Chaos, Solitons and Fractals: the interdisciplinary journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena, ISSN 0960-0779, 09/2017, Volume 102, pp. 135 - 139

This paper derives the stochastic solution of a Cauchy problem for the distribution of a fractional diffusion process. The governing equation involves the...

Fractional diffusion | Bessel-Riesz subordinator | Bessel-Riesz Lévy motion | Stochastic solution | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Bessel-Riesz Levy motion | PHYSICS, MULTIDISCIPLINARY | PEARSON DIFFUSIONS | PHYSICS, MATHEMATICAL | EQUATION

Fractional diffusion | Bessel-Riesz subordinator | Bessel-Riesz Lévy motion | Stochastic solution | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | Bessel-Riesz Levy motion | PHYSICS, MULTIDISCIPLINARY | PEARSON DIFFUSIONS | PHYSICS, MATHEMATICAL | EQUATION

Journal Article

Stochastic Processes and their Applications, ISSN 0304-4149, 11/2017, Volume 127, Issue 11, pp. 3512 - 3535

We define heavy-tailed fractional reciprocal gamma and Fisher–Snedecor diffusions by a non-Markovian time change in the corresponding Pearson diffusions....

Transition density | Fractional diffusion | Pearson diffusion | Mittag-Leffler function | Hypergeometric function | Fractional backward Kolmogorov equation | Spectral representation | Whittaker function | BROWNIAN-MOTION | TIME RANDOM-WALKS | STATISTICS & PROBABILITY | ANOMALOUS DIFFUSION | STATISTICAL-INFERENCE | DYNAMICS | FISHER-SNEDECOR DIFFUSION | Mathematics - Probability

Transition density | Fractional diffusion | Pearson diffusion | Mittag-Leffler function | Hypergeometric function | Fractional backward Kolmogorov equation | Spectral representation | Whittaker function | BROWNIAN-MOTION | TIME RANDOM-WALKS | STATISTICS & PROBABILITY | ANOMALOUS DIFFUSION | STATISTICAL-INFERENCE | DYNAMICS | FISHER-SNEDECOR DIFFUSION | Mathematics - Probability

Journal Article

The Annals of Statistics, ISSN 0090-5364, 10/2008, Volume 36, Issue 5, pp. 2153 - 2182

A class of estimators of the Rényi and Tsallis entropies of an unknown distribution f in ${\Bbb R}^{m}$ is presented. These estimators are based on the kth...

Density estimation | Gaussian distributions | Shannon entropy | Entropy | Sampling distributions | Statistics | Estimators | Consistent estimators | Estimation methods | Estimation of divergence | Rényi entropy | Tsallis entropy | Entropy estimation | Estimation of statistical distance | Havrda-Charvát entropy | Nearest-neighbor distances | nearest-neighbor distances | estimation of divergence | STATISTICS | STATISTICS & PROBABILITY | NEAREST NEIGHBOR DISTANCES | GRAPHS | DISTRIBUTIONS | estimation of statistical distance | CONSISTENCY | LIMIT-THEOREMS | ENTROPY ESTIMATORS | ASYMPTOTICS | SAMPLE ENTROPY | Havrda-Charvat entropy | FUNCTIONALS | Renyi entropy | Studies | Statistical analysis | Normal distribution | Estimates | Statistics Theory | Mathematics | 94A15 | Havrda–Charvát entropy | 62G20

Density estimation | Gaussian distributions | Shannon entropy | Entropy | Sampling distributions | Statistics | Estimators | Consistent estimators | Estimation methods | Estimation of divergence | Rényi entropy | Tsallis entropy | Entropy estimation | Estimation of statistical distance | Havrda-Charvát entropy | Nearest-neighbor distances | nearest-neighbor distances | estimation of divergence | STATISTICS | STATISTICS & PROBABILITY | NEAREST NEIGHBOR DISTANCES | GRAPHS | DISTRIBUTIONS | estimation of statistical distance | CONSISTENCY | LIMIT-THEOREMS | ENTROPY ESTIMATORS | ASYMPTOTICS | SAMPLE ENTROPY | Havrda-Charvat entropy | FUNCTIONALS | Renyi entropy | Studies | Statistical analysis | Normal distribution | Estimates | Statistics Theory | Mathematics | 94A15 | Havrda–Charvát entropy | 62G20

Journal Article

Journal of Statistical Physics, ISSN 0022-4715, 2/2018, Volume 170, Issue 4, pp. 700 - 730

We present new properties for the Fractional Poisson process (FPP) and the Fractional Poisson field on the plane. A martingale characterization for FPPs is...

