Stability of exponential utility maximization with respect to market perturbations

We investigate the continuity of expected exponential utility maximization with respect to perturbation of the Sharpe ratio of markets. By focusing only on continuity, we impose weaker regularity conditions than those found in the literature. Specifically, we require, in addition to the V$V$-compactness hypothesis of Larsen and ?itkovi? (2007) [13], a local bmo$bmo$ hypothesis, a condition which is essentially implicit in the setting of [13]. For markets of the form S=M+∫λd〈M〉$S=M+\int \lambda d〈M〉$, these conditions are simultaneously implied by the existence of a uniform bound on the norm of λ⋅M$\lambda \cdot M$ in a suitable bmo$bmo$ space.     

Stability of generalized monotone maps with respect to their characterizations

We show that the known types of generalized monotone maps are not stable with respect to their characterizations (i.e. the characterizations are not maintained if an arbitrary map of this type is disturbed by an element with sufficiently small norm) and introduce s-quasimonotone maps, which are stable with respect to their characterization. For gradient maps, s-quasimonotonicity is related to s-quasiconvexity (introduced by Phu in Optimization, 38, 1996) of the underlying function. A necessary and sufficient condition for a univariate polynomial to be s-quasimonotone is given. Furthermore, some stability properties of s-quasiconvex functions are presented.     

Stability of elliptic PDEs with respect to perturbations of the domain

The stability of the Poho?aev nonexistence property for stationary Schrödinger equations under perturbations of the domain is investigated in this paper. We prove that the sharp threshold for the regularity comes precisely with C¹$C^1$-perturbations of the domain.     

Spectral approach to white noise analysis

By using the spectral projection theorem, we construct the classical Segal transformation as a Fourier transformation in the generalized joint eigenvectors of a certain family of field operators. It is noted that the spectral approach to the Segal transformation, which forms the basis of the analysis of Gaussian white noise, enables one to construct a significant generalization of this transformation.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 3, pp. 177–197, March, 1994.This research was supported by the Ukrainian State Committee on Science and Technology and by the Swiss National Foundation (SNF).     

Stability of plane Couette flows with respect to small periodic perturbations

We consider the plane Couette flow v₀=(x_n,0,…,0) in the infinite layer domain , where n≥2 is an integer. The exponential stability of v₀ in Lⁿ is shown under the condition that the initial perturbation is periodic in (x₁,…,x_n−1) and sufficiently small in the Lⁿ-norm.     

Stability with respect to part of the variables in systems with impulse effect

Effective sufficient conditions are found for stability with respect to part of the variables in systems of ordinary differential equations with impulse effect. The approach presented is based on the specially introduced piecewise continuous Ljapunov functions.     

Stabilization of the radial equilibrium of a tethered satellite with respect to out-of-plane initial perturbations

We investigate the stabilization of the radial equilibrium of a tethered satellite by tension control, if both in-plane and out-of-plane deviations from the vertical position are taken into account. While in-plane perturbations can be eliminated in finite time, the length rate change of the tether acts as parametric control on the out-of-plane deviations. Therefore the control becomes less effective, if the perturbation decreases. In order to improve the convergence we investigate the optimal control problem assuming no costs for the applied tension force but restricting the control force to a finite interval. For tether cconfigurations close to the vertical target position this approach yields a solution with singular control, which leads to a faster decay of the deviations. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stability radii for linear time-varying differential-algebraic equations with respect to dynamic perturbations

This paper is concerned with the robust stability for linear time-varying differential-algebraic equations. We consider the systems under the effect of uncertain dynamic perturbations. A formula of the structured stability radius is obtained. The result is an extension of a previous result for time-varying ordinary differential equations proven by Birgit Jacob [B. Jacob, A formula for the stability radius of time-varying systems, J. Differential Equations 142 (1998) 167-187].     

Stability of line bundle transforms on curves with respect to low codimensional subspaces

We show the stability of certain syzygies of line bundles oncurves, which we call line bundle transforms. Furthermore, weprove the existence of reducible theta divisors for the transformshaving integral slope. A line bundle transform is the kernelof the evaluation map on a subspace of the space of global sections.     

Stability for the class of uniformly starlike functions with respect to symmetric points

In this paper we investigate the problem of stability for the class of uniformly starlike functions with respect to symmetric points and we give the lower bounds of their radius of stability.     

Stability analysis with respect to two measures of impulsive systems under structural perturbations

The asymptotic stability with respect to two measures of impulsive systems under structural perturbations is investigated. Conditions of asymptotic (ρ₀, ρ)-stability of the system in terms of the fixed signs of some special matrices are established. Published in Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 11, pp. 1476–1484, November, 1999.     

Stability of linear functional differential systems with a multivalued feedback with respect to impulse disturbances

We consider a linear controlled functional differential system with a linear feedback channel. The system is assumed to be exponentially stable in the closed state. The feedback is assumed to be nonideal, which consists in an uncertain delay either distributed or not. The only assumption is that this delay is sufficiently small. Such a nonideal system is described by a functional differential inclusion of special type. A generalized derivative of a function of locally bounded variation is admitted to the input of the system as a free term. We obtain exponential estimates for solutions of the resulting system.     

Stochastic evolution equations with general white noise disturbance

Existence and uniqueness theorems are proved for a general class of stochastic linear abstract evolution equations, with a general type of stochastic forcing term. The abstract evolution equation is modeled using an evolution operator (or 2-parameter semigroup) approach and this includes linear partial differential equations and linear differential delay equations. The stochastic forcing term is modeled by defining an Itô stochastic integral with respect to a Hilbert space-valued orthogonal increments process, which can be used to model both Gaussian and non-Gaussian white noise processes. The theory is illustrated by examples of stochastic partial differential equations and delay equations, which arise in filtering problems for distributed and delay systems.     

Stability of wavelet frames and Riesz bases, with respect to dilations and translations

We consider the perturbation problem of wavelet frame (Riesz basis) about dilation and translation parameters and . For wavelet functions whose Fourier transforms have small supports, we give a method to determine whether the perturbation system is a frame (Riesz basis) and prove the stability about dilation parameter on Paley-Wiener space. For a great deal of wavelet functions, we give a definite answer to the stability about translation . Moreover, if the Fourier transform has small support, we can estimate the frame bounds about the perturbation of translation parameter . Our methods can be used to handle nonhomogeneous frames (Riesz basis).

     

Minimax filtering of homogeneous random fields with white noise

We consider mean-square optimal linear estimation of the transform $$A\xi = \sum\limits_{k,j = 0}^\infty {a(k,j)} \xi ( - k, - j)$$ of the homogeneous random field ξ(k, j) with density f(λ, Μ) from the observations ξ(k, j) + η(k, j) with k ≤ 0, j ≤ 0, where η(k, j) is a random field with orthogonal values uncorrelated with ξ(k, j) (white noise). We determine the worst spectral densitiesf ₀(λ, Μ) ∈ and the minimax (robust) spectral characteristics of the optimal estimator of the transform Aξ for various density classes .