Search results for "Stochastic process"

Modeling long-range memory with stationary Markovian processes

2009

In this paper we give explicit examples of power-law correlated stationary Markovian processes y(t) where the stationary pdf shows tails which are gaussian or exponential. These processes are obtained by simply performing a coordinate transformation of a specific power-law correlated additive process x(t), already known in the literature, whose pdf shows power-law tails 1/x^a. We give analytical and numerical evidence that although the new processes (i) are Markovian and (ii) have gaussian or exponential tails their autocorrelation function still shows a power-law decay =1/T^b where b grows with a with a law which is compatible with b=a/2-c, where c is a numerical constant. When a<2(1+c) th…

SIRV epidemic model with stochastic perturbation

2014

We propose a stochastic disease model where vaccination is included and such that the immunity is permanent. The existence, uniqueness and positivity of the solution and the stability of the disease free-equilibrium are studied

Asymptotic Hölder regularity for the ellipsoid process

2020

We obtain an asymptotic Hölder estimate for functions satisfying a dynamic programming principle arising from a so-called ellipsoid process. By the ellipsoid process we mean a generalization of the random walk where the next step in the process is taken inside a given space dependent ellipsoid. This stochastic process is related to elliptic equations in non-divergence form with bounded and measurable coefficients, and the regularity estimate is stable as the step size of the process converges to zero. The proof, which requires certain control on the distortion and the measure of the ellipsoids but not continuity assumption, is based on the coupling method.

Empirical Study on the Relationship between the Cross-Correlation among Stocks and the Stocks' Volatility Clustering

2013

In this paper we discuss univariate and multivariate statistical properties of volatility with the aim of understanding how these two aspects are interrelated. Specifically, we focus on the relationship between the cross-correlation among stock's volatilities and the volatility clustering. Volatility clustering is related to the memory property of the volatility time-series and therefore to its predictability. Our results show that there exists a relationship between the level of predictability of any volatility time-series and the amount of its inter-dependence with other assets. In all considered cases, the more the asset is linked to other assets, the more its volatility keeps memory of …

Deterministic folding in stiff elastic membranes.

2008

Crumpled membranes have been found to be characterized by complex patterns of spatially seemingly random facets separated by narrow ridges of high elastic energy. We demonstrate by numerical simulations that compression of stiff elastic membranes with small randomness in their initial configurations leads to either random ridge configurations (high entropy) or nearly deterministic folds (low elastic energy). For folding with symmetric ridge configurations to appear in part of the crumpling processes, the crumpling rate must be slow enough. Folding stops when the thickness of the folded structure becomes important, and crumpling continues thereafter as a random process.

Directionlets: Anisotropic Multidirectional representation with separable filtering

2006

In spite of the success of the standard wavelet transform (WT) in image processing in recent years, the efficiency of its representation is limited by the spatial isotropy of its basis functions built in the horizontal and vertical directions. One-dimensional (1-D) discontinuities in images (edges and contours) that are very important elements in visual perception, intersect too many wavelet basis functions and lead to a nonsparse representation. To efficiently capture these anisotropic geometrical structures characterized by many more than the horizontal and vertical directions, a more complex multidirectional (M-DIR) and anisotropic transform is required. We present a new lattice-based pe…

Ghost stochastic resonance in FitzHugh–Nagumo circuit

2014

International audience; The response of a neural circuit submitted to a bi-chromatic stimulus and corrupted by noise is investigated. In the presence of noise, when the spike firing of the circuit is analysed, a frequency not present at the circuit input appears. For a given range of noise intensities, it is shown that this ghost frequency is almost exclusively present in the interspike interval distribution. This phenomenon is for the first time shown experimentally in a FitzHugh-Nagumo circuit.

Gradient walks and $p$-harmonic functions

2017

Decoupling on the Wiener space and variational estimates for BSDEs

2015

Stability of stochastic nonlinear systems with state-dependent switching

2013

In this paper, the problem of stability on stochastic systems with state-dependent switching is investigated. To analyze properties of the switched system by means of Itô’s formula and Dynkin’s formula, it is critical to show switching instants being stopping times. When the given active-region set can be replaced by its interior, the local solution of the switched system is constructed by defining a series of stopping times as switching instants, and the criteria on global existence and stability of solution are presented by Lyapunov approach. For the case where the active-region set can not be replaced by its interior, the switched systems do not necessarily have solutions, thereby quasi-…