Search results for "EQUATIONS"
showing 10 items of 955 documents
Fourth Moments and Independent Component Analysis
2015
In independent component analysis it is assumed that the components of the observed random vector are linear combinations of latent independent random variables, and the aim is then to find an estimate for a transformation matrix back to these independent components. In the engineering literature, there are several traditional estimation procedures based on the use of fourth moments, such as FOBI (fourth order blind identification), JADE (joint approximate diagonalization of eigenmatrices), and FastICA, but the statistical properties of these estimates are not well known. In this paper various independent component functionals based on the fourth moments are discussed in detail, starting wi…
Random walk approximation of BSDEs with H{\"o}lder continuous terminal condition
2018
In this paper, we consider the random walk approximation of the solution of a Markovian BSDE whose terminal condition is a locally Hölder continuous function of the Brownian motion. We state the rate of the L2-convergence of the approximated solution to the true one. The proof relies in part on growth and smoothness properties of the solution u of the associated PDE. Here we improve existing results by showing some properties of the second derivative of u in space. peerReviewed
Steady-state dynamic response of various hysteretic systems endowed with fractional derivative elements
2019
In this paper, the steady-state dynamic response of hysteretic oscillators comprising fractional derivative elements and subjected to harmonic excitation is examined. Notably, this problem may arise in several circumstances, as for instance, when structures which inherently exhibit hysteretic behavior are supplemented with dampers or isolators often modeled by employing fractional terms. The amplitude of the steady-state response is determined analytically by using an equivalent linearization approach. The procedure yields an equivalent linear system with stiffness and damping coefficients which are related to the amplitude of the response, but also, to the order of the fractional derivativ…
Spatio-temporal behaviour of the deep chlorophyll maximum in Mediterranean Sea: Development of a stochastic model for picophytoplankton dynamics
2013
In this paper, by using a stochastic reaction-diffusion-taxis model, we analyze the picophytoplankton dynamics in the basin of the Mediterranean Sea, characterized by poorly mixed waters. The model includes intraspecific competition of picophytoplankton for light and nutrients. The multiplicative noise sources present in the model account for random fluctuations of environmental variables. Phytoplankton distributions obtained from the model show a good agreement with experimental data sampled in two different sites of the Sicily Channel. The results could be extended to analyze data collected in different sites of the Mediterranean Sea and to devise predictive models for phytoplankton dynam…
Modeling of Sensory Characteristics Based on the Growth of Food Spoilage Bacteria
2016
During last years theoretical works shed new light and proposed new hypothesis on the mechanisms which regulate the time behaviour of biological populations in different natural systems. Despite of this, the role of environmental variables in ecological systems is still an open question. Filling this gap of knowledge is a crucial task for a deeper comprehension of the dynamics of biological populations in real ecosystems. In this work we study how the dynamics of food spoilage bacteria influences the sensory characteristics of fresh fish specimens. This topic is crucial for a better understanding of the role played by the bacterial growth on the organoleptic properties, and for the quality …
Mean-field games and two-point boundary value problems
2014
A large population of agents seeking to regulate their state to values characterized by a low density is considered. The problem is posed as a mean-field game, for which solutions depend on two partial differential equations, namely the Hamilton-Jacobi-Bellman equation and the Fokker-Plank-Kolmogorov equation. The case in which the distribution of agents is a sum of polynomials and the value function is quadratic is considered. It is shown that a set of ordinary differential equations, with two-point boundary value conditions, can be solved in place of the more complicated partial differential equations associated with the problem. The theory is illustrated by a numerical example.
Oscillation of second-order neutral differential equations
2015
Author's version of an article in the journal: Funkcialaj Ekvacioj. Also available from the publisher at: http://www.math.kobe-u.ac.jp/~fe/
Stochastic Differential Equations
2020
Stochastic differential equations describe the time evolution of certain continuous n-dimensional Markov processes. In contrast with classical differential equations, in addition to the derivative of the function, there is a term that describes the random fluctuations that are coded as an Ito integral with respect to a Brownian motion. Depending on how seriously we take the concrete Brownian motion as the driving force of the noise, we speak of strong and weak solutions. In the first section, we develop the theory of strong solutions under Lipschitz conditions for the coefficients. In the second section, we develop the so-called (local) martingale problem as a method of establishing weak so…