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…

Mathematics::Functional AnalysisMathematics::Operator AlgebrasFunction spaceGeneral Mathematics010102 general mathematicsType (model theory)Hardy space01 natural sciencesNoncommutative geometryCombinatorics010104 statistics & probabilitysymbols.namesakeSymmetric spaceBounded functionsymbols0101 mathematicsMartingale (probability theory)MathematicsJournal of the London Mathematical Society
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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.

Mathematics::Functional AnalysisSmoothness (probability theory)General MathematicsProbability (math.PR)Mathematics::Analysis of PDEsScale (descriptive set theory)Numerical Analysis (math.NA)Lipschitz continuitySobolev spaceStochastic partial differential equation60H15 Secondary: 46E35 65C30WaveletRate of convergenceBounded functionFOS: MathematicsApplied mathematicsMathematics - Numerical AnalysisMathematics - ProbabilityMathematicsStudia Mathematica
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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.

Mathematics::K-Theory and HomologyMathematical analysisOne-dimensional spaceMathematics::Analysis of PDEsEquivariant mapGeneral MedicineStability (probability)Mathematics::Algebraic TopologyMathematical PhysicsMathematics35L67 35L70 65M20 65P10 74H35
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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.

Mathematics::LogicProbability (math.PR)FOS: MathematicsMathematics - Probability
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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.

Mathematics::Probability60G51 60H07Mathematics - Probability
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"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.

Mathematics::ProbabilityDN/DMHEAVY-JETAstrophysics::High Energy Astrophysical PhenomenaE+ E- --&gt; HADRONSE+ E- --&gt; JETSE+ E- ScatteringExclusiveHigh Energy Physics::ExperimentSingle Differential DistributionJet ProductionNuclear Experiment183.0
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"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.

Mathematics::ProbabilityDN/DMLIGHT-JETAstrophysics::High Energy Astrophysical PhenomenaE+ E- --&gt; HADRONSE+ E- --&gt; JETSE+ E- ScatteringExclusiveHigh Energy Physics::ExperimentSingle Differential DistributionJet ProductionNuclear Experiment183.0
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Mappings of finite distortion: The sharp modulus of continuity

2003

We establish an essentially sharp modulus of continuity for mappings of subexponentially integrable distortion.

Mathematics::ProbabilityIntegrable systemApplied MathematicsGeneral MathematicsDistortionMathematical analysisGeometryComputer Science::Computational ComplexityComputer Science::Data Structures and AlgorithmsModulus of continuityMathematicsTransactions of the American Mathematical Society
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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.

Mathematics::ProbabilityMathematics - Probability
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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 $\xi_1$.

Mathematics::ProbabilityProbability (math.PR)FOS: Mathematics60F10 60E07 92D10Mathematics - Probability
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