Search results for "PROBABILITY"

showing 10 items of 3417 documents

Dyck paths with a first return decomposition constrained by height

2018

International audience; We study the enumeration of Dyck paths having a first return decomposition with special properties based on a height constraint. We exhibit new restricted sets of Dyck paths counted by the Motzkin numbers, and we give a constructive bijection between these objects and Motzkin paths. As a byproduct, we provide a generating function for the number of Motzkin paths of height k with a flat (resp. with no flats) at the maximal height. (C) 2018 Elsevier B.V. All rights reserved.KeywordsKeyWords Plus:STATISTICS; STRINGS

Discrete mathematicsMathematics::CombinatoricsFirst return decompositionDyck and Motzkin pathsEnumerationHeightStatisticsGenerating function0102 computer and information sciences01 natural sciencesConstructiveTheoretical Computer ScienceConstraint (information theory)Combinatorics010104 statistics & probability010201 computation theory & mathematicsEnumerationBijectionDecomposition (computer science)Discrete Mathematics and CombinatoricsStrings0101 mathematics[MATH]Mathematics [math]MathematicsPeak
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Interpolation and approximation in L2(γ)

2007

Assume a standard Brownian motion W=(W"t)"t"@?"["0","1"], a Borel function f:R->R such that f(W"1)@?L"2, and the standard Gaussian measure @c on the real line. We characterize that f belongs to the Besov space B"2","q^@q(@c)@?(L"2(@c),D"1","2(@c))"@q","q, obtained via the real interpolation method, by the behavior of a"X(f(X"1);@t)@[email protected]?f(W"1)-P"X^@tf(W"1)@?"L"""2, where @t=(t"i)"i"="0^n is a deterministic time net and P"X^@t:L"2->L"2 the orthogonal projection onto a subspace of 'discrete' stochastic integrals x"[email protected]?"i"="1^nv"i"-"1(X"t"""i-X"t"""i"""-"""1) with X being the Brownian motion or the geometric Brownian motion. By using Hermite polynomial expansions the…

Discrete mathematicsNumerical AnalysisHermite polynomialsGeneric propertyApplied MathematicsGeneral MathematicsLinear equation over a ringGaussian measuresymbols.namesakeWiener processsymbolsBesov spaceMartingale (probability theory)Real lineAnalysisMathematicsJournal of Approximation Theory
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Property (gab) through localized SVEP

2015

In this article we study the property (gab) for a bounded linear operator T 2 L(X) on a Banach space X which is a stronger variant of Browder's theorem. We shall give several characterizations of property (gab). These characterizations are obtained by using typical tools from local spectral theory. We also show that property (gab) holds for large classes of operators and prove the stability of property (gab) under some commuting perturbations. 2010 Mathematics Subject Classication. Primary 47A10, 47A11; Secondary 47A53, 47A55.

Discrete mathematicsNumerical AnalysisPure mathematicsControl and OptimizationSpectral theoryProperty (philosophy)Property (gab) local spectral subspaces Browder type theorems.Applied Mathematics010102 general mathematicsBanach space010103 numerical & computational mathematics01 natural sciencesStability (probability)Bounded operatorSettore MAT/05 - Analisi Matematica0101 mathematicsAnalysisMathematics
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Lackadaisical Quantum Walks with Multiple Marked Vertices

2019

The concept of lackadaisical quantum walk – quantum walk with self loops – was first introduced for discrete-time quantum walk on one-dimensional line [8]. Later it was successfully applied to improve the running time of the spacial search on two-dimensional grid [16].

Discrete mathematicsPhysicsMathematics::Probability0103 physical sciencesLine (geometry)Quantum walk010306 general physicsGrid01 natural sciences010305 fluids & plasmasRunning time
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Codimension and colength sequences of algebras and growth phenomena

2015

We consider non necessarily associative algebras over a field of characteristic zero and their polynomial identities. Here we describe some of the results obtained in recent years on the sequence of codimensions and the sequence of colengths of an algebra.

Discrete mathematicsPolynomialPure mathematicsSequenceMathematics::Commutative AlgebraGeneral Mathematics010102 general mathematicsZero (complex analysis)Field (mathematics)Codimension01 natural sciences010101 applied mathematicsSettore MAT/02 - AlgebraComputational Theory and Mathematics0101 mathematicsStatistics Probability and UncertaintyVariety (universal algebra)Algebra over a fieldPolynomial identities Variety Almost nilpotent Codimension.Associative propertyMathematicsSão Paulo Journal of Mathematical Sciences
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On algebras of polynomial codimension growth

2016

Let A be an associative algebra over a field F of characteristic zero and let $$c_n(A), n=1, 2, \ldots $$ , be the sequence of codimensions of A. It is well-known that $$c_n(A), n=1, 2, \ldots $$ , cannot have intermediate growth, i.e., either is polynomially bounded or grows exponentially. Here we present some results on algebras whose sequence of codimensions is polynomially bounded.

