Asymptotic Analysis - Volume 75, issue 3-4

Authors: Helffer, B. | Laleg-Kirati, T.M.

Article Type: Research Article

Abstract: This study explores the reconstruction of a signal using spectral quantities associated with some self-adjoint realization of an h-dependent Schrödinger operator −h2 (d2 /dx2 )−y(x), h>0, when the parameter h tends to 0. Theoretical results in semi-classical analysis are proved. Some numerical results are also presented. We first consider as a toy model the sech 2 function. Then we study a real signal given by arterial blood pressure measurements. This approach seems to be very promising in signal analysis. Indeed it provides new spectral quantities that can give relevant information on some signals as it is the case for arterial …blood pressure signal. Show more

Keywords: semi-classical analysis, Schrödinger operator, signal analysis, arterial blood pressure

DOI: 10.3233/ASY-2011-1054

Citation: Asymptotic Analysis, vol. 75, no. 3-4, pp. 125-144, 2011

Authors: Kaligotla, S. | Lototsky, S.V.

Article Type: Research Article

Abstract: It has been known for a while that a nonlinear equation driven by singular noise must be interpreted in the renormalized, or Wick, form. For the stochastic Burgers equation, Wick nonlinearity forces the solution to be a generalized process no matter how regular the random perturbation is, whence the curse. On the other hand, certain multiplicative random perturbations of the deterministic Burgers equation can only be interpreted in the Wick form, whence the cure. The analysis is based on the study of the coefficients of the chaos expansion of the solution at different stochastic scales.

Keywords: Catalan numbers, Hida–Kondratiev spaces, polynomial chaos

DOI: 10.3233/ASY-2011-1058

Citation: Asymptotic Analysis, vol. 75, no. 3-4, pp. 145-168, 2011

Authors: Tamura, Takashi | Watanabe, Yûsuke

Article Type: Research Article

Abstract: We consider a market model where risky securities are affected by “hidden” economic factors, which evolve as a finite-state Markov chain. Our problem is optimizing an expected risk-averse power utility of wealth on finite and infinite time horizons. We construct a classical solution of the Hamilton–Jacobi–Bellman equation corresponding to the problem. We also prove some verification theorems.

Keywords: risk-sensitive control, hidden Markov models, Wonham filter, ergodic control

DOI: 10.3233/ASY-2011-1059

Citation: Asymptotic Analysis, vol. 75, no. 3-4, pp. 169-209, 2011

Authors: Wang, X.-S. | Wong, R.

Article Type: Research Article

Abstract: Using the steepest descent method for oscillatory Riemann–Hilbert problems introduced by Deift and Zhou [Ann. Math. 137 (1993), 295–368], we derive asymptotic formulas for the Meixner polynomials in two regions of the complex plane separated by the boundary of a rectangle. The asymptotic formula on the boundary of the rectangle is obtained by taking limits from either inside or outside. Our results agree with the ones obtained earlier for z on the positive real line by using the steepest descent method for integrals [Constr. Approx. 14 (1998), 113–150].

Keywords: global asymptotics, Meixner polynomials, Riemann–Hilbert problems, Airy function

DOI: 10.3233/ASY-2011-1060

Citation: Asymptotic Analysis, vol. 75, no. 3-4, pp. 211-231, 2011

Authors: Dimassi, Mouez | Zerzeri, Maher

Article Type: Research Article

Abstract: In the large coupling constant limit, we obtain an asymptotic expansion in powers of μ−1/δ of the derivative of the spectral shift function corresponding to the pair (Pμ =P0 +μW(x),P0 =−Δx +V(x)), where W(x) is positive, W(x)~w0 (x/|x|)|x|−δ near infinity for some δ>n and w0 ∈C∞ (Sn−1 ;R+ ). Here Sn−1 is the unite sphere of the space Rn and μ is a large parameter. The potential V is real-valued, smooth and periodic with respect to a lattice Γ in Rn .

Keywords: periodic Schrödinger operator, spectral shift function, asymptotic expansions, limiting absorption theorem

DOI: 10.3233/ASY-2011-1062

Citation: Asymptotic Analysis, vol. 75, no. 3-4, pp. 233-250, 2011

Article Type: Other

Citation: Asymptotic Analysis, vol. 75, no. 3-4, pp. 251-251, 2011