Related papers: Asymptotic Expansion for Nonlinear Filtering in th…

In this paper, we propose a new asymptotic expansion approach for nonlinear filtering based on a small parameter in the system noise. This method expresses the filtering distribution as a power series in the noise level, where the…

This paper develops an asymptotic expansion technique in momentum space for stochastic filtering. It is shown that Fourier transformation combined with a polynomial-function approximation of the nonlinear terms gives a closed recursive…

We deduce the asymptotic error distribution of the Euler method for the nonlinear filtering problem with continuous-time observations. Previous works by several authors have shown that the error structure of the method is characterized by…

Asymptotic expansions are derived as power series in a small coefficient entering a nonlinear multiplicative noise and a deterministic driving term in a nonlinear evolution equation. Detailed estimates on remainders are provided.

In this paper, we derive new asymptotic expansions for the solutions of higher order elliptic equations in the presence of small inclusions. As a byproduct, we derive a topological derivative based algorithm for the reconstruction of…

We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. The model considered in the paper is very general as we do not impose any…

This article is focused on the asymptotic expansions, as time tends to infinity, of solutions of a system of ordinary differential equations with non-smooth nonlinear terms. The forcing function decays to zero in a very complicated but…

We provide a rigorous derivation of an asymptotic formula for perturbations in the resonance values caused by the presence of finite number of anisotropic imperfections of small shapes with constitutive parameters different from the…

New algorithms for construction of asymptotic expansions for stationary distributions of nonlinearly perturbed semi-Markov processes with finite phase spaces are presented. These algorithms are based on a special technique of sequential…

We construct asymptotic expansions for ordinary differential equations with highly oscillatory forcing terms, focussing on the case of multiple, non-commensurate frequencies. We derive an asymptotic expansion in inverse powers of the…

We propose a method to detect model misspecifications in nonlinear causal additive and potentially heteroscedastic noise models. We aim to identify predictor variables for which we can infer the causal effect even in cases of such…

The article is devoted to the nonparametric estimation of the quadratic covariation of non-synchronously observed It\^o processes in an additive microstructure noise model. In a high-frequency setting, we aim at establishing an asymptotic…

In this paper, an alternative approximation to the innovation method is introduced for the parameter estimation of diffusion processes from partial and noisy observations. This is based on a convergent approximation to the first two…

In this paper, we develop an asymptotic expansion-regularization (AER) method for inverse source problems in two-dimensional nonlinear and nonstationary singularly perturbed partial differential equations (