(t); t ∈ [0; 1]} be an F-Brownian bridge process. We study the asymptoticbehaviour of non-linear functionals of regularizations by convolution of this process and apply these results to the estimation of the variance of a non-homogeneous diusion and to the convergence of the number of crossings of a level by the regularized process to a modication of the local time of the Brownian bridge as the regularization parameter goes to 0. c 2001 Elsevier Science B.V. All rights reserved.
Secondly, the reformulation of the solution of (2.1) in Theorem 3.1 has certain advantages; if an almost sure estimate on the rate of decay of U can be obtained, the problem reduces to studying the asymptoticbehaviour of the function x in (3.4), a problem which, owing to the fact that it is defined pathwise, can essentially be studied using the methods of the theory of deterministic ordinary differential equations. However, the study of the asymptoticbehaviour of X through x and U must be achieved by studying the asymptoticbehaviour of the random functions x( · , ω), U ( · , ω) for each ω in an almost sure set. This is because x(t), U (t) are not F B (t)-measurable random variables as x(t, ω), U (t, ω)
Intuitively, it would appear that the decay rate of (3) is slower than that of (1) when k is subexponential on account of the strength of the state-dependent stochastic perturbation as the solution approaches zero. Therefore, we might conjecture that the solution of a stochastic perturbation of (1) would have the same asymptoticbehaviour as (1) if the state-dependent diffusion term is sufficiently small.
a Brownian bridge is derived in Bischoff et al. (2003a), whereas in Bischoff et al. (2003b) the exact asymptoticbehaviour is obtained for h, u both piecewise linear continuous functions. In an unrelated paper Lifshits and Shi (2002) showed in Lemma 2.3 the following asymptotic lower bound
(where a and b are constants, a > 0) is also studied. The exact asymptoticbehaviour of the solutions as t → ∞ is known [1, 2, 8]. In the special case a = b the follow- ing assertion is proved. For any solution x(t) there exists an infinitely many times differentiable, periodic function ψ of period 1 such that
We extend the inductive approach to the lace expansion, previously developed to study models with critical dimension 4, to be applicable more generally. In particular, the result of this note has recently been used to prove Gaussian asymptoticbehaviour for the Fourier transform of the two-point function for suﬃciently spread-out lattice trees in dimensions d > 8, and it is potentially also applicable to percolation in dimensions d > 6.
Using the asymptotic expansion of solutions of strongly elliptic pseudodiffe- rential equations obtained in  (see also , ) and also the asymptotic expansion of potential-type functions , we obtain a complete asymptotic ex- pansion of solutions of boundary-contact problems near the contact boundaries and near the crack edge. Here it is worth noticing the effective formulae for calculating the exponent of the first terms of asymptotic expansion of solu- tions of these problems by means of the symbol of the corresponding boundary pseudodifferential equations.
Penelitian ini bertujuan menganalisis distribusi medan dan relasi dispersi gelom- bang elektromagnetik pada antaramuka gradasi Right handed material-left handed metamaterial (RH-LH) menggunakan Asymptotic Iteration Method (AIM). Analisis distribusi medan dan relasi dispersi gelombang melalui struktur RH-LH dikerjakan dengan pemodelan. Sifat gradasi RH-LH didesain dari fungsi spatial hiperbolik dengan variasi gradasi. Persamaan diferensial gelombang elektromag- netik dalam antarmuka dibangun menggunakan Persamaan Maxwell untuk media nonkonduktor (tanpa rapat muatan) dengan permetivitas dan permeabilitas tak homogen. Selanjutnya persamaan diferensial tersebut dikonversi ke persamaan diferensial biasa orde dua homogen dalam kasus satu dimensi sehingga persamaan Maxwell dapat diselesaikan secara analitik dalam domain ini.
In this paper we present alternative representations of the asymptotic distributions of the RRR estimates of impulse responses with the convergent asymptotic variances for cointegrated VAR systems. The derivation closely follows that of Phillips (1998) except one important difference concerning the treatment of unit roots. Our derivation explicitly utilizes the fact that s 5 m 2 r unit roots are not estimated by a RRR, where m is the dimension of VAR system and r is the cointegration rank. This difference leads to the asymptotic distributions with the convergent asymptotic variances even if the lead time goes to infinity.
For nonlinear systems, the Lyapunov function is a general tool for stability and robustness analysis. Nonlinear systems, contrasting linear systems, require more treatment from nonlinear controllers such as the one proposed in this paper - a backstepping and Lyapunov redesign technique. However, need to limit the control signal may offers some additional method to be pondered. In this paper, Sontag universal formulas [5-6] that mainly reported for systems without uncertainties are embedded with Backstepping and Lyapunov redesign, in order to obtain the asymptotic stability and the asymptotic disturbance rejection with less control effort. Theoretical background on backstepping technique can be reviewed in [7-9]. Theoretical background on mixed backstepping and Lyapunov redesign can be reviewed in [10-12].