Rate of Convergence

This paper introduces a new stochastic process, a collection of U-statis-tics indexed by a family of symmetric kemels. Conditions are found for the uniform almost-sure convergence of a sequence of such processes. Rates of convergence are obtained. An application to cross-validation ...

The convergence properties of the new regularized Euclidean residual method for solving general nonlinear least-squares and nonlinear equation problems are investigated. This method, derived from a proposal by Nesterov [Optim. Methods Softw., 22 (2007), pp. 469-483], uses a model of the objective function consisting of the unsquared Euclidean linearized residual regularized by a quadratic term. At variance with previous analysis, its convergence properties are here considered without assuming uniformly nonsingular ...

This paper presents a synthesis on the mathematical work done on level crossings of stationary Gaussian processes, with some extensions. The main results [(factorial) moments, representation into the Wiener Chaos, asymptotic results, rate of convergence, local time and number of crossings] are described, as well as the different approaches [normal comparison method, Rice method, Stein-Chen method, a general m-dependent method] used to obtain them; these methods are also very useful in the general context of Gaussian fields. Finally some extensions [time occupation functionals, number of maxima in an interval, process indexed by a bidimensional set] are proposed, illustrating the generality of the methods. A large inventory of papers and books on the subject ends the survey.

Let f(·,t) be the probability density function which represents the solution of Kac's equation at time t, with initial data f_0, and let g_σ be the Gaussian density with zero mean and variance σ^2, σ^2 being the value of the second moment of f_0. This is the first study which proves that the total variation distance between f(·,t) and g_σ goes to zero, as t→ +∞, with an exponential rate equal to -1/4. In the present paper, this fact is proved on the sole assumption that f_0 has finite fourth moment and its Fourier transform φ_0 satisfies |φ_0(ξ)|=o(|ξ|^-p) as |ξ|→+∞, for some p>0. These hypotheses are definitely weaker than those considered so far in the state-of-the-art literature, which in any case, obtains less precise rates.

In this paper, a pipelined version of genetic algorithm, called PLGA, and a corresponding hardware platform are described. The basic operations of conventional GA (CGA) are made pipelined using an appropriate selection scheme. The selection operator, used here, is stochastic in nature and is called SA-selection. This helps maintaining the basic generational nature of the proposed pipelined GA (PLGA). A

In this article we obtain rates of convergence to equilibrium of marked Hawkes processes in two situations. Firstly, the stationary process is the empty process, in which case we speak of the rate of extinction. Secondly, the stationary process is the unique stationary and nontrivial marked Hawkes process, in which case we speak of the rate of installation. The first situation models small epidemics, whereas the results in the second case are useful in deriving stopping rules for simulation algorithms of Hawkes processes with random marks.

Cam clay models are one of the popularly used soil plasticity models. Finite element implementation of these models requires integration of constitutive relations and load stepping scheme. There have been considerable advances in the integration of constitutive relations. These methods can be grouped as explicit and implicit methods. The superiority of one over the other lies in the context of convergence, accuracy, stability, consistency and simplicity of implementation. In this paper these issues have been addressed in the context of solution of algebraic-differential equations. This approach is extension of the work of Ellsiepen and Hartmaan to modified Cam clay model. Treating nonlinear problem of Cam clay plasticity in this way facilitates to apply all the numerical algorithm of mathematics for the solution of algebraic differential equations. Numerical analysis of this approach gives the better proof for convergence and stability. This approach combines the time integration me...

We present an analysis of a recently proposed integral-equation method for the solution of high-frequency electromagnetic and acoustic scattering problems that delivers error-controllable solutions in frequency-independent computational times. Within single scattering ...

This paper shows how large-dimensional dynamic factor models are suitable for structural analysis. We argue that all identification schemes employed in structural vector autoregression (SVAR) analysis can be easily adapted in dynamic factor models. Moreover, the “problem of fundamentalness,” which is intractable in SVARs, can be solved, provided that the impulse-response functions are sufficiently heterogeneous. We provide consistent estimators for the impulse-response functions and for (n, T) rates of convergence. An exercise with U.S. macroeconomic data shows that our solution of the fundamentalness problem may have important empirical consequences.

Often considered in numerical simulations related to the control of quantum systems, the so-called monotonic schemes have not been so far much studied from the functional analysis point of view. Yet, these procedures provide an efficient constructive method for solving a certain class of optimal control problems. This paper aims both at extending the results already available about these algorithms in the finite dimensional case (i.e., the time-discretized case) and at completing those of the continuous case. This paper starts with some results about the regularity of a functional related to a wide class of model in quantum chemistry. Those enable us to extend an inequality due to