Search results for "Probability"
showing 10 items of 3417 documents
Noise Induced Phenomena in the Dynamics of Two Competing Species
2015
Noise through its interaction with the nonlinearity of the living systems can give rise to counter-intuitive phenomena. In this paper we shortly review noise induced effects in different ecosystems, in which two populations compete for the same resources. We also present new results on spatial patterns of two populations, while modeling real distributions of anchovies and sardines. The transient dynamics of these ecosystems are analyzed through generalized Lotka-Volterra equations in the presence of multiplicative noise, which models the interaction between the species and the environment. We find noise induced phenomena such as quasi-deterministic oscillations, stochastic resonance, noise …
A Scenario Simulation Model of Stock's Volatility Based on a Stationary Markovian Process
2013
In this paper we discuss univariate statistical properties of volatility. We present a parsimonious univariate model that well reproduces two stylized facts of volatility: the power-law decay of the volatility probability density function with exponent α and the power-law decay of the autocorrelation function with exponent β. Such model also reproduces, at least qualitatively, the empirical observation than when the probability density function decays faster, then the autocorrelation decays slower. Another important feature investigated within the model is the mean First Passage Time (mFPT) Tx0 (Λ) of volatility time-series. We show that the proposed model allows to obtain the mFPT in terms…
THE KEY ROLE OF LIQUIDITY FLUCTUATIONS IN DETERMINING LARGE PRICE CHANGES
2005
Recent empirical analyses have shown that liquidity fluctuations are important for understanding large price changes of financial assets. These liquidity fluctuations are quantified by gaps in the order book, corresponding to blocks of adjacent price levels containing no quotes. Here we study the statistical properties of the state of the limit order book for 16 stocks traded at the London Stock Exchange (LSE). We show that the time series of the first three gaps are characterized by fat tails in the probability distribution and are described by long memory processes.
Informative model for national development management
2010
Strategic planning experience shows the major problem of the national planning system - plan- ning documents are faintly intercorrelative (including aspects "from long-term to short-term" and "from general to concrete"), as well non-linked with managing and implementing institutions (public sector func- tions and services) and budgetary appropriation. It creates huge barriers to carry out plans. Structurization of all system's objects in logical units and determination of strict interrelations between them is the pro- posed solution of the problem. Informative model of planning system have to be developed as depository of logical units and their interlinkage. It becomes possible to manage i…
Deformation Quantization by Moyal Star-Product and Stratonovich Chaos
2012
We make a deformation quantization by Moyal star-product on a space of functions endowed with the normalized Wick product and where Stratonovich chaos are well defined.
Set-valued and fuzzy stochastic differential equations driven by semimartingales
2013
Abstract In the paper we present set-valued and fuzzy stochastic integrals with respect to semimartingale integrators as well as their main properties. Then we study the existence of solutions to set-valued and fuzzy-set-valued stochastic differential equations driven by semimartingales. The stability of solutions is also established.
The Itô Integral
2014
The Ito integral allows us to integrate stochastic processes with respect to the increments of a Brownian motion or a somewhat more general stochastic process. We develop the Ito integral first for Brownian motion and then for generalized diffusion processes (so called Ito processes). In the third section, we derive the celebrated Ito formula. This is the chain rule for the Ito integral that enables us to do explicit calculations with the Ito integral. In the fourth section, we use the Ito formula to obtain a stochastic solution of the classical Dirichlet problem. This in turn is used in the fifth section in order to show that like symmetric simple random walk, Brownian motion is recurrent …
Fuzzy Stochastic Integral Equations Driven by Martingales
2011
Exploiting the properties of set-valued stochastic trajectory integrals we consider a notion of fuzzy stochastic Lebesgue–Stieltjes trajectory integral and a notion of fuzzy stochastic trajectory integral with respect to martingale. Then we use these integrals in a formulation of fuzzy stochastic integral equations. We investigate the existence and uniqueness of solution to such the equations.
Numerical simulation of resonant activation in a fluctuating metastable model system
1998
We study the escape time from a metastable overdamped model system in the presence of two noise sources: a white noise and a random telegraph noise. The random telegraph noise controls the height of the potential barrier of the metastable system while the white noise mimics the presence of a given temperature. We report on numerical simulations about: (i) the average residence time of the system in the metastable state; (ii) the probability density function (PDF) of the residence time at various values of the correlation time T c of the random telegraph noise. Resonant activation is observed in the dynamics of the investigated system. The PDF shows different shapes for different values of τ…
Calculation of modification of alkali metal atomic transition probability in strong external magnetic field and its application
2010
International audience; Interaction of alkali atoms with external magnetic field induced a splitting and a shift of their energy levels. We have study this interaction for external field from 0 to 5000 Gauss when the alkali vapor is confined in submicron thin vapor cell with thickness L = λ/2. Rubidium and Sodium vapors have been studied. The Hamiltonian can be expressed as the sum of the unperturbated atomic Hamiltonian and the so-called Zeeman Hamiltonian. The probability of a transition, induced by the laser electric field is proportional to the square of the transfer coefficients modified by the presence of the magnetic field. We will show that the strong nonlinearity of the transition …