1981, Lecture Notes in Mathematics, ISBN 9780387105758, Volume 849., vii, 126

Book

PHYSICAL REVIEW LETTERS, ISSN 0031-9007, 07/2019, Volume 123, Issue 2, p. 020201

We revisit a family of integrals that delude intuition and that recently appeared in mathematical literature in connection with computer algebra package verification...

PHYSICS, MULTIDISCIPLINARY | SINC | Random walk theory | Program verification (computers) | Integrals | Computer algebra | Random walk | Physics

PHYSICS, MULTIDISCIPLINARY | SINC | Random walk theory | Program verification (computers) | Integrals | Computer algebra | Random walk | Physics

Journal Article

Economic theory, ISSN 1432-0479, 2013, Volume 56, Issue 1, pp. 33 - 58

This paper introduces a novel approach to integrals with respect to capacities. Any random variable is decomposed as a combination of indicators...

Mathematical monotonicity | Algebra | Mathematical integrals | Decision theory | Essential properties | Expected values | Random variables | Expected utility | Concavity | D84 | Economics general | Choquet integral | Decision making | Non-additive probability | Game Theory, Economics, Social and Behav. Sciences | Economics / Management Science | Decomposition-integral | Capacity | Economic Theory | Concave integral | C71 | D81 | D80 | DECISION | NONADDITIVE PROBABILITIES | RISK | BI-CAPACITIES | SUBJECTIVE EXPECTED UTILITY | EQUILIBRIUM | UNCERTAINTY | BELIEFS | AMBIGUITY | ECONOMICS | ADDITIVITY | Decision-making | Analysis | Methods | Decomposition (Chemistry) | Studies | Economic theory

Mathematical monotonicity | Algebra | Mathematical integrals | Decision theory | Essential properties | Expected values | Random variables | Expected utility | Concavity | D84 | Economics general | Choquet integral | Decision making | Non-additive probability | Game Theory, Economics, Social and Behav. Sciences | Economics / Management Science | Decomposition-integral | Capacity | Economic Theory | Concave integral | C71 | D81 | D80 | DECISION | NONADDITIVE PROBABILITIES | RISK | BI-CAPACITIES | SUBJECTIVE EXPECTED UTILITY | EQUILIBRIUM | UNCERTAINTY | BELIEFS | AMBIGUITY | ECONOMICS | ADDITIVITY | Decision-making | Analysis | Methods | Decomposition (Chemistry) | Studies | Economic theory

Journal Article

Reports on progress in physics, ISSN 1361-6633, 2017, Volume 80, Issue 4, p. 046601

This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals...

rare event probabilities | path summation | Markov processes | spectral analysis | master equations | stochastic processes | path integrals | FOKKER-PLANCK EQUATION | RENORMALIZATION-GROUP | BIRTH-DEATH PROCESSES | PHYSICS, MULTIDISCIPLINARY | REACTION-DIFFUSION PROCESSES | ASYMMETRIC EXCLUSION MODEL | NON-MARKOV PROCESSES | NEAR-CRITICAL POINT | RELATIVE SPECIES ABUNDANCE | ANNIHILATING RANDOM-WALKS | ONSAGER-MACHLUP FUNCTION

rare event probabilities | path summation | Markov processes | spectral analysis | master equations | stochastic processes | path integrals | FOKKER-PLANCK EQUATION | RENORMALIZATION-GROUP | BIRTH-DEATH PROCESSES | PHYSICS, MULTIDISCIPLINARY | REACTION-DIFFUSION PROCESSES | ASYMMETRIC EXCLUSION MODEL | NON-MARKOV PROCESSES | NEAR-CRITICAL POINT | RELATIVE SPECIES ABUNDANCE | ANNIHILATING RANDOM-WALKS | ONSAGER-MACHLUP FUNCTION

Journal Article

ELECTRONIC JOURNAL OF PROBABILITY, ISSN 1083-6489, 2019, Volume 24

Asymptotic expansion of the distribution of a perturbation Z(n) of a Skorohod integral jointly with a reference variable X-n is derived...

BROWNIAN-MOTION | quasi tangent | quasi torsion | quadratic form | modified quasi torsion | STATISTICS & PROBABILITY | fractional Brownian motion | Skorohod integral | MALLIAVIN CALCULUS | CENTRAL LIMIT-THEOREMS | interpolation | WIENER | RESPECT | WEIGHTED POWER VARIATIONS | CONVERGENCE | Malliavain covariance | FUNCTIONALS | asymptotic expansion | random symbol

BROWNIAN-MOTION | quasi tangent | quasi torsion | quadratic form | modified quasi torsion | STATISTICS & PROBABILITY | fractional Brownian motion | Skorohod integral | MALLIAVIN CALCULUS | CENTRAL LIMIT-THEOREMS | interpolation | WIENER | RESPECT | WEIGHTED POWER VARIATIONS | CONVERGENCE | Malliavain covariance | FUNCTIONALS | asymptotic expansion | random symbol

Journal Article

Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability, ISSN 1350-7265, 2019, Volume 25, Issue 3, pp. 1755 - 1769

.... In this paper, we establish a growth condition in terms of q and f such that the perpetual integral integral(infinity)(0) integral(X...