60G57 | Martingale characterization | Theoretical, Mathematical and Computational Physics | 60G60 | Quantum Physics | Inverse subordinator | Physics | Second order statistics | Statistical Physics and Dynamical Systems | Fractional Poisson fields | Primary: 60G55 | Fractional differential equations | Physical Chemistry | Secondary: 60G44 | 62E10 | 60E07 | TIMES | PATHS | DIFFERENTIAL-EQUATIONS | MARKOV | SPATIAL POISSON | PHYSICS, MATHEMATICAL | Differential equations | Queuing theory | Poisson density functions | Difference equations | Mathematical analysis | Martingales

60G57 | Martingale characterization | Theoretical, Mathematical and Computational Physics | 60G60 | Quantum Physics | Inverse subordinator | Physics | Second order statistics | Statistical Physics and Dynamical Systems | Fractional Poisson fields | Primary: 60G55 | Fractional differential equations | Physical Chemistry | Secondary: 60G44 | 62E10 | 60E07 | TIMES | PATHS | DIFFERENTIAL-EQUATIONS | MARKOV | SPATIAL POISSON | PHYSICS, MATHEMATICAL | Differential equations | Queuing theory | Poisson density functions | Difference equations | Mathematical analysis | Martingales

Journal Article

Stochastic Analysis and Applications, ISSN 0736-2994, 05/2017, Volume 35, Issue 3, pp. 452 - 464

We present a new construction of the Student and Student-like fractal activity time model for risky asset. The construction uses the diffusion processes and...

60H10 | geometric Brownian motion | 60G10 | option pricing formula | fractal activity time | Student distribution | reciprocal gamma diffusion | Risky asset model | 60J25 | 60F05 | DISTRIBUTIONS | MATHEMATICS, APPLIED | STATISTICS & PROBABILITY | Stochastic models | Fractal models | Asymptotic properties | Superposition (mathematics) | Self-similarity | Students | Fractal analysis | Fractals | Construction specifications | Stochasticity | Diffusion

60H10 | geometric Brownian motion | 60G10 | option pricing formula | fractal activity time | Student distribution | reciprocal gamma diffusion | Risky asset model | 60J25 | 60F05 | DISTRIBUTIONS | MATHEMATICS, APPLIED | STATISTICS & PROBABILITY | Stochastic models | Fractal models | Asymptotic properties | Superposition (mathematics) | Self-similarity | Students | Fractal analysis | Fractals | Construction specifications | Stochasticity | Diffusion

Journal Article

Bernoulli, ISSN 1350-7265, 11/2018, Volume 24, Issue 4B, pp. 3603 - 3627

Continuous time random walks have random waiting times between particle jumps. We define the correlated continuous time random walks (CTRWs) that converge to...

Wright–Fisher model | Markov chains | Fractional diffusion | Urn-scheme models | Pearson diffusions | Continuous time random walks | urn-scheme models | fractional diffusion | LIMIT-THEOREMS | continuous time random walks | STATISTICS & PROBABILITY | Wright-Fisher model | MARKOV-PROCESSES

Wright–Fisher model | Markov chains | Fractional diffusion | Urn-scheme models | Pearson diffusions | Continuous time random walks | urn-scheme models | fractional diffusion | LIMIT-THEOREMS | continuous time random walks | STATISTICS & PROBABILITY | Wright-Fisher model | MARKOV-PROCESSES

Journal Article

Journal of Statistical Physics, ISSN 0022-4715, 9/2017, Volume 168, Issue 6, pp. 1276 - 1301

We construct classes of homogeneous random fields on a three-dimensional Euclidean space that take values in linear spaces of tensors of a fixed rank and are...

Isotropy | Physical Chemistry | Theoretical, Mathematical and Computational Physics | Homogeneity | 60G60 | Quantum Physics | Group representation | Spectral density | 62M40 | Physics | Statistical Physics and Dynamical Systems | Euclidean geometry | Tensors | Euclidean space | Fields (mathematics) | Vector spaces | Naturvetenskap | Homogeneity; Isotropy; Group representation; Spectral density | Mathematics | Natural Sciences | Mathematics/Applied Mathematics | Matematik | Sannolikhetsteori och statistik | matematik/tillämpad matematik | Probability Theory and Statistics

