Stochastic Models, ISSN 1532-6349, 10/2018, Volume 34, Issue 4, pp. 409 - 434

We construct "self-stabilizing" processes . These are random processes which when "localized," that is scaled around t to a fine limit, have the distribution...

stable process | Local form | self-stabilizing | 60G18 | 60G52 | STATISTICS & PROBABILITY | LOCAL-STRUCTURE

stable process | Local form | self-stabilizing | 60G18 | 60G52 | STATISTICS & PROBABILITY | LOCAL-STRUCTURE

Journal Article

The Annals of statistics, ISSN 0090-5364, 6/2007, Volume 35, Issue 3, pp. 1183 - 1212

We apply the techniques of stochastic integration with respect to fractional Brownian motion and the theory of regularity and supremum estimation for...

Brownian motion | Integers | Maximum likelihood estimation | Stochastic processes | Differential equations | Inference for Stochastic Processes | Maximum likelihood estimators | Calculus | Random variables | Estimators | Consistent estimators | Maximum | Strong consistency | Hurst parameter | Likelihood estimator | Malliavin calculus | Fractional Brownian motion | Stochastic differential equation | maximum likelihood estimator | MAXIMUM-LIKELIHOOD-ESTIMATION | MODELS | stochastic differential equation | strong consistency | DIFFERENTIAL-EQUATIONS | STATISTICS & PROBABILITY | fractional Brownian motion | INFERENCE | Probability | Statistics | Mathematics | Maximum likelihood estimator | 60H10 | 62M09 | 60H07 | 60G18

Brownian motion | Integers | Maximum likelihood estimation | Stochastic processes | Differential equations | Inference for Stochastic Processes | Maximum likelihood estimators | Calculus | Random variables | Estimators | Consistent estimators | Maximum | Strong consistency | Hurst parameter | Likelihood estimator | Malliavin calculus | Fractional Brownian motion | Stochastic differential equation | maximum likelihood estimator | MAXIMUM-LIKELIHOOD-ESTIMATION | MODELS | stochastic differential equation | strong consistency | DIFFERENTIAL-EQUATIONS | STATISTICS & PROBABILITY | fractional Brownian motion | INFERENCE | Probability | Statistics | Mathematics | Maximum likelihood estimator | 60H10 | 62M09 | 60H07 | 60G18

Journal Article

Annales de l'institut Henri Poincare (B) Probability and Statistics, ISSN 0246-0203, 11/2018, Volume 54, Issue 4, pp. 2349 - 2360

In this paper we consider the distribution of the location of the path supremum in a fixed interval for self-similar processes with stationary increments. A...

Random locations | Stationary increment processes | Self-similar processes | STATISTICS & PROBABILITY | MAXIMUM

Random locations | Stationary increment processes | Self-similar processes | STATISTICS & PROBABILITY | MAXIMUM

Journal Article

The Annals of probability, ISSN 0091-1798, 2015, Volume 43, Issue 5, pp. 2205 - 2249

We study one-dimensional exact scaling lognormal multiplicative chaos measures at criticality. Our main results are the determination of the exact asymptotics...

Multiplicative chaos | Critical temperature | critical temperature | MARTINGALES | RANDOM-WALKS | STATISTICS & PROBABILITY | TURBULENCE | CASCADES | POINTS | 60G57 | 60G18 | 83C45

Multiplicative chaos | Critical temperature | critical temperature | MARTINGALES | RANDOM-WALKS | STATISTICS & PROBABILITY | TURBULENCE | CASCADES | POINTS | 60G57 | 60G18 | 83C45

Journal Article

Journal of applied probability, ISSN 0021-9002, 12/2007, Volume 44, Issue 4, pp. 950 - 959

We construct a process with gamma increments, which has a given convex autocorrelation function and asymptotically a self-similar limit. This construction...

