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We study asymptotic behavior of one-step $M$-estimators based on samples from arrays of not necessarily identically distributed random variables and representing explicit approximations to the corresponding consistent $M$-estimators. These…
In recent decades, there have been many attempts to construct symplectic integrators with variable time steps, with rather disappointing results. In this paper we identify the causes for this lack of performance, and find that they fall…
We study asymptotic behavior of one-step weighted $M$-estimators based on samples from arrays of not necessarily identically distributed random variables and representing explicit approximations to the corresponding consistent weighted…
The present work provides a comprehensive study of symmetric-conjugate operator splitting methods in the context of linear parabolic problems and demonstrates their additional benefits compared to symmetric splitting methods. Relevant…
We give a proof of Local Decay Estimates for Schr\"odinger type equations, which is based on the knowledge of Asymptotic Completeness (AC). This approach extends to time dependent potential perturbations, as it does not rely on Resolvent…
We derive a fully computable aposteriori error estimator for a Galerkin finite element solution of the wave equation with explicit leapfrog time-stepping. Our discrete formulation accommodates both time evolving meshes and leapfrog based…
With regard to a three-step estimation procedure, proposed without theoretical discussion by Li and You in Journal of Applied Statistics and Management, for a nonparametric regression model with time-varying regression function, local…
In this paper, robust nonparametric estimators, instead of local linear estimators, are adapted for infinitesimal coefficients associated with integrated jump-diffusion models to avoid the impact of outliers on accuracy. Furthermore,…
We propose new local error estimators for splitting and composition methods. They are based on the construction of lower order schemes obtained at each step as a linear combination of the intermediate stages of the integrator, so that the…
The evolution of any factorized time-reversible symplectic integrators, when applied to the harmonic oscillator, can be exactly solved in a closed form. The resulting modified Hamiltonians demonstrate the convergence of the Lie series…
We study the existence, strong consistency and asymptotic normality of estimators obtained from estimating functions, that are p-dimensional martingale transforms. The problem is motivated by the analysis of evolutionary clustered data,…
The error behavior of exponential operator splitting methods for nonlinear Schr{\"o}dinger equations in the semiclassical regime is studied. For the Lie and Strang splitting methods, the exact form of the local error is determined and the…
We analyze the preservation properties of a family of reversible splitting methods when they are applied to the numerical time integration of linear differential equations defined in the unitary group. The schemes involve complex…
Known as no fast-forwarding theorem in quantum computing, the simulation time for the Hamiltonian evolution needs to be $O(\|H\| t)$ in the worst case, which essentially states that one can not go across the multiple scales as the…
Starting from a recent a posteriori error estimator for the finite element solution of the wave equation with explicit time-stepping [Grote, Lakkis, Santos, 2024], we devise a space-time adaptive strategy which includes both time evolving…
Explicit step-truncation tensor methods have recently proven successful in integrating initial value problems for high-dimensional partial differential equations (PDEs). However, the combination of non-linearity and stiffness may introduce…
It has previously been shown that varying the numerical timestep during a symplectic orbital integration leads to a random walk in energy and angular momentum, destroying the phase space-conserving property of symplectic integrators. Here…
We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…
Calculating the long term solution of ordinary differential equations, such as those of the $N$-body problem, is central to understanding a wide range of dynamics in astrophysics, from galaxy formation to planetary chaos. Because generally…
Motivated by neural network training in finite-precision arithmetic environments, this work studies the convergence of perturbed iterate SGD using adaptive step sizes in an environment with numerical error. Considering a general stochastic…