Isotropy | Physical Chemistry | Theoretical, Mathematical and Computational Physics | Homogeneity | 60G60 | Quantum Physics | Group representation | Spectral density | 62M40 | Physics | Statistical Physics and Dynamical Systems | Euclidean geometry | Tensors | Euclidean space | Fields (mathematics) | Vector spaces | Naturvetenskap | Homogeneity; Isotropy; Group representation; Spectral density | Mathematics | Natural Sciences | Mathematics/Applied Mathematics | Matematik | Sannolikhetsteori och statistik | matematik/tillämpad matematik | Probability Theory and Statistics

Journal Article

JOURNAL OF STATISTICAL PHYSICS, ISSN 0022-4715, 09/2017, Volume 168, Issue 6, pp. 1276 - 1301

We construct classes of homogeneous random fields on a three-dimensional Euclidean space that take values in linear spaces of tensors of a fixed rank and are...

Isotropy | Homogeneity | Group representation | Spectral density | PHYSICS, MATHEMATICAL | CROSS-COVARIANCE FUNCTIONS | MULTIVARIATE RANDOM-FIELDS | Mathematics - Probability

Isotropy | Homogeneity | Group representation | Spectral density | PHYSICS, MATHEMATICAL | CROSS-COVARIANCE FUNCTIONS | MULTIVARIATE RANDOM-FIELDS | Mathematics - Probability

Journal Article

JOURNAL OF APPLIED PROBABILITY, ISSN 0021-9002, 03/2019, Volume 56, Issue 1, pp. 246 - 264

The fractional nonhomogeneous Poisson process was introduced by a time change of the nonhomogeneous Poisson process with the inverse alpha-stable subordinator....

LONG-RANGE DEPENDENCE | Levy process | additive process | STATISTICS & PROBABILITY | Fractional point processes | time change | Poisson process | limit theorem | subordination | Theorems | Parameter estimation | Computer simulation | Queuing theory | Poisson density functions | Stochastic models | Laplace transforms | Markov analysis | Martingales | Repair & maintenance

LONG-RANGE DEPENDENCE | Levy process | additive process | STATISTICS & PROBABILITY | Fractional point processes | time change | Poisson process | limit theorem | subordination | Theorems | Parameter estimation | Computer simulation | Queuing theory | Poisson density functions | Stochastic models | Laplace transforms | Markov analysis | Martingales | Repair & maintenance

Journal Article

Fractals, ISSN 0218-348X, 08/2018, Volume 26, Issue 4, p. 1850055

The multifractal analysis of stochastic processes deals with the fine scale properties of the sample paths and seeks for some global scaling property that...

Article | Spectrum of Singularities | Self-Similar | Multifractal | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PRODUCTS | FRACTIONAL STABLE MOTION | MULTIDISCIPLINARY SCIENCES | FORMALISM | FRACTAL SIGNALS | SIMULATION | SAMPLE PATH PROPERTIES | MOMENTS | Stochastic processes | Analysis | Divergence | Singularities | Fractal analysis | Scaling | Partitions (mathematics) | Stochastic models | Markov analysis | Self-similarity

Article | Spectrum of Singularities | Self-Similar | Multifractal | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | PRODUCTS | FRACTIONAL STABLE MOTION | MULTIDISCIPLINARY SCIENCES | FORMALISM | FRACTAL SIGNALS | SIMULATION | SAMPLE PATH PROPERTIES | MOMENTS | Stochastic processes | Analysis | Divergence | Singularities | Fractal analysis | Scaling | Partitions (mathematics) | Stochastic models | Markov analysis | Self-similarity

Journal Article

Statistics and Probability Letters, ISSN 0167-7152, 06/2018, Volume 137, pp. 235 - 242

We study the limiting behavior of continuous time trawl processes which are defined using an infinitely divisible random measure of a time dependent set. In...

Trawl processes | Moments | Cumulants | Intermittency | STATISTICS & PROBABILITY | LEVY PROCESSES

Trawl processes | Moments | Cumulants | Intermittency | STATISTICS & PROBABILITY | LEVY PROCESSES

Journal Article

Journal of Time Series Analysis, ISSN 0143-9782, 09/2013, Volume 34, Issue 5, pp. 602 - 603

Journal Article

Communications in Statistics - Theory and Methods, ISSN 0361-0926, 05/2019, pp. 1 - 23

Journal Article

Stochastic Analysis and Applications, ISSN 0736-2994, 07/2016, Volume 34, Issue 4, pp. 610 - 643

We investigate the properties of multifractal products of geometric Gaussian processes with possible long-range dependence and geometric Ornstein-Uhlenbeck...