Research Papers | Variance-gamma distribution | Construction | Gamma process | Long-range dependence | Self-similarity | Subordinator model | T distribution | subordinator model | 62P20 | variance-gamma distribution | 60G10 | long-range dependence | t distribution | construction | 60G18 | self-similarity

Research Papers | Variance-gamma distribution | Construction | Gamma process | Long-range dependence | Self-similarity | Subordinator model | T distribution | subordinator model | 62P20 | variance-gamma distribution | 60G10 | long-range dependence | t distribution | construction | 60G18 | self-similarity

Journal Article

The Annals of applied probability, ISSN 1050-5164, 12/2011, Volume 21, Issue 6, pp. 2109 - 2145

Computing smoothing distributions, the distributions of one or more states conditional on past, present, and future observations is a recurring problem when...

Approximation | Filtration | Infinity | Particle interactions | Markov chains | Markov models | Random variables | Data smoothing | Estimators | Perceptron convergence procedure | Sequential Monte Carlo methods | Smoothing | Hidden Markov models | Particle filter | hidden Markov models | NONLINEAR FILTERS | STABILITY | STATISTICS & PROBABILITY | particle filter | smoothing | SIMULATION | Mathematics - Probability | 60G10 | 60G18 | 60K35 | Naturvetenskap | hidden | Mathematics | Natural Sciences | Matematik | Sannolikhetsteori och statistik | Probability Theory and Statistics

Approximation | Filtration | Infinity | Particle interactions | Markov chains | Markov models | Random variables | Data smoothing | Estimators | Perceptron convergence procedure | Sequential Monte Carlo methods | Smoothing | Hidden Markov models | Particle filter | hidden Markov models | NONLINEAR FILTERS | STABILITY | STATISTICS & PROBABILITY | particle filter | smoothing | SIMULATION | Mathematics - Probability | 60G10 | 60G18 | 60K35 | Naturvetenskap | hidden | Mathematics | Natural Sciences | Matematik | Sannolikhetsteori och statistik | Probability Theory and Statistics

Journal Article

Journal of Theoretical Probability, ISSN 0894-9840, 9/2015, Volume 28, Issue 3, pp. 1227 - 1249

The Rosenblatt process was obtained by Taqqu (Z. Wahr. Verw. Geb. 31:287–302, 1975) from convergence in distribution of partial sums of strongly dependent...

Rosenblatt process | Particle system | Primary 60G18 | Probability Theory and Stochastic Processes | Mathematics | Secondary 60F17 | Statistics, general | Long-range dependence | Intersection local time | DENSITY PROCESSES | LIMIT-THEOREMS | FRACTIONAL BROWNIAN-MOTION | CONVERGENCE | SYSTEMS | STATISTICS & PROBABILITY | SELF-SIMILAR PROCESSES | PARTICLE PICTURE APPROACH | Mathematics - Probability

Rosenblatt process | Particle system | Primary 60G18 | Probability Theory and Stochastic Processes | Mathematics | Secondary 60F17 | Statistics, general | Long-range dependence | Intersection local time | DENSITY PROCESSES | LIMIT-THEOREMS | FRACTIONAL BROWNIAN-MOTION | CONVERGENCE | SYSTEMS | STATISTICS & PROBABILITY | SELF-SIMILAR PROCESSES | PARTICLE PICTURE APPROACH | Mathematics - Probability

Journal Article

Journal of statistical physics, ISSN 1572-9613, 2019, Volume 175, Issue 5, pp. 1022 - 1041

We start by providing an explicit characterization and analytical properties, including the persistence phenomena, of the distribution of the extinction time...

Fréchet distribution | First passage times | Self-similar processes | Theoretical, Mathematical and Computational Physics | Primary 60G18 | Quantum Physics | Physics | Statistical Physics and Dynamical Systems | Secondary 42A38, 33E50 | Bernstein-gamma functions | Physical Chemistry | Bernstein functions | Mellin transform

Fréchet distribution | First passage times | Self-similar processes | Theoretical, Mathematical and Computational Physics | Primary 60G18 | Quantum Physics | Physics | Statistical Physics and Dynamical Systems | Secondary 42A38, 33E50 | Bernstein-gamma functions | Physical Chemistry | Bernstein functions | Mellin transform

