Search results for "Mathematical analysis"
showing 10 items of 2409 documents
Juggler's exclusion process
2012
Juggler's exclusion process describes a system of particles on the positive integers where particles drift down to zero at unit speed. After a particle hits zero, it jumps into a randomly chosen unoccupied site. We model the system as a set-valued Markov process and show that the process is ergodic if the family of jump height distributions is uniformly integrable. In a special case where the particles jump according to a set-avoiding memoryless distribution, the process reaches its equilibrium in finite nonrandom time, and the equilibrium distribution can be represented as a Gibbs measure conforming to a linear gravitational potential.
Tests for real and complex unit roots in vector autoregressive models
2014
The article proposes new tests for the number of real and complex unit roots in vector autoregressive models. The tests are based on the eigenvalues of the sample companion matrix. The limiting distributions of the eigenvalues converging to the unit eigenvalues turn out to be of a non-standard form and expressible in terms of Brownian motions. The tests are defined such that the null distributions related to eigenvalues +/-1 are the same. The tests for the unit eigenvalues with nonzero imaginary part are defined independently of the angular frequency. When the tests are adjusted for deterministic terms, the null distributions usually change. Critical values are tabulated via simulations. Al…
Characteristic Functions and the Central Limit Theorem
2020
The main goal of this chapter is the central limit theorem (CLT) for sums of independent random variables (Theorem 15.37) and for independent arrays of random variables (Lindeberg–Feller theorem, Theorem 15.43). For the latter, we prove only that one of the two implications (Lindeberg’s theorem) that is of interest in the applications.
Riemann-Type Definition of the Improper Integrals
2004
Riemann-type definitions of the Riemann improper integral and of the Lebesgue improper integral are obtained from McShane's definition of the Lebesgue integral by imposing a Kurzweil-Henstock's condition on McShane's partitions.
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…
Oxygen Consuming Regions in EMT60/Ro Multicellular Tumour Spheroids Determined by Nonlinear Regression Analysis of Experimental PO2 Profiles
1987
Malignant cells can be studied in vitro, in a tumour-like microenvironment, by growing multicellular tumour spheroids in culture (Sutherland, McCredie and Inch, 1971). Franko and Sutherland (1979) utilized diffusion theory to explain the viable rim thicknesses of spheroids measured histologically. Without PO2 profiles, however, an unequivocal interpretation of their results was not possible. Systematic studies of the PO2 profiles in spheroids have since been made with oxygen microelectrodes by several groups (Carlsson et al., 1979; Kaufman et al., 1981; Mueller-Klieser and Sutherland, 1982a,b). Based on these measurements, new analyses utilizing diffusion theory are being developed to chara…
A class of stochastic differential equations with non-Lipschitzian coefficients: pathwise uniqueness and no explosion
2003
Abstract A new result for the pathwise uniqueness of solutions of stochastic differential equations with non-Lipschitzian coefficients is established. Furthermore, we prove that the solution has no explosion under the growth ξlogξ. To cite this article: S. Fang, T. Zhang, C. R. Acad. Sci. Paris, Ser. I 337 (2003).
Ito and Stratonovich integrals for delta-correlated processes
1993
Abstract In this paper the generalization of the Itd and Stratonovich integrals for the case of non-linear systems excited by parametric delta-correlated processes is presented. This generalization gives a new light on the corrective coefficients in the stochastic differential equations driven by parametric delta-correlated processes. The full significance of these corrective terms is evidenced by means of some examples.
Stability under influence of noise with regulated periodicity
2009
A very simple stochastic differential equation with quasi‐periodical multiplicative noise is investigated analytically. For fixed noise intensity the system can be stable at high noise periodicity and unstable at low noise periodicity.
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.