Discrete mathematicsPolynomialSequenceMathematics::Commutative AlgebraGeneral Mathematics010102 general mathematicsZero (complex analysis)Field (mathematics)Codimension01 natural sciencesSettore MAT/02 - AlgebraComputational Theory and MathematicsBounded function0103 physical sciencesAssociative algebraPolynomial identities Codimensions Codimension growth010307 mathematical physics0101 mathematicsStatistics Probability and UncertaintyMathematicsSão Paulo Journal of Mathematical Sciences
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Quantum extensions of semigroups generated by Bessel processes

1996

We construct a quantum extension of the Markov semigroup of the classical Bessel process of orderv≥1 to the noncommutative von Neumann algebra s(L2(0, +∞)) of bounded operators onL2(0, +∞).

Discrete mathematicsPure mathematicsBessel processMathematics::Operator AlgebrasSemigroupGeneral MathematicsNoncommutative geometryQuantum dynamical semigroupsymbols.namesakeQuantum probabilityVon Neumann algebraBounded functionsymbolsBessel functionMathematicsMathematical Notes
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On a multiplication and a theory of integration for belief and plausibility functions

1987

Abstract Belief and plausibility functions have been introduced as generalizations of probability measures, which abandon the axiom of additivity. It turns out that elementwise multiplication is a binary operation on the set of belief functions. If the set functions of the type considered here are defined on a locally compact and separable space X , a theorem by Choquet ensures that they can be represented by a probability measure on the space containing the closed subsets of X , the so-called basic probability assignment. This is basic for defining two new types of integrals. One of them may be used to measure the degree of non-additivity of the belief or plausibility function. The other o…

Discrete mathematicsPure mathematicsFuzzy measure theoryApplied MathematicsLebesgue integrationMeasure (mathematics)symbols.namesakeChoquet integralSet functionBinary operationsymbolsLocally compact spaceAnalysisMathematicsProbability measureJournal of Mathematical Analysis and Applications
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Stochastic differential equations with coefficients in Sobolev spaces

2010

We consider It\^o SDE $\d X_t=\sum_{j=1}^m A_j(X_t) \d w_t^j + A_0(X_t) \d t$ on $\R^d$. The diffusion coefficients $A_1,..., A_m$ are supposed to be in the Sobolev space $W_\text{loc}^{1,p} (\R^d)$ with $p>d$, and to have linear growth; for the drift coefficient $A_0$, we consider two cases: (i) $A_0$ is continuous whose distributional divergence $\delta(A_0)$ w.r.t. the Gaussian measure $\gamma_d$ exists, (ii) $A_0$ has the Sobolev regularity $W_\text{loc}^{1,p'}$ for some $p'>1$. Assume $\int_{\R^d} \exp\big[\lambda_0\bigl(|\delta(A_0)| + \sum_{j=1}^m (|\delta(A_j)|^2 +|\nabla A_j|^2)\bigr)\big] \d\gamma_d0$, in the case (i), if the pathwise uniqueness of solutions holds, then the push-f…

Discrete mathematicsPure mathematicsOrnstein–Uhlenbeck semigroupLebesgue measureSobolev space coefficientsProbability (math.PR)Density60H10 (Primary) 34F05 (Secondary) 60J60 37C10Density estimatePathwise uniquenessGaussian measureLipschitz continuitySobolev spaceStochastic differential equationStochastic flowsGaussian measureBounded functionFOS: Mathematics: Mathematics [G03] [Physical chemical mathematical & earth Sciences]Vector fieldUniqueness: Mathématiques [G03] [Physique chimie mathématiques & sciences de la terre]AnalysisMathematics - ProbabilityMathematics
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Quadratic variation of martingales in Riesz spaces

2014

We derive quadratic variation inequalities for discrete-time martingales, sub- and supermartingales in the measure-free setting of Riesz spaces. Our main result is a Riesz space analogue of Austinʼs sample function theorem, on convergence of the quadratic variation processes of martingales http://www.journals.elsevier.com/journal-of-mathematical-analysis-and-applications/ http://dx.doi.org/10.1016/j.jmaa.2013.08.037 National Research Foundation of South Africa (Grant specific unique reference number (UID) 85672) and by GNAMPA of Italy (U 2012/000574 20/07/2012 and U 2012/000388 09/05/2012)

Discrete mathematicsPure mathematicsRiesz potentialRiesz representation theoremApplied MathematicsmartingaleRiesz spaceRiesz spacevector latticeQuadratic variationquadratic variationM. Riesz extension theoremSettore MAT/05 - Analisi MatematicaAustin’s theorem Martingale Measure-free stochastic processes Quadratic variation Riesz space Vector latticemeasure-free stochastic processesAustinʼs theoremMartingale (probability theory)AnalysisMathematics
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