Stationary states in Langevin dynamics under asymmetric L\'evy noises

Properties of systems driven by white non-Gaussian noises can be very different from these systems driven by the white Gaussian noise. We investigate stationary probability densities for systems driven by $\alpha$-stable L\'evy type noises, which provide natural extension to the Gaussian noise having however a new property mainly a possibility of being asymmetric. Stationary probability densities are examined for a particle moving in parabolic, quartic and in generic double well potential models subjected to the action of $\alpha$-stable noises. Relevant solutions are constructed by methods of stochastic dynamics. In situations where analytical results are known they are compared with numerical results. Furthermore, the problem of estimation of the parameters of stationary densities is investigated.Comment: 9 pages, 9 figures, 3 table

Levy stable noise induced transitions: stochastic resonance, resonant activation and dynamic hysteresis

A standard approach to analysis of noise-induced effects in stochastic dynamics assumes a Gaussian character of the noise term describing interaction of the analyzed system with its complex surroundings. An additional assumption about the existence of timescale separation between the dynamics of the measured observable and the typical timescale of the noise allows external fluctuations to be modeled as temporally uncorrelated and therefore white. However, in many natural phenomena the assumptions concerning the abovementioned properties of "Gaussianity" and "whiteness" of the noise can be violated. In this context, in contrast to the spatiotemporal coupling characterizing general forms of non-Markovian or semi-Markovian L\'evy walks, so called L\'evy flights correspond to the class of Markov processes which still can be interpreted as white, but distributed according to a more general, infinitely divisible, stable and non-Gaussian law. L\'evy noise-driven non-equilibrium systems are known to manifest interesting physical properties and have been addressed in various scenarios of physical transport exhibiting a superdiffusive behavior. Here we present a brief overview of our recent investigations aimed to understand features of stochastic dynamics under the influence of L\'evy white noise perturbations. We find that the archetypal phenomena of noise-induced ordering are robust and can be detected also in systems driven by non-Gaussian, heavy-tailed fluctuations with infinite variance.Comment: 7 pages, 8 figure

Analysis of time dynamics in wind records by means of multifractal detrended fluctuation analysis and Fisher-Shannon information plane

The time structure of more than 10 years of hourly wind data measured in one site in northern Italy from April 1996 to December 2007 is analysed. The data are recorded by the Sodar Rass system, which measures the speed and the direction of the wind at several heights above the ground level. To investigate the wind speed time series at seven heights above the ground level we used two different approaches: i) the Multifractal Detrended Fluctuation Analysis (MF-DFA), which permits the detection of multifractality in nonstationary series, and ii) the Fisher-Shannon (FS) information plane, which allows to discriminate dynamical features in complex time series. Our results point out to the existence of multifractal time fluctuations in wind speed and to a dependence of the results on the height of the wind sensor. Even in the FS information plane a height-dependent pattern is revealed, indicating a good agreement with the multifractality. The obtained results could contribute to a better understanding of the complex dynamics of wind phenomenon

Conversion of Society for Maternal-Fetal Medicine abstract presentations to manuscript publications

To evaluate the rate of conversion of Society for Maternal Fetal Medicine (SMFM) Annual Meeting abstract presentations to full manuscript publications over time

A detection algorithm for the first jump time in sample trajectories of jump-diffusions driven by α-stable white noise

The purpose of this paper is to develop a detection algorithm for the first jump point in sampling trajectories of jump-diffusions which are described as solutions of stochastic differential equations driven by $\alpha$-stable white noise. This is done by a multivariate Lagrange interpolation approach. To this end, we utilise computer simulation algorithm in MATLAB to visualise the sampling trajectories of the jump-diffusions for various combinations of parameters arising in the modelling structure of stochastic differential equations

Multiplicative L\'evy processes: It\^o versus Stratonovich interpretation

Langevin equation with a multiplicative stochastic force is considered. That force is uncorrelated, it has the L\'evy distribution and the power-law intensity. The Fokker-Planck equations, which correspond both to the It\^o and Stratonovich interpretation of the stochastic integral, are presented. They are solved for the case without drift and for the harmonic oscillator potential. The variance is evaluated; it is always infinite for the It\^o case whereas for the Stratonovich one it can be finite and rise with time slower that linearly, which indicates subdiffusion. Analytical results are compared with numerical simulations.Comment: 11 pages, 6 figure

Effects of Dementia Care Mapping on well-being and quality of life of older people with intellectual disability:A quasi-experimental study

BACKGROUND: The ageing of people with intellectual disability, accompanied with consequences like dementia, challenges intellectual disability-care staff and creates a need for supporting methods, with Dementia Care Mapping (DCM) as a promising possibility. This study examined the effect of DCM on the quality of life of older people with intellectual disability.METHODS: We performed a quasi-experimental study in 23 group homes for older people with intellectual disability in the Netherlands, comparing DCM (n = 113) with care-as-usual (CAU; n = 111). Using three measures, we assessed the staff-reported quality of life of older people with intellectual disability.RESULTS: DCM achieved no significantly better or worse quality of life than CAU. Effect sizes varied from 0.01 to -0.22. Adjustments for covariates and restriction of analyses to people with dementia yielded similar results.CONCLUSION: The finding that DCM does not increase quality of life of older people with intellectual disability contradicts previous findings and deserves further study.</p

The Schroedinger Problem, Levy Processes Noise in Relativistic Quantum Mechanics

The main purpose of the paper is an essentially probabilistic analysis of relativistic quantum mechanics. It is based on the assumption that whenever probability distributions arise, there exists a stochastic process that is either responsible for temporal evolution of a given measure or preserves the measure in the stationary case. Our departure point is the so-called Schr\"{o}dinger problem of probabilistic evolution, which provides for a unique Markov stochastic interpolation between any given pair of boundary probability densities for a process covering a fixed, finite duration of time, provided we have decided a priori what kind of primordial dynamical semigroup transition mechanism is involved. In the nonrelativistic theory, including quantum mechanics, Feyman-Kac-like kernels are the building blocks for suitable transition probability densities of the process. In the standard "free" case (Feynman-Kac potential equal to zero) the familiar Wiener noise is recovered. In the framework of the Schr\"{o}dinger problem, the "free noise" can also be extended to any infinitely divisible probability law, as covered by the L\'{e}vy-Khintchine formula. Since the relativistic Hamiltonians $|\nabla |$ and $\sqrt {-\triangle +m^2}-m$ are known to generate such laws, we focus on them for the analysis of probabilistic phenomena, which are shown to be associated with the relativistic wave (D'Alembert) and matter-wave (Klein-Gordon) equations, respectively. We show that such stochastic processes exist and are spatial jump processes. In general, in the presence of external potentials, they do not share the Markov property, except for stationary situations. A concrete example of the pseudodifferential Cauchy-Schr\"{o}dinger evolution is analyzed in detail. The relativistic covariance of related waveComment: Latex fil