Journal Article

Random Operators and Stochastic Equations, ISSN 0926-6364, 12/2019, Volume 27, Issue 4, pp. 213 - 223

Hermite processes are self-similar processes with stationary increments; the Hermite process of order 1 is fractional Brownian motion (fBm) and the Hermite...

mild solutions | Stochastic partial differential equations | 60G22 | Rosenblatt process | 60H20 | fractional powers of closed operators | asymptotic behaviour | 60G18 | Mathematical analysis | Brownian movements | Differential equations | Dependence | Uniqueness | Self-similarity

mild solutions | Stochastic partial differential equations | 60G22 | Rosenblatt process | 60H20 | fractional powers of closed operators | asymptotic behaviour | 60G18 | Mathematical analysis | Brownian movements | Differential equations | Dependence | Uniqueness | Self-similarity

Journal Article

Journal of Statistical Physics, ISSN 0022-4715, 7/2016, Volume 164, Issue 2, pp. 438 - 448

Imposing some flexible sampling scheme we provide some discretization of continuous time discrete scale invariant (DSI) processes which is a subsidiary...

60G99 | Physical Chemistry | Theoretical, Mathematical and Computational Physics | Quantum Physics | 60G18 | Statistical Physics, Dynamical Systems and Complexity | Discretization of continuous time DSI processes | Spectral representation | Physics | Time dependent Hurst parameter estimation | SELF-SIMILAR PROCESSES | INDEX | SIMILARITY | PHYSICS, MATHEMATICAL | Statistics - Methodology

60G99 | Physical Chemistry | Theoretical, Mathematical and Computational Physics | Quantum Physics | 60G18 | Statistical Physics, Dynamical Systems and Complexity | Discretization of continuous time DSI processes | Spectral representation | Physics | Time dependent Hurst parameter estimation | SELF-SIMILAR PROCESSES | INDEX | SIMILARITY | PHYSICS, MATHEMATICAL | Statistics - Methodology

Journal Article

Journal of Theoretical Probability, ISSN 0894-9840, 12/2018, Volume 31, Issue 4, pp. 2072 - 2111

In this paper, we consider accessibility percolation on hypercubes, i.e., we place i.i.d. uniform [0, 1] random variables on vertices of a hypercube, and study...

Second moment method | Hypercube | 60J80 | Probability Theory and Stochastic Processes | Mathematics | Statistics, general | Accessibility percolation | 60G18 | Phase transition | PATHS | STATISTICS & PROBABILITY | LANDSCAPES

Second moment method | Hypercube | 60J80 | Probability Theory and Stochastic Processes | Mathematics | Statistics, general | Accessibility percolation | 60G18 | Phase transition | PATHS | STATISTICS & PROBABILITY | LANDSCAPES

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 3/2013, Volume 16, Issue 1, pp. 158 - 170

The micro/mesoscopic theory of dielectric relaxation has been developed. Based on the fractional kinetics it gives a possibility to obtain the desired...

60G22 | Cole-Davidson expression | 28A80 | 34K37 | Mathematics | Integral Transforms, Operational Calculus | 34A08 | fractals | excess wing | Abstract Harmonic Analysis | dielectric permittivity | Functional Analysis | Analysis | fractal kinetics | 60G18 | Cole-Cole expression | 60G18; 60G22; 34A08 | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PROPYLENE CARBONATE | MESOSCALE REGION | EQUATIONS | DYNAMICS

60G22 | Cole-Davidson expression | 28A80 | 34K37 | Mathematics | Integral Transforms, Operational Calculus | 34A08 | fractals | excess wing | Abstract Harmonic Analysis | dielectric permittivity | Functional Analysis | Analysis | fractal kinetics | 60G18 | Cole-Cole expression | 60G18; 60G22; 34A08 | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PROPYLENE CARBONATE | MESOSCALE REGION | EQUATIONS | DYNAMICS

Journal Article

Statistical papers (Berlin, Germany), ISSN 1613-9798, 2017, Volume 60, Issue 6, pp. 2253 - 2271

In this paper, we consider the problem of parameter estimation for Ornstein–Uhlenbeck processes with small fractional Lévy noises, based on discrete...