Feller process | Levy process | perpetual integral | STATISTICS & PROBABILITY | conservativeness | random time change | FUNCTIONALS

Feller process | Levy process | perpetual integral | STATISTICS & PROBABILITY | conservativeness | random time change | FUNCTIONALS

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 10/2015, Volume 298, pp. 254 - 265

...–Volterra integral equations. First, a stochastic operational matrix for the Chebyshev wavelets is presented and a general procedure for forming this matrix is given...

Stochastic Itô–Volterra integral equations | Itô integral | Chebyshev wavelets | Stochastic operational matrix | Stochastic Itô-Volterra integral equations | Ito integral | OPERATIONAL MATRIX | NUMERICAL-SOLUTION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | RANDOM DIFFERENTIAL-EQUATIONS | PHYSICS, MATHEMATICAL | Stochastic Ito-Volterra integral equations | Wavelet | Error analysis | Computation | Integral equations | Chebyshev approximation | Mathematical models | Stochasticity | Convergence | POLYNOMIALS | ERRORS | STOCHASTIC PROCESSES | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | MATRICES | VOLTERRA INTEGRAL EQUATIONS | CONVERGENCE | ACCURACY

Stochastic Itô–Volterra integral equations | Itô integral | Chebyshev wavelets | Stochastic operational matrix | Stochastic Itô-Volterra integral equations | Ito integral | OPERATIONAL MATRIX | NUMERICAL-SOLUTION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | RANDOM DIFFERENTIAL-EQUATIONS | PHYSICS, MATHEMATICAL | Stochastic Ito-Volterra integral equations | Wavelet | Error analysis | Computation | Integral equations | Chebyshev approximation | Mathematical models | Stochasticity | Convergence | POLYNOMIALS | ERRORS | STOCHASTIC PROCESSES | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | MATRICES | VOLTERRA INTEGRAL EQUATIONS | CONVERGENCE | ACCURACY

Journal Article

Annals of physics, ISSN 0003-4916, 2016, Volume 368, pp. 191 - 247

We study the partition function of two versions of the continuum directed polymer in 1+1 dimension. In the full-space version, the polymer starts at the origin...

Bethe ansatz | Lieb–Liniger model | Kardar–Parisi–Zhang | Delta Bose gas | Directed polymers | Kardar-Parisi-Zhang | Lieb-Liniger model | KPZ EQUATION | PHYSICS, MULTIDISCIPLINARY | HIGH-TEMPERATURE | BODY PROBLEM | BETHE-ANSATZ | ONE-DIMENSION | DELTA-FUNCTION INTERACTION | PARTICLE-SYSTEMS | RANDOM IMPURITIES | FREE-ENERGY | WHITTAKER FUNCTIONS | Polymers | Analysis | Polymer industry | Materials science | Origins | Partitions | Shape | Half spaces | Mathematical analysis | Mathematical models | Formulas (mathematics)

Bethe ansatz | Lieb–Liniger model | Kardar–Parisi–Zhang | Delta Bose gas | Directed polymers | Kardar-Parisi-Zhang | Lieb-Liniger model | KPZ EQUATION | PHYSICS, MULTIDISCIPLINARY | HIGH-TEMPERATURE | BODY PROBLEM | BETHE-ANSATZ | ONE-DIMENSION | DELTA-FUNCTION INTERACTION | PARTICLE-SYSTEMS | RANDOM IMPURITIES | FREE-ENERGY | WHITTAKER FUNCTIONS | Polymers | Analysis | Polymer industry | Materials science | Origins | Partitions | Shape | Half spaces | Mathematical analysis | Mathematical models | Formulas (mathematics)

Journal Article

Journal of Computational Physics, ISSN 0021-9991, 08/2014, Volume 270, pp. 402 - 415

...–Volterra integral equations. In this way, a new stochastic operational matrix for generalized hat functions on the finite interval [0,T] is obtained...

