frank t-norm. By examining different cases, in the setting of coherence, we show each time that the conjunction coincides with a suitable Frank t-norm. In particular, the conjunction may coincide with the Product t-norm, the Minimum t-norm, and Lukasiewicz t-norm. We show by a counterexample, that the prevision assessments obtained by Lukasiewicz t-norm may be not coherent. Then, we give some conditions of coherence when using Lukasiewicz t-norm.
Malliavin smoothness on the L\'evy space with H\"older continuous or $BV$ functionals
2018
We consider Malliavin smoothness of random variables $f(X_1)$, where $X$ is a pure jump L\'evy process and $f$ is either bounded and H\"older continuous or of bounded variation. We show that Malliavin differentiability and fractional differentiability of $f(X_1)$ depend both on the regularity of $f$ and the Blumenthal-Getoor index of the L\'evy measure.
"Table 28" of "Energy dependence of event shapes and of alpha(s) at LEP-2."
1999
Distribution of the Heavy Jet Masses (MH**2/EVIS**2) at cm energy 183 GeV.
"Table 30" of "Energy dependence of event shapes and of alpha(s) at LEP-2."
1999
Distribution of the Light Jet Masses (ML**2/EVIS**2) at cm energy 183 GeV.
Mappings of finite distortion: The sharp modulus of continuity
2003
We establish an essentially sharp modulus of continuity for mappings of subexponentially integrable distortion.
Product and Moment Formulas for Iterated Stochastic Integrals (associated with L\'evy Processes)
2018
In this paper, we obtain explicit product and moment formulas for products of iterated integrals generated by families of square integrable martingales associated with an arbitrary L\'evy process. We propose a new approach applying the theory of compensated-covariation stable families of martingales. Our main tool is a representation formula for products of elements of a compensated-covariation stable family, which enables to consider L\'evy processes, with both jumps and Gaussian part.
Probabilities of large values for sums of i.i.d. non-negative random variables with regular tail of index $-1$
2021
Let $\xi_1, \xi_2, \dots$ be i.i.d. non-negative random variables whose tail varies regularly with index $-1$, let $S_n$ be the sum and $M_n$ the largest of the first $n$ values. We clarify for which sequences $x_n\to\infty$ we have $\mathbb P(S_n \ge x_n) \sim \mathbb P(M_n \ge x_n)$ as $n\to\infty$. Outside this regime, the typical size of $S_n$ conditioned on exceeding $x_n$ is not completely determined by the largest summand and we provide an appropriate correction term which involves the integrated tail of $\xi_1$.