Related papers: Generalizing the Markov and covariance interpolati…
We investigate aspects of semimartingale decompositions, approximation and the martingale representation for multidimensional correlated Markov processes. A new interpretation of the dependence among processes is given using the martingale…
We investigate superconvergence properties of the spectral interpolation involving fractional derivatives. Our interest in this superconvergence problem is, in fact, twofold: when interpolating function values, we identify the points at…
In the space of holomorphic functions in a convex domain it is studied the interpolation problem by means of sums of the series of exponentials converging uniformly on all compact sets of the domain. The discrete set of the interpolation…
In this paper we use a Variational Quantum Algorithm to solve Initial Value Problems with the Implicit Crank-Nicolson and the Method of Lines (MoL) evolution schemes. The unknown functions use a spectral decomposition with the Fourier…
We propose a method derived from the simple plane wave expansion that can easily solve the interface problem between vacuum and a semi-infinite photonic crystal. The method is designed to find the complete set of all the eigenfunctions,…
This report derives a generalized, converted measurement Kalman filter for the class of filtering problems with a linear state equation and nonlinear measurement equation, for which a bijective mapping exists between the state and…
This paper describes applications of extrapolation for the computation of coefficients in an expansion of infrared divergent integrals. An extrapolation procedure is performed with respect to a parameter introduced by dimensional…
The connection between forward backward doubly stochastic differential equations and the optimal filtering problem is established without using the Zakai's equation. The solutions of forward backward doubly stochastic differential equations…
Implicit particle filters for data assimilation generate high-probability samples by representing each particle location as a separate function of a common reference variable. This representation requires that a certain underdetermined…
Making use of the Whittaker-Shannon interpolation formula with shifted sampling points, we propose in this paper a well-posed semi-discretization of the stationary Wigner equation with inflow BCs. The convergence of the solutions of the…
The main results presented in this paper provide a complete and explicit description of all solutions to the left tangential operator Nevanlinna- Pick interpolation problem assuming the associated Pick operator is strictly positive. The…
We start by presenting a generalization of a discrete wave equation that is particularly satisfied by the entries of the matrix coefficients of the refinement equation corresponding to the multiresolution analysis of Alpert. The entries are…
Along this work we study an indefinite abstract smoothing problem. After establishing necessary and sufficient conditions for the existence of solutions to this problem, the set of admissible parameters is discussed in detail. Then, its…
For Markov processes with absorption, we provide general criteria ensuring the existence and the exponential non-uniform convergence in total variation norm to a quasi-stationary distribution. We also characterize a subset of its domain of…
We explore the consequences of the so-called intertwinings between gradients and Markov diffusion operators on $R^d$ in terms of second-order Brascamp-Lieb inequalities for log-concave distributions and beyond, extending our inequalities…
When approximating a function that depends on a parameter, one encounters many practical examples where linear interpolation or linear approximation with respect to the parameters prove ineffective. This is particularly true for responses…
We introduce a method for calculating the stationary state of a translation invariant array of weakly coupled cavities in the presence of dissipation and coherent as well as incoherent drives. Instead of computing the full density matrix…
Marchenko focusing functions are in their essence wavefields that satisfy the wave equation subject to a set of boundary, initial, and focusing conditions. Here, we show how Marchenko focusing functions can be modeled by finding the…
We introduce a model with diffusive and evaporation/condensation processes, depending on 3 parameters obeying some inequalities. The model can be solved in the sense that all correlation functions can be computed exactly without the use of…
We formulate three boundary Nevanlinna-Pick interpolation problems for generalized Nevanlinna functions. For each problem, we parameterize the set of all solutions in terms of a linear fractional transformation with an extended Nevanlinna…