Brownian motion process | Stochastic Itô–Volterra integral equations | Generalized hat basis functions | Itô integral | Stochastic operational matrix | ItÔ integral | Stochastic ItÔ-Volterra integral equations | Ito integral | NUMERICAL-SOLUTION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | RANDOM DIFFERENTIAL-EQUATIONS | INTEGRODIFFERENTIAL EQUATIONS | PHYSICS, MATHEMATICAL | Stochastic Ito Volterra integral equations | Basis functions | Computation | Integral equations | Mathematical analysis | Blocking | Texts | Mathematical models | Stochasticity | INTEGRALS | STOCHASTIC PROCESSES | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | MATRICES | VOLTERRA INTEGRAL EQUATIONS | CONVERGENCE | BROWNIAN MOVEMENT | RELIABILITY | COMPARATIVE EVALUATIONS | ACCURACY | PULSES

Brownian motion process | Stochastic Itô–Volterra integral equations | Generalized hat basis functions | Itô integral | Stochastic operational matrix | ItÔ integral | Stochastic ItÔ-Volterra integral equations | Ito integral | NUMERICAL-SOLUTION | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | RANDOM DIFFERENTIAL-EQUATIONS | INTEGRODIFFERENTIAL EQUATIONS | PHYSICS, MATHEMATICAL | Stochastic Ito Volterra integral equations | Basis functions | Computation | Integral equations | Mathematical analysis | Blocking | Texts | Mathematical models | Stochasticity | INTEGRALS | STOCHASTIC PROCESSES | CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS | MATRICES | VOLTERRA INTEGRAL EQUATIONS | CONVERGENCE | BROWNIAN MOVEMENT | RELIABILITY | COMPARATIVE EVALUATIONS | ACCURACY | PULSES

Journal Article

The Annals of probability, ISSN 0091-1798, 3/2014, Volume 42, Issue 2, pp. 497 - 526

We characterize the asymptotic independence between blocks consisting of multiple Wiener–Itô integrals...

Integers | Brownian motion | Cauchy Schwarz inequality | Tensors | Mathematical theorems | Covariance | Skis | Mathematical integrals | Articles | Mathematical moments | Random variables | Multiple Wiener-Itô integral | Limit theorems | Multiplication formula | multiplication formula | Multiple Wiener-Ito integral | THEOREMS | CONVERGENCE | STATISTICS & PROBABILITY | limit theorems | FUNCTIONALS | Probability | Mathematics | 60H07 | 60H05 | 60F05 | 60G15 | Multiple Wiener–Itô integral

Integers | Brownian motion | Cauchy Schwarz inequality | Tensors | Mathematical theorems | Covariance | Skis | Mathematical integrals | Articles | Mathematical moments | Random variables | Multiple Wiener-Itô integral | Limit theorems | Multiplication formula | multiplication formula | Multiple Wiener-Ito integral | THEOREMS | CONVERGENCE | STATISTICS & PROBABILITY | limit theorems | FUNCTIONALS | Probability | Mathematics | 60H07 | 60H05 | 60F05 | 60G15 | Multiple Wiener–Itô integral

Journal Article

Pattern recognition, ISSN 0031-3203, 2013, Volume 46, Issue 11, pp. 3056 - 3065

.... Based on that, Path Integral, which has been introduced in statistical...

Graph algorithms | Path integral | Random walk | Agglomerative clustering | IMAGE SEGMENTATION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Algorithms | Integrals | Mathematical analysis | Exact solutions | Clusters | Agglomeration | Clustering | Dynamical systems

Graph algorithms | Path integral | Random walk | Agglomerative clustering | IMAGE SEGMENTATION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Algorithms | Integrals | Mathematical analysis | Exact solutions | Clusters | Agglomeration | Clustering | Dynamical systems

Journal Article

Inventiones mathematicae, ISSN 0020-9910, 6/2014, Volume 196, Issue 3, pp. 589 - 650

We prove that a set of density one satisfies the local-global conjecture for integral Apollonian gaskets...

Mathematics, general | Mathematics | MATHEMATICS | CIRCLE PACKINGS | GENERATION | RANDOM-WALKS | EXPANSION | GEOMETRY | Integers | Obstructions | Integrals | Mathematical analysis | Gaskets | Density | Curvature

Mathematics, general | Mathematics | MATHEMATICS | CIRCLE PACKINGS | GENERATION | RANDOM-WALKS | EXPANSION | GEOMETRY | Integers | Obstructions | Integrals | Mathematical analysis | Gaskets | Density | Curvature

Journal Article

Journal of Theoretical Probability, ISSN 0894-9840, 9/2016, Volume 29, Issue 3, pp. 717 - 736

Weak convergence of various general functionals of partial sums of dependent random variables to stochastic integrals now plays a major role in modern statistics theory...

