(t); t ∈ [0; 1]} be an F-Brownian bridge process. We study the **asymptotic** **behaviour** 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 **asymptotic** **behaviour** 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 **asymptotic** **behaviour** of X through x and U must be achieved by studying the **asymptotic** **behaviour** 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)

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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 **asymptotic** **behaviour** as (1) if the state-dependent diffusion term is sufficiently small.

ASYMPTOTIC BEHAVIOUR OF SOLUTIONS OF SOME DIFFERENTIAL EQUATIONS WITH AN UNBOUNDED DELAY Jan ˇCerm´ak A bstract.We investigate the asymptotic properties of all solutions of the functio[r]

Asymptotic behaviour of positive solutions of the model which describes cell differentiation Svetlin Georgiev Georgiev University of Veliko Tarnovo, Department of Mathematical analysis[r]

Regularity, nonoscillation and asymptotic behaviour of solutions of second order linear equations Vojislav Mari´c Serbian Academy of Sciences and Arts, Belgrade, Novi Sad Branch, 2100[r]

[11] Karsai J., On the asymptotic behaviour of solution of second order linear differential equations with small damping, Acta Math.. [12] Karsai J., Attractivity criteria for intermitte[r]

a Brownian bridge is derived in Bischoff et al. (2003a), whereas in Bischoff et al. (2003b) the exact **asymptotic** **behaviour** 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 **asymptotic** **behaviour** 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 **asymptotic** **behaviour** 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.

Menurut Becker salah satu klasifikasi perilaku yang berhubungan dengan kesehatan Healt Related Behaviour yaitu perilaku sehat healthy behaviour yaitu perilaku untuk mempertahankan dan m[r]

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Errora Asymptotic Sig.b Lower Bound Upper Bound Asymptotic 95% Confidence Interval The test result variables: LEUKOSIT has at least one tie between the positive actual state group an[r]

Using the **asymptotic** expansion of solutions of strongly elliptic pseudodiffe- rential equations obtained in [10] (see also [18], [3]) and also the **asymptotic** expansion of potential-type functions [9], 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.

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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.

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Perilaku Spontan spontaneus behaviour Perilaku Spontan spontaneus behaviour adalah perilaku yang dilakukan berdasar desakan emosi dan dilakukan tanpa sensor serta revisi secara kognisi.[r]

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.

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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].

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All other tests assume asymptotic normality.. Intermediate ADF test results IPM?[r]

Errora Asymptotic Sig.b Asymptotic 95% Confidence Interval Lower Bound Upper Bound .904 .054 .000 .799 1.009 The test result variables: Cirrhosis Index has at least one tie between t[r]

Because of the apparently clear-cut nature of the assignment of profit responsibility in a business unit organization, designers of management control systems sometimes recommend suc[r]