Search results for "Asymptotic analysi"
showing 10 items of 21 documents
Dimensional reduction for energies with linear growth involving the bending moment
2008
A $\Gamma$-convergence analysis is used to perform a 3D-2D dimension reduction of variational problems with linear growth. The adopted scaling gives rise to a nonlinear membrane model which, because of the presence of higher order external loadings inducing a bending moment, may depend on the average in the transverse direction of a Cosserat vector field, as well as on the deformation of the mid-plane. The assumption of linear growth on the energy leads to an asymptotic analysis in the spaces of measures and of functions with bounded variation.
Cluster size distributions in particle systems with asymmetric dynamics
2001
We present exact and asymptotic results for clusters in the one-dimensional totally asymmetric exclusion process (TASEP) with two different dynamics. The expected length of the largest cluster is shown to diverge logarithmically with increasing system size for ordinary TASEP dynamics and as a logarithm divided by a double logarithm for generalized dynamics, where the hopping probability of a particle depends on the size of the cluster it belongs to. The connection with the asymptotic theory of extreme order statistics is discussed in detail. We also consider a related model of interface growth, where the deposited particles are allowed to relax to the local gravitational minimum.
On the effect of damping on dispersion curves in plates
2013
AbstractThis paper presents a study on quantitative prediction and understanding of time-harmonic wave characteristics in damped plates. Material dissipation is modelled by using complex-valued velocities of free dilatation and shear waves in an unbounded volume. As a numerical example, solution of the classical Rayleigh–Lamb problem for a viscoelastic plate is presented to illustrate and discuss the role of dissipation in the cut-off phenomenon and in the phenomenon of veering for dispersion curves. These phenomena are explained in more detail considering a simple model, which allows accurate asymptotic analysis of the perturbation of dispersion curves in the regions of cut-off and veering.
Asymptotic optimality of myopic information-based strategies for Bayesian adaptive estimation
2016
This paper presents a general asymptotic theory of sequential Bayesian estimation giving results for the strongest, almost sure convergence. We show that under certain smoothness conditions on the probability model, the greedy information gain maximization algorithm for adaptive Bayesian estimation is asymptotically optimal in the sense that the determinant of the posterior covariance in a certain neighborhood of the true parameter value is asymptotically minimal. Using this result, we also obtain an asymptotic expression for the posterior entropy based on a novel definition of almost sure convergence on "most trials" (meaning that the convergence holds on a fraction of trials that converge…
Portfolio optimisation with strictly positive transaction costs and impulse control
1998
One crucial assumption in modern portfolio theory of continuous-time models is the no transaction cost assumption. This assumption normally leads to trading strategies with infinite variation. However, following such a strategy in the presence of transaction costs will lead to immediate ruin. We present an impulse control approach where the investor can change his portfolio only finitely often in finite time intervals. Further, we consider transaction costs including a fixed and a proportional cost component. For the solution of the resulting control problems we present a formal optimal stopping approach and an approach using quasi-variational inequalities. As an application we derive a non…
ASYMPTOTIC CURVES ON SURFACES IN ℝ5
2008
We study asymptotic curves on generically immersed surfaces in ℝ5. We characterize asymptotic directions via the contact of the surface with flat objects (k-planes, k = 1 - 4), give the equation of the asymptotic curves in terms of the coefficients of the second fundamental form and study their generic local configurations.
MUSIC-characterization of small scatterers for normal measurement data
2009
We investigate the reconstruction of the positions of a collection of small metallic objects buried beneath the ground from measurements of the vertical component of scattered fields corresponding to vertically polarized dipole excitations on a horizontal two-dimensional measurement device above the surface of the ground. A MUSIC reconstruction method for this problem has recently been proposed by Iakovleva et al (2007 IEEE Trans. Antennas Propag. 55 2598). In this paper, we give a rigorous theoretical justification of this method. To that end we prove a characterization of the positions of the scatterers in terms of the measurement data, applying an asymptotic analysis of the scattered fie…
Option Pricing and Hedging in the Presence of Transaction Costs and Nonlinear Partial Differential Equations
2008
In the presence of transaction costs the perfect option replication is impossible which invalidates the celebrated Black and Scholes (1973) model. In this chapter we consider some approaches to option pricing and hedging in the presence of transaction costs. The distinguishing feature of all these approaches is that the solution for the option price and hedging strategy is given by a nonlinear partial differential equation (PDE). We start with a review of the Leland (1985) approach which yields a nonlinear parabolic PDE for the option price, one of the first such in finance. Since the Leland's approach to option pricing has been criticized on different grounds, we present a justification of…
European Option Pricing with Transaction Costs and Stochastic Volatility: an Asymptotic Analysis
2015
In this paper the valuation problem of a European call option in presence of both stochastic volatility and transaction costs is considered. In the limit of small transaction costs and fast mean reversion, an asymptotic expression for the option price is obtained. While the dominant term in the expansion it is shown to be the classical Black and Scholes solution, the correction terms appear at $O(\varepsilon^{1/2})$ and $O(\varepsilon)$. The optimal hedging strategy is then explicitly obtained for the Scott's model.
On some bifurcation analysis techniques for continuous systems
2016
This paper is devoted to techniques in bifurcation analysis for continuous mechanical systems, concentrating on polynomial equations and implicitly given functions. These are often encountered in problems of mechanics and especially in stability analysis. Taking a classical approach, we summarize the relevant features of the cubic polynomial equation, and present some new aspects for asymptotics and parametric representation of the solutions. This is followed by a brief look into the implicit function theorem as a tool for analyzing bifurcations. As an example from mechanics, we consider bifurcations in the transverse free vibration problem of an axially compressed beam. peerReviewed