Weak convergence | Causal process | Probability Theory and Stochastic Processes | Mathematics | Statistics, general | 60H05 | 60F17 | Stochastic integral | REGRESSION | ITERATED RANDOM FUNCTIONS | UNIT-ROOT | STATISTICS & PROBABILITY | LINEAR-PROCESSES | ASYMPTOTICS | CENTRAL-LIMIT-THEOREM | Stochastic processes

Weak convergence | Causal process | Probability Theory and Stochastic Processes | Mathematics | Statistics, general | 60H05 | 60F17 | Stochastic integral | REGRESSION | ITERATED RANDOM FUNCTIONS | UNIT-ROOT | STATISTICS & PROBABILITY | LINEAR-PROCESSES | ASYMPTOTICS | CENTRAL-LIMIT-THEOREM | Stochastic processes

Journal Article

The Annals of probability, ISSN 0091-1798, 7/2009, Volume 37, Issue 4, pp. 1412 - 1426

Fix ν > 0, denote by G(ν/2) a Gamma random variable with parameter ν/2 and let n ≥ 2 be a fixed even integer. Consider a sequence ${F_{k}}_{k\geq1}$ of square...

Integers | Mathematical sequences | Mathematical theorems | Central limit theorem | Business orders | Mathematical integrals | Chaos theory | Integration by parts | Random variables | Perceptron convergence procedure | Weak convergence | Noncentral limit theorems | Multiple stochastic integrals | Malliavin calculus | Gaussian processes | multiple stochastic integrals | CENTRAL LIMIT-THEOREMS | FIELDS | noncentral limit theorems | GAUSSIAN-PROCESSES | NONLINEAR FUNCTIONALS | STOCHASTIC INTEGRALS | STATISTICS & PROBABILITY | weak convergence | Mathematics - Probability | Probability | Mathematics | 60H07 | 60H05 | 60F05 | 60G15

Integers | Mathematical sequences | Mathematical theorems | Central limit theorem | Business orders | Mathematical integrals | Chaos theory | Integration by parts | Random variables | Perceptron convergence procedure | Weak convergence | Noncentral limit theorems | Multiple stochastic integrals | Malliavin calculus | Gaussian processes | multiple stochastic integrals | CENTRAL LIMIT-THEOREMS | FIELDS | noncentral limit theorems | GAUSSIAN-PROCESSES | NONLINEAR FUNCTIONALS | STOCHASTIC INTEGRALS | STATISTICS & PROBABILITY | weak convergence | Mathematics - Probability | Probability | Mathematics | 60H07 | 60H05 | 60F05 | 60G15

Journal Article

Quarterly of Applied Mathematics, ISSN 0033-569X, 2018, Volume 76, Issue 3, pp. 577 - 600

.... We evaluate these sums with multiple integration, a modern technique. First, we start with three different double integrals that have been previously used in the literature to show zeta(2) = pi(2...

Polytope | Multiple integrals | Random variables | Basel Problem | ZETA | MATHEMATICS, APPLIED | random variables | PROOF | multiple integrals | polytope | Mathematics - Probability

Polytope | Multiple integrals | Random variables | Basel Problem | ZETA | MATHEMATICS, APPLIED | random variables | PROOF | multiple integrals | polytope | Mathematics - Probability

Journal Article

Journal of Theoretical Probability, ISSN 0894-9840, 6/2019, Volume 32, Issue 2, pp. 1051 - 1075

We consider the spherical integral of real symmetric or Hermitian matrices when the rank of one matrix is one...

15B52 | Random matrices | Free probability | Asymptotic expansion | Probability Theory and Stochastic Processes | Mathematics | Statistics, general | Spherical integral | 46L54 | STATISTICS & PROBABILITY

15B52 | Random matrices | Free probability | Asymptotic expansion | Probability Theory and Stochastic Processes | Mathematics | Statistics, general | Spherical integral | 46L54 | STATISTICS & PROBABILITY

Journal Article

Expositiones mathematicae, ISSN 0723-0869, 2011, Volume 29, Issue 1, pp. 67 - 109

We present the Walsh theory of stochastic integrals with respect to martingale measures, and various extensions of this theory, alongside of the Da Prato and Zabczyk theory of stochastic integrals...

Random field solution | Cylindrical Wiener process | Stochastic wave equation | Stochastic heat equation | Stochastic partial differential equation | Spatially homogeneous Gaussian noise | Hilbert-space-valued Wiener process | Stochastic integral | Martingale measure | EXISTENCE | LAW | SMOOTHNESS | CAUCHY-PROBLEM | NOISE | SPACE | MATHEMATICS | DIMENSIONS | WIENER PROCESS | WAVE-EQUATION

Random field solution | Cylindrical Wiener process | Stochastic wave equation | Stochastic heat equation | Stochastic partial differential equation | Spatially homogeneous Gaussian noise | Hilbert-space-valued Wiener process | Stochastic integral | Martingale measure | EXISTENCE | LAW | SMOOTHNESS | CAUCHY-PROBLEM | NOISE | SPACE | MATHEMATICS | DIMENSIONS | WIENER PROCESS | WAVE-EQUATION

Journal Article