stationary processes | Primary 60G57 | log normal tempered stable scenario | log-normal scenario | 60G10 | long-range dependence | Rényi function | superpositions | scaling of moments | geometric Gaussian process | Multifractal products | multifractal scenarios | log-variance gamma scenario | geometric Ornstein-Uhlenbeck processes | log-gamma scenario | short-range dependence | 60G17 | Lévy processes | Multifractal scenarios | Stationary processes | Log normal tempered stable scenario | Scaling of moments | Geometric Gaussian process | Geometric Ornstein-Uhlenbeck processes | Log-variance gamma scenario | Short-range dependence | Log-gamma scenario | Log-normal scenario | Long-range dependence | Superpositions | MATHEMATICS, APPLIED | LOG-GAMMA | Levy processes | STATISTICS & PROBABILITY | Renyi function | DYNAMICS | TURBULENCE | Construction | Gaussian | Stochasticity | Ornstein-Uhlenbeck process | Mathematical analysis

stationary processes | Primary 60G57 | log normal tempered stable scenario | log-normal scenario | 60G10 | long-range dependence | Rényi function | superpositions | scaling of moments | geometric Gaussian process | Multifractal products | multifractal scenarios | log-variance gamma scenario | geometric Ornstein-Uhlenbeck processes | log-gamma scenario | short-range dependence | 60G17 | Lévy processes | Multifractal scenarios | Stationary processes | Log normal tempered stable scenario | Scaling of moments | Geometric Gaussian process | Geometric Ornstein-Uhlenbeck processes | Log-variance gamma scenario | Short-range dependence | Log-gamma scenario | Log-normal scenario | Long-range dependence | Superpositions | MATHEMATICS, APPLIED | LOG-GAMMA | Levy processes | STATISTICS & PROBABILITY | Renyi function | DYNAMICS | TURBULENCE | Construction | Gaussian | Stochasticity | Ornstein-Uhlenbeck process | Mathematical analysis

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 07/2013, Volume 403, Issue 2, pp. 532 - 546

Pearson diffusions are governed by diffusion equations with polynomial coefficients. Fractional Pearson diffusions are governed by the corresponding...

Eigenfunction expansion | Stable process | Pearson diffusion | Mittag-Leffler function | Hitting time | Fractional derivative | BROWNIAN-MOTION | MATHEMATICS, APPLIED | TIME RANDOM-WALKS | MATHEMATICS | ANOMALOUS DIFFUSION | STATISTICAL-INFERENCE | CAUCHY-PROBLEMS | MODELS | LIMIT-THEOREMS | DYNAMICS | stable process | fractional derivative | hitting time | eigenfunction expansion

Eigenfunction expansion | Stable process | Pearson diffusion | Mittag-Leffler function | Hitting time | Fractional derivative | BROWNIAN-MOTION | MATHEMATICS, APPLIED | TIME RANDOM-WALKS | MATHEMATICS | ANOMALOUS DIFFUSION | STATISTICAL-INFERENCE | CAUCHY-PROBLEMS | MODELS | LIMIT-THEOREMS | DYNAMICS | stable process | fractional derivative | hitting time | eigenfunction expansion

Journal Article

Stochastic Processes and their Applications, ISSN 0304-4149, 04/2015, Volume 125, Issue 4, pp. 1629 - 1652

We obtain central limit theorems for additive functionals of stationary fields under integrability conditions on the higher-order spectral densities. The...

Integral of random fields | Hölder–Young–Brascamp–Lieb inequality | Higher-order spectral densities | Asymptotic normality | Hölder-Young-Brascamp-Lieb inequality | SEQUENCES | STATISTICS & PROBABILITY | Holder-Young-Brascamp-Lieb inequality | ASYMPTOTICS | INVARIANCE-PRINCIPLE | HOLDER INEQUALITY

Integral of random fields | Hölder–Young–Brascamp–Lieb inequality | Higher-order spectral densities | Asymptotic normality | Hölder-Young-Brascamp-Lieb inequality | SEQUENCES | STATISTICS & PROBABILITY | Holder-Young-Brascamp-Lieb inequality | ASYMPTOTICS | INVARIANCE-PRINCIPLE | HOLDER INEQUALITY

Journal Article

Journal of Statistical Physics, ISSN 0022-4715, 10/2016, Volume 165, Issue 2, pp. 390 - 408

The phenomenon of intermittency has been widely discussed in physics literature. This paper provides a model of intermittency based on Lévy driven...

Weak convergence | Ornstein–Uhlenbeck type processes | 60G99 | 60G10 | Physical Chemistry | Theoretical, Mathematical and Computational Physics | Quantum Physics | 60F06 | Physics | Long range dependence | Statistical Physics and Dynamical Systems | Intermittency | RISKY ASSET | TIME | DRIVEN | PHYSICS, MATHEMATICAL | Ornstein-Uhlenbeck type processes | DEPENDENCE | DISTRIBUTIONS | ANDERSON MODEL | DIFFUSION | LEVY | Gaussian process | Sums | Mathematics - Probability

Weak convergence | Ornstein–Uhlenbeck type processes | 60G99 | 60G10 | Physical Chemistry | Theoretical, Mathematical and Computational Physics | Quantum Physics | 60F06 | Physics | Long range dependence | Statistical Physics and Dynamical Systems | Intermittency | RISKY ASSET | TIME | DRIVEN | PHYSICS, MATHEMATICAL | Ornstein-Uhlenbeck type processes | DEPENDENCE | DISTRIBUTIONS | ANDERSON MODEL | DIFFUSION | LEVY | Gaussian process | Sums | Mathematics - Probability

Journal Article

Bernoulli, ISSN 1350-7265, 11/2016, Volume 22, Issue 4, pp. 2579 - 2608

We investigate the properties of multifractal products of geometric Gaussian processes with possible long-range dependence and geometric Ornstein-Uhlenbeck...

Rényi function | Multifractal scenarios | Stationary processes | Multifractal products | Scaling of moments | Log-normal tempered stable scenario | Geometric Gaussian process | Log-variance gamma scenario | Short-range dependence | Log-gamma scenario | Log-normal scenario | Geometric Ornstein Uhlenbeck processes | Long-range dependence | Lévy processes | Superpositions | stationary processes | GAMMA | log-normal scenario | log-normal tempered stable scenario | long-range dependence | superpositions | scaling of moments | geometric Gaussian process | Levy processes | STATISTICS & PROBABILITY | Renyi function | multifractal scenarios | multifractal products | log-variance gamma scenario | geometric Ornstein-Uhlenbeck processes | log-gamma scenario | DYNAMICS | TURBULENCE | short-range dependence

Rényi function | Multifractal scenarios | Stationary processes | Multifractal products | Scaling of moments | Log-normal tempered stable scenario | Geometric Gaussian process | Log-variance gamma scenario | Short-range dependence | Log-gamma scenario | Log-normal scenario | Geometric Ornstein Uhlenbeck processes | Long-range dependence | Lévy processes | Superpositions | stationary processes | GAMMA | log-normal scenario | log-normal tempered stable scenario | long-range dependence | superpositions | scaling of moments | geometric Gaussian process | Levy processes | STATISTICS & PROBABILITY | Renyi function | multifractal scenarios | multifractal products | log-variance gamma scenario | geometric Ornstein-Uhlenbeck processes | log-gamma scenario | DYNAMICS | TURBULENCE | short-range dependence

Journal Article

Mathematics, ISSN 2227-7390, 2018, Volume 6, Issue 9, p. 159

Starting from the definition of fractional M/M/1 queue given in the reference by Cahoy et al. in 2015 and M/M/1 queue with catastrophes given in the reference...

Fractional differential-difference equations | Fractional queues | Fractional birth-death processes | Busy period | MATHEMATICS | fractional queues | fractional differential-difference equations | fractional birth-death processes | POISSON-PROCESS | M/M/1 QUEUE | busy period | Customer services | Queuing theory | Queues | Stochastic models | Banach spaces | Laplace transforms | Markov analysis

Fractional differential-difference equations | Fractional queues | Fractional birth-death processes | Busy period | MATHEMATICS | fractional queues | fractional differential-difference equations | fractional birth-death processes | POISSON-PROCESS | M/M/1 QUEUE | busy period | Customer services | Queuing theory | Queues | Stochastic models | Banach spaces | Laplace transforms | Markov analysis

Journal Article

Statistics and Probability Letters, ISSN 0167-7152, 01/2020, Volume 156

This paper deals with a class of second-order vector random fields in the unit ball of , whose direct/cross covariances are invariant or isotropic with respect...

Direct covariance | Elliptically contoured random field | Distance on the unit ball | Cross covariance | Covariance matrix function

Direct covariance | Elliptically contoured random field | Distance on the unit ball | Cross covariance | Covariance matrix function

Journal Article

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