Related papers: On parametric Gevrey asymptotics for some nonlinea…
A singularly perturbed linear system of second order partial differential equations of parabolic reaction-diffusion type with given initial and boundary conditions is considered. The leading term of each equation is multiplied by a small…
We develop asymptotic approximations that can be applied to sequential estimation and inference problems, adaptive randomized controlled trials, and related settings. In batched adaptive settings where the decision at one stage can affect…
The estimation of the covariance structure from a discretely observed multivariate Gaussian process under asynchronicity and noise is analysed under high-frequency asymptotics. Asymptotic lower and upper bounds are established for a general…
We study spectral asymptotics for small non-selfadjoint perturbations of selfadjoint $h$-pseudodifferential operators in dimension 2, assuming that the classical flow of the unperturbed part possesses several invariant Lagrangian tori…
We derive asymptotic formulae for the coefficients of bivariate generating functions with algebraic and logarithmic factors. Logarithms appear when encoding cycles of combinatorial objects, and also implicitly when objects can be broken…
In some estimation problems, especially in applications dealing with information theory, signal processing and biology, theory provides us with additional information allowing us to restrict the parameter space to a finite number of points.…
The first focus of this paper is the characterization of the spectrum and the singular values of the coefficient matrix stemming from the discretization with space-time grid for a parabolic diffusion problem and from the approximation of…
In this paper following the same methods in [M. Kadakal, O. Sh. Mukhtarov, Sturm-Liouville problems with discontinuities at two points, Comput. Math. Appl., 54 (2007) 1367-1379] we investigate discontinuous two-point boundary value problems…
In this article we show that the Euler equations, when linearized around a low frequency perturbation to Couette flow, exhibit norm inflation in Gevrey-type spaces as time tends to infinity. Thus, echo chains are shown to be a (secondary)…
An autonomous system of ordinary differential equations describing nonlinear oscillations on the plane is considered. The influence of time-dependent perturbations decaying at infinity in time is investigated. It is assumed that the…
We investigate the effect of small diffusion on the principal eigenvalues of linear time-periodic parabolic operators with zero Neumann boundary conditions in one dimensional space. The asymptotic behaviors of the principal eigenvalues, as…
We study upper bounds and the asymptotic behavior of high order moments for solutions to a family of linear and nonlinear Schroedinger equations.
We study an asymptotic preserving scheme for the temporal discretization of a system of parabolic semilinear SPDEs with two time scales. Owing to the averaging principle, when the time scale separation $\epsilon$ vanishes, the slow…
This article introduces a nonparametric approach to multivariate time-varying power spectrum analysis. The procedure adaptively partitions a time series into an unknown number of approximately stationary segments, where some spectral…
We deal with a singularly perturbed optimal control problem with slow and fast variable depending on a parameter {\epsilon}. We study the asymptotic, as {\epsilon} goes to 0, of the corresponding value functions, and show convergence, in…
In this work we study the asymptotic distribution of eigenvalues in one-dimensional open sets. The method of proof is rather elementary, based on the Dirichlet lattice points problem, which enable us to consider sets with infinite measure.…
We examine a misleadingly simple linear second-order eigenvalue problem (the Hermite-with-pole equation) that was previously proposed as a model problem of an equatorially-trapped Rossby wave. In the singularly perturbed limit representing…
We consider an elliptic PDE in two variables. As one parameter approaches zero, this PDE collapses to a parabolic one, that is forward parabolic in a part of the domain and backward parabolic in the remainder. Such problems arise naturally…
We derive the asymptotic behavior for an additive functional of two independent self-similar Gaussian processes when their intersection local time exists, using the method of moments.
We study diffusion-type equations supported on structures that are randomly varying in time. After settling the issue of well-posedness, we focus on the asymptotic behavior of solutions: our main result gives sufficient conditions for…