Search results for "LIMIT"
showing 10 items of 2826 documents
Entry with two correlated signals : the case of industrial espionage and its positive competitive effects
2021
Recent advances in information and communication technologies have increased the incentives for firms to acquire information about rivals. These advances may have major implications for market entry because they make it easier for potential entrants to gather valuable information about, for example, an incumbent’s cost structure. However, little theoretical research has actually analyzed this question. This paper advances the literature by extending a one-sided asymmetric information version of Milgrom and Roberts’ (1982) limit pricing model. Here, the entrant is allowed access to an intelligence system (IS) of a certain precision that generates a noisy signal on the incumbent’s cost struct…
Large deviations results for subexponential tails, with applications to insurance risk
1996
AbstractConsider a random walk or Lévy process {St} and let τ(u) = inf {t⩾0 : St > u}, P(u)(·) = P(· | τ(u) < ∞). Assuming that the upwards jumps are heavy-tailed, say subexponential (e.g. Pareto, Weibull or lognormal), the asymptotic form of the P(u)-distribution of the process {St} up to time τ(u) is described as u → ∞. Essentially, the results confirm the folklore that level crossing occurs as result of one big jump. Particular sharp conclusions are obtained for downwards skip-free processes like the classical compound Poisson insurance risk process where the formulation is in terms of total variation convergence. The ideas of the proof involve excursions and path decompositions for Mark…
Confidence bands for Horvitz-Thompson estimators using sampled noisy functional data
2013
When collections of functional data are too large to be exhaustively observed, survey sampling techniques provide an effective way to estimate global quantities such as the population mean function. Assuming functional data are collected from a finite population according to a probabilistic sampling scheme, with the measurements being discrete in time and noisy, we propose to first smooth the sampled trajectories with local polynomials and then estimate the mean function with a Horvitz-Thompson estimator. Under mild conditions on the population size, observation times, regularity of the trajectories, sampling scheme, and smoothing bandwidth, we prove a Central Limit theorem in the space of …
From deterministic cellular automata to coupled map lattices
2016
A general mathematical method is presented for the systematic construction of coupled map lattices (CMLs) out of deterministic cellular automata (CAs). The entire CA rule space is addressed by means of a universal map for CAs that we have recently derived and that is not dependent on any freely adjustable parameters. The CMLs thus constructed are termed real-valued deterministic cellular automata (RDCA) and encompass all deterministic CAs in rule space in the asymptotic limit $\kappa \to 0$ of a continuous parameter $\kappa$. Thus, RDCAs generalize CAs in such a way that they constitute CMLs when $\kappa$ is finite and nonvanishing. In the limit $\kappa \to \infty$ all RDCAs are shown to ex…
A form factor approach to the asymptotic behavior of correlation functions in critical models
2011
We propose a form factor approach for the computation of the large distance asymptotic behavior of correlation functions in quantum critical (integrable) models. In the large distance regime we reduce the summation over all excited states to one over the particle/hole excitations lying on the Fermi surface in the thermodynamic limit. We compute these sums, over the so-called critical form factors, exactly. Thus we obtain the leading large distance behavior of each oscillating harmonic of the correlation function asymptotic expansion, including the corresponding amplitudes. Our method is applicable to a wide variety of integrable models and yields precisely the results stemming from the Lutt…
Thermal form factors of the XXZ chain and the large-distance asymptotics of its temperature dependent correlation functions
2013
We derive expressions for the form factors of the quantum transfer matrix of the spin-1/2 XXZ chain which are suitable for taking the infinite Trotter number limit. These form factors determine the finitely many amplitudes in the leading asymptotics of the finite-temperature correlation functions of the model. We consider form-factor expansions of the longitudinal and transversal two-point functions. Remarkably, the formulae for the amplitudes are in both cases of the same form. We also explain how to adapt our formulae to the description of ground state correlation functions of the finite chain. The usefulness of our novel formulae is demonstrated by working out explicit results in the hig…
Thermodynamic limit of particle-hole form factors in the massless XXZ Heisenberg chain
2010
We study the thermodynamic limit of the particle-hole form factors of the XXZ Heisenberg chain in the massless regime. We show that, in this limit, such form factors decrease as an explicitly computed power-law in the system-size. Moreover, the corresponding amplitudes can be obtained as a product of a "smooth" and a "discrete" part: the former depends continuously on the rapidities of the particles and holes, whereas the latter has an additional explicit dependence on the set of integer numbers that label each excited state in the associated logarithmic Bethe equations. We also show that special form factors corresponding to zero-energy excitations lying on the Fermi surface decrease as a …
Ergodicity and limit theorems for degenerate diffusions with time periodic drift. Application to a stochastic Hodgkin−Huxley model
2016
We formulate simple criteria for positive Harris recurrence of strongly degenerate stochastic differential equations with smooth coefficients on a state space with certain boundary conditions. The drift depends on time and space and is periodic in the time argument. There is no time dependence in the diffusion coefficient. Control systems play a key role, and we prove a new localized version of the support theorem. Beyond existence of some Lyapunov function, we only need one attainable inner point of full weak Hoermander dimension. Our motivation comes from a stochastic Hodgkin−Huxley model for a spiking neuron including its dendritic input. This input carries some deterministic periodic si…
Recursive estimation of the conditional geometric median in Hilbert spaces
2012
International audience; A recursive estimator of the conditional geometric median in Hilbert spaces is studied. It is based on a stochastic gradient algorithm whose aim is to minimize a weighted L1 criterion and is consequently well adapted for robust online estimation. The weights are controlled by a kernel function and an associated bandwidth. Almost sure convergence and L2 rates of convergence are proved under general conditions on the conditional distribution as well as the sequence of descent steps of the algorithm and the sequence of bandwidths. Asymptotic normality is also proved for the averaged version of the algorithm with an optimal rate of convergence. A simulation study confirm…
Stochastic model for the epitaxial growth of two-dimensional islands in the submonolayer regime
2016
The diffusion-based growth of islands composed of clusters of metal atoms on a substrate is considered in the aggregation regime. A stochastic approach is proposed to describe the dynamics of island growth based on a Langevin equation with multiplicative noise. The distribution of island sizes, obtained as a solution of the corresponding Fokker-Planck equation, is derived. The time-dependence of island growth on its fractal dimension is analysed. The effect of mobility of the small islands on the growth of large islands is considered. Numerical simulations are in a good agreement with theoretical results.