1,739,651 research outputs found
On asymptotically periodic solutions of linear discrete Volterra equations
Full text linkWe show that a class of linear nonconvolution discrete Volterra equations has asymptotically periodic solutions. We also examine an example for which the calculations can be done explicitly. The results are established using theorems on the boundedness and convergence to a finite limit of solutions of linear discrete Volterra equations
Filtros volterra adaptativos: estruturas interpoladas e modelos estocásticos
Full text linkTese (doutorado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Engenharia Elétrica, Florianópolis, 2009.Este trabalho de pesquisa visa o estudo de filtros Volterra adaptativos objetivando desenvolver novas estruturas que apresentem um bom compromisso entre desempenho e complexidade computacional. Nesse contexto, abordagens interpoladas são consideradas em filtros Volterra adaptativos. Tais abordagens utilizam um filtro esparso (visando reduzir a complexidade) combinado com um interpolador para recriar os coeficientes zerados do filtro esparso. Dessa forma, diversas estruturas para a implementação eficiente de filtros Volterra adaptativos são obtidas. Algumas características importantes das estruturas interpoladas, como, por exemplo, a existência de um efeito de borda indesejável, são evidenciadas e estudas. Com vistas ao efeito de borda, um procedimento para a sua remoção é apresentado, melhorando consideravelmente o desempenho de filtros interpolados adaptativos tanto nos casos lineares quanto nos Volterra. Adicionalmente, são estudas estruturas interpoladas inteiramente adaptativas considerando filtros lineares como também filtros Volterra. Análises estatísticas de algumas estruturas Volterra adaptativas são também apresentadas com o objetivo de obter modelos estocásticos de primeira e segunda ordens para predizer o comportamento de tais estruturas. Exemplos de aplicações são considerados visando avaliar tanto os novos algoritmos desenvolvidos quanto seus modelos estatísticos
Volterra integral equations and fractional calculus: Do neighbouring solutions intersect?
Full text linkThis is the author's PDF version of an article published in Journal of Integral Equations
and Applications. The definitive version is available at rmmc.asu.edu/jie/jie.html.This journal article considers the question of whether or not the solutions to two Volterra integral equations which have the same kernel but different forcing terms may intersect at some future time
Competitive Lotka–Volterra population dynamics with jumps
No full textThis paper considers competitive Lotka–Volterra population dynamics with jumps. The contributions of this paper are as follows. (a) We show that a stochastic differential equation (SDE) with jumps associated with the model has a unique global positive solution; (b) we discuss the uniform boundedness of the pth moment with p > 0 and reveal the sample Lyapunov exponents; (c) using a variation-of-constants formula for a class of SDEs with jumps, we provide an explicit solution for one-dimensional competitive Lotka–Volterra population dynamics with jumps, and investigate the sample Lyapunov exponent for each component and the extinction of our n-dimensional model
The relation between a 2D Lotka-Volterra equation and a 2D Toda lattice
Full text linkIt is shown that the 2-discrete dimensional Lotka-Volterra lattice, the two dmensional Toda lattice equation and the recent 2-discrete dimensional Toda lattice equation of Santini et al can be obtained from a 2-discrete 2-continuous dimensional Lotka-Volterra lattice
On the asymptotic behaviour of deterministic and stochastic volterra integro-differential equations
Full text linkThis thesis examines a question of stability in stochastic and deterministic systems with memory, and involves studying the asymptotic properties of Volterra integro-differential equations. The type of stability that has been established for this class of equations is important in a variety of real-world problems which involve feedback from the past, and are subject to external random forces. These include modelling endemic diseases, and more particularly the modelling of inefficient financial markets.
The theine of the thesis is to subject a dynamical system with memory to increasingly trong and unpredictable external noise. Firstly, a fundamental deterministic Volterra quation is considered. Necessary and sufficient conditions for the solution to approach nontrivial limit are known. A strengthened version of these conditions is shown to be necessary and sufficient for exponential convergence to a nontrivial limit.
