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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
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
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
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
Journal Article
The Annals of applied probability, ISSN 1050-5164, 12/2011, Volume 21, Issue 6, pp. 2109 - 2145
Journal Article
Journal of Theoretical Probability, ISSN 0894-9840, 9/2015, Volume 28, Issue 3, pp. 1227 - 1249
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
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
Journal Article
Journal of Statistical Physics, ISSN 0022-4715, 7/2016, Volume 164, Issue 2, pp. 438 - 448
Journal Article
by Li, Li and Li, Li
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
Journal Article
Fractional Calculus and Applied Analysis, ISSN 1311-0454, 3/2013, Volume 16, Issue 1, pp. 158 - 170
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
Journal Article
The Annals of probability, ISSN 0091-1798, 1/2015, Volume 43, Issue 1, pp. 240 - 285
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
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
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
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
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
Journal Article
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