Statistics for Business, Management, Economics, Finance, Insurance | 65C30 | Operations Research/Decision Theory | 93E24 | Economic Theory/Quantitative Economics/Mathematical Methods | Probability Theory and Stochastic Processes | Least squares estimator | Asymptotic distribution | 60G18 | Statistics | Fractional Lévy processes | Ornstein–Uhlenbeck processes | Economic models | Parameter estimation | Regression analysis | Least squares method

Statistics for Business, Management, Economics, Finance, Insurance | 65C30 | Operations Research/Decision Theory | 93E24 | Economic Theory/Quantitative Economics/Mathematical Methods | Probability Theory and Stochastic Processes | Least squares estimator | Asymptotic distribution | 60G18 | Statistics | Fractional Lévy processes | Ornstein–Uhlenbeck processes | Economic models | Parameter estimation | Regression analysis | Least squares method

Journal Article

Nonlinearity, ISSN 0951-7715, 11/2016, Volume 29, Issue 12, pp. 3871 - 3896

This paper aims to develop a rigorous asymptotic analysis of an approximate renormalization group recursion for inverse participation ratios P-q of critical...

15B52 | multifractality | 82B44 | powerlaw random band matrix Mathematics Subject Classification numbers: 60G18 | branching recursion | powerlaw random band matrix | TRANSITION | MATHEMATICS, APPLIED | ENERGY | LAW | FLUCTUATIONS | CONVERGENCE | PHYSICS, MATHEMATICAL | BRANCHING RANDOM-WALK

15B52 | multifractality | 82B44 | powerlaw random band matrix Mathematics Subject Classification numbers: 60G18 | branching recursion | powerlaw random band matrix | TRANSITION | MATHEMATICS, APPLIED | ENERGY | LAW | FLUCTUATIONS | CONVERGENCE | PHYSICS, MATHEMATICAL | BRANCHING RANDOM-WALK

Journal Article

The Annals of probability, ISSN 0091-1798, 1/2015, Volume 43, Issue 1, pp. 240 - 285

We establish a new class of functional central limit theorems for partial sum of certain symmetric stationary infinitely divisible processes with regularly...

Selfsimilar process | Central limit theorem | Conservative flow | Darling-Kac theorem | Infinitely divisible process | Pointwise dual ergodicity | APPROXIMATION | STATISTICS & PROBABILITY | self-similar process | LOCAL-TIMES | conservative flow | SUMS | pointwise dual ergodicity | central limit theorem | MOVING AVERAGES | CONVERGENCE | ERGODIC PROPERTIES | TRANSFORMATIONS | Mathematics - Probability | 37A40 | Darling–Kac theorem | 60G52 | 60G18 | 60F17

Selfsimilar process | Central limit theorem | Conservative flow | Darling-Kac theorem | Infinitely divisible process | Pointwise dual ergodicity | APPROXIMATION | STATISTICS & PROBABILITY | self-similar process | LOCAL-TIMES | conservative flow | SUMS | pointwise dual ergodicity | central limit theorem | MOVING AVERAGES | CONVERGENCE | ERGODIC PROPERTIES | TRANSFORMATIONS | Mathematics - Probability | 37A40 | Darling–Kac theorem | 60G52 | 60G18 | 60F17

Journal Article

Nonlinearity, ISSN 0951-7715, 05/2017, Volume 30, Issue 7, pp. 2592 - 2611

Scaling properties of time series are usually studied in terms of the scaling laws of empirical moments, which are the time average estimates of moments of the...

62M10 | 91B20 | 60G52 | 60G51 | 60G50 | 60G18 | Lévy processes | empirical moments | scaling laws Mathematics Subject Classification numbers: 60F15 | MATHEMATICS, APPLIED | MOTION | Levy processes | scaling laws | FINANCIAL TIME-SERIES | COMPONENTS | FLIGHTS | PHYSICS, MATHEMATICAL | ASSET RETURNS

62M10 | 91B20 | 60G52 | 60G51 | 60G50 | 60G18 | Lévy processes | empirical moments | scaling laws Mathematics Subject Classification numbers: 60F15 | MATHEMATICS, APPLIED | MOTION | Levy processes | scaling laws | FINANCIAL TIME-SERIES | COMPONENTS | FLIGHTS | PHYSICS, MATHEMATICAL | ASSET RETURNS

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2018, Volume 2018, Issue 1, pp. 1 - 20

Let BH,K={BH,K(t),t≥0} $B^{H,K}=\{B^{H,K}(t), t \geq 0\}$ be a d-dimensional bifractional Brownian motion with Hurst parameters H∈(0,1) $H\in (0,1)$ and...

Self-intersection local time | Analysis | Bifractional Brownian motion | Mathematics, general | Mathematics | Renormalization | Applications of Mathematics | 60G18 | 60F05 | 60G15 | Existence | MATHEMATICS | MATHEMATICS, APPLIED | SMOOTHNESS | Brownian movements | Random walk theory | Delta function | Research

Self-intersection local time | Analysis | Bifractional Brownian motion | Mathematics, general | Mathematics | Renormalization | Applications of Mathematics | 60G18 | 60F05 | 60G15 | Existence | MATHEMATICS | MATHEMATICS, APPLIED | SMOOTHNESS | Brownian movements | Random walk theory | Delta function | Research

Journal Article

Stochastics, ISSN 1744-2508, 01/2020, Volume 92, Issue 1, pp. 1 - 23

Let be a real-valued N-parameter harmonizable fractional stable sheet with index . We establish a random wavelet series expansion for which is almost surely...

Hausdorff dimension | strong local nondeterminism | wavelet series representation | inverse image | Harmonizable fractional stable sheets | local times | LePage representation | 60G52 | 60G60 | 60G18 | 60G17

Hausdorff dimension | strong local nondeterminism | wavelet series representation | inverse image | Harmonizable fractional stable sheets | local times | LePage representation | 60G52 | 60G60 | 60G18 | 60G17

Journal Article

Fractional Calculus and Applied Analysis, ISSN 1311-0454, 10/2017, Volume 20, Issue 5, pp. 1263 - 1280

In this paper the accurate relationships between the averaging procedure of a smooth function over 1D- fractal sets and the fractional integral of the RL-type...

26A30 | Secondary: 60G18 | Cantor set | 26A33 | 28A78 | spatial fractional integral | Primary 28A80 | fractal object | averaging of smooth functions on spatial fractal sets | self-similar object | Fractal object | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | CALCULUS | Smoothing (Statistics) | Research | Integrals | Mathematical research

26A30 | Secondary: 60G18 | Cantor set | 26A33 | 28A78 | spatial fractional integral | Primary 28A80 | fractal object | averaging of smooth functions on spatial fractal sets | self-similar object | Fractal object | MATHEMATICS | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | CALCULUS | Smoothing (Statistics) | Research | Integrals | Mathematical research

Journal Article

Stochastic Processes and their Applications, ISSN 0304-4149, 08/2015, Volume 125, Issue 11, pp. 4117 - 4141

In this paper, we study the 1H-variation of stochastic divergence integrals Xt =∫0t us δ Bs with respect to a fractional Brownian motion B with Hurst parameter...

60H07 | MSC 60H05 | 60G18 | GAUSSIAN-PROCESSES | STOCHASTIC CALCULUS | BESSEL PROCESSES | STATISTICS & PROBABILITY | Malliavin calculus | Fractional Brownian motion | Skorohod integral | Fractional Bessel processes

60H07 | MSC 60H05 | 60G18 | GAUSSIAN-PROCESSES | STOCHASTIC CALCULUS | BESSEL PROCESSES | STATISTICS & PROBABILITY | Malliavin calculus | Fractional Brownian motion | Skorohod integral | Fractional Bessel processes

Journal Article

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