Next, a Volterra equation with a fading stochastic perturbation is studied. Two types f stochastic convergence are considered: mean square and almost sure convergence. Conditions re found which ensure that the solution converges to a non-equilibrium random imit. Moreover, the rate at which this limit is approached is established. In the mean quare case, necessary and sufficient conditions on the resolvent, kernel and noise are determined o ensure this rate of convergence. In the almost sure case, the same conditions re found to be sufficient; furthermore, it is shown that the conditions on the resolvent and he kernel are necessary. A correspoilding result was also found to hold for a more general lass of weakly singular kernels. As in the deterministic case, necessary and sufficient onditions for the solution to converge exponentially fast to its limit are found.
Finally, a stochastic Volterra equation with constant noise intensity is considered. This ives rise to the process analogous to Brownian motion, which has applications to mathematical inance. It can be shown that the increments of the process converge to a stationary tatistical distribution, which is Gaussian distributed. The conditions under which uch convergence can take place are completely characterised. In fact, a solution of a orresponding Volterra equation with infinite memory is shown to have exactly stationary ncrements which match the limiting distributions of the increments of solutions
Cyclic behaviour of Volterra composition operators
No full textWe determine the cyclic behaviour of Volterra composition operators, which are defined as (V_\phif)(x) =\int_0^{\phi(x)}f(t) dt, , 1\leq p <\infty?V_\phi\phi$ at 0 and at 1. As a particular result, we provide new examples of quasinilpotent supercyclic operators, which extend and complement previous ones of Hector Salas
Population dynamical behavior of non-autonomous Lotka-Volterra competitive system with random perturbation
No full textIn this paper, we consider a non-autonomous stochastic Lotka-Volterra competitive system dxi(t) = xi(t)[(bi(t)¡ nPj=1aij (t)xj (t))dt+¾i(t)dBi(t)], where Bi(t) (i = 1; 2; ¢ ¢ ¢ ; n) are independent standard Brownian motions. Some dynamical properties are discussed and the su±cient conditions for the existence of global positive solutions, stochastic permanence, extinction as well as global attractivity are obtained. In addition, the limit of the average in time of the sample paths of solutions is estimated
High-order volterra model predictive control and its application to a nonlinear polymerisation process
Full text linkModel Predictive Control (MPC) has recently found wide acceptance in the process industry, but the existing design and implementation methods are restricted to linear process models. A chemical process involves, however, severe nonlinearity which cannot be ignored in practice. This paper aims to solve this nonlinear control problem by extending MPC to nonlinear models. It develops an analytical framework for nonlinear model predictive control (NMPC), and also offers a third-order Volterra series based nonparametric nonlinear modelling technique for NMPC design which relieves practising engineers from the need for first deriving a physical-principles based model. An on-line realisation technique for implementing the NMPC is also developed. The NMPC is then applied to a Mitsubishi Chemicals polymerisation reaction process. The results show that this nonlinear MPC technique is feasible and very effective. It considerably outperforms linear and low-order Volterra model based methods. The advantages of the approach developed lie not only in control performance superior to existing NMPC methods, but also in relieving practising engineers from the need for deriving an analytical model and then converting it to a Volterra model through which the model can only be obtained up to the second order
Almost sure subexponential decay rates of scalar Ito-Volterra equations.
Full text linkThe paper studies the subexponential convergence of
solutions of scalar Itˆo-Volterra equations. First, we consider linear
equations with an instantaneous multiplicative noise term with
intensity . If the kernel obeys
lim
t!1
k0(t)/k(t) = 0,
and another nonexponential decay criterion, and the solution X
tends to zero as t ! 1, then
limsup
t!1
log |X(t)|
log(tk(t))
= 1 − (||), a.s.
where the random variable (||) ! 0 as ! 1 a.s. We also
prove a decay result for equations with a superlinear diffusion coefficient
at zero. If the deterministic equation has solution which is
uniformly asymptotically stable, and the kernel is subexponential,
the decay rate of the stochastic problem is exactly the same as that
of the underlying deterministic problem
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