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Journal Article
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, 08/2012, Volume 86, Issue 2, p. 021117
A random walk scheme, consisting of alternating phases of regular Brownian motion and Levy walks, is proposed as a model for run-and-tumble bacterial motion.... 
LEVY WALKS | SEARCH | PHYSICS, FLUIDS & PLASMAS | BEHAVIOR | PATTERNS | SYSTEMS | PHYSICS, MATHEMATICAL | MOTILITY | Physics - Biological Physics
Journal Article
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 09/2017, Volume 482, pp. 486 - 500
In this paper we study the stable Lévy motion subordinated by the so-called inverse Gaussian process. This process extends the well known normal inverse... 
Subordination | Stable Lévy motion | Estimation | Inverse Gaussian process | DISTRIBUTIONS | ANOMALOUS DIFFUSION | PHYSICS, MULTIDISCIPLINARY | Stable Levy motion | MODEL
Journal Article
Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 06/2018, Volume 51, Issue 27, p. 275001
Motivated by recent studies of record statistics in relation to strongly correlated time series, we consider explicitly the drawdown time of a Levy process,... 
Brownian motion | extreme statistics | Wiener-Hopf | Lévy process | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | Levy process | Mathematics - Probability
Journal Article
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
Journal Article
Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 09/2016, Volume 49, Issue 39, p. 394002
A combined dynamics consisting of Brownian motion and Levy flights is exhibited by a variety of biological systems performing search processes. Assessing the... 
Brownian motion | Lévy flights | first arrival | random search process | first passage | ANIMALS | WALKS | PHYSICS, MULTIDISCIPLINARY | FLIGHTS | PHYSICS, MATHEMATICAL | STRATEGIES | Levy flights | ANOMALOUS DIFFUSION | DNA COILING | MOVEMENT PATTERNS | DYNAMICS | WANDERING ALBATROSSES | SCALING LAWS
Journal Article
Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 07/2018, Volume 60, pp. 100 - 106
•We analyze the asymptotic behaviour of Levy-Lorentz gas.•We derive the diffusion limit of the studied process (functional convergence in the Skorokhod... 
Brownian motion | Continuous-time random walk | Lévy-Lorentz gas | Convergence in distribution | Diffusion limit | Levy-Lorentz gas | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | RANDOM-WALKS | PHYSICS, FLUIDS & PLASMAS | MODEL | PHYSICS, MATHEMATICAL
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 11/2018, Volume 337, pp. 618 - 634
For non-Gaussian stochastic dynamical systems, mean exit time and escape probability are important deterministic quantities, which can be obtained from... 
Asymmetric Lévy motion | Escape probability | Integro-differential equation | First exit time | Stochastic dynamical systems | MATHEMATICS, APPLIED | PARTIAL-DIFFERENTIAL-EQUATIONS | DYNAMICAL-SYSTEMS | DRIVEN | Asymmetric Levy motion
Journal Article
The Annals of Probability, ISSN 0091-1798, 1/2015, Volume 43, Issue 1, pp. 405 - 434
Let W denote d-dimensional Brownian motion. We find an explicit formula for the essential supremum of Hausdorff dimension of W(E) ⋂ F, where E ⊂ (0, ∞) and F ⊂... 
Brownian motion | Thermal capacity | Euclidean | Space-time | Hausdorff dimension | HAUSDORFF | TREES | Euclidean and space-time Hausdorff dimension | HEAT-EQUATION | SETS | STATISTICS & PROBABILITY | thermal capacity | ADDITIVE LEVY PROCESSES | Mathematics - Probability | 60J65 | Euclidean and space–time Hausdorff dimension | 28A78 | 28A80 | 60G17 | 60G15 | 60J45
Journal Article
Scientific Reports, ISSN 2045-2322, 07/2016, Volume 6, Issue 1, p. 30520
It is quite generally assumed that the overdamped Langevin equation provides a quantitative description of the dynamics of a classical Brownian particle in the... 
GRANULAR GASES | SELF-DIFFUSION | INTRACELLULAR-TRANSPORT | KINETIC-THEORY | MODELS | RANDOM-WALKS | MULTIDISCIPLINARY SCIENCES | LEVY FLIGHTS | CYTOPLASM | LANGEVIN-EQUATIONS | LIVING CELLS
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 03/2016, Volume 278, pp. 1 - 20
Journal Article