Search results for "Stochastic Proce"
showing 10 items of 349 documents
Synchronization and fluctuations for interacting stochastic systems with individual and collective reinforcement
2020
The Pólya urn is the paradigmatic example of a reinforced stochastic process. It leads to a random (non degenerated) time-limit. The Friedman urn is a natural generalization whose a.s. time-limit is not random anymore. In this work, in the stream of previous recent works, we introduce a new family of (finite) systems of reinforced stochastic processes, interacting through an additional collective reinforcement of mean field type. The two reinforcement rules strengths (one componentwise, one collective) are tuned through (possibly) different rates n −γ. In the case the reinforcement rates are like n −1 , these reinforcements are of Pólya or Friedman type as in urn contexts and may thus lead …
Generation of aperiodic picosecond pulses sequences from incoherent optical waves
2007
We present an original method to generate optical pulses trains with random time-interval values from incoherent broadband sources. Our technique relies on the remarkable properties of a line made of cascaded SPM-based optical regenerators.
Stochastic Graph Filtering Under Asymmetric Links in Wireless Sensor Networks
2018
Wireless sensor networks (WSN s) are often characterized by random and asymmetric packet losses due to the wireless medium, leading to network topologies that can be modeled as random, time-varying and directed graphs. Most of existing works related to graph filtering in the context of WSNs assume that the probability of delivering an information from one node to a neighbor node is the same as in the reverse direction. This assumption is not realistic due to the typical link asymmetry in WSNs caused by interferences and background noise. In this work, we analyze the problem of applying stochastic graph filtering over random time-varying asymmetric network topologies. We show that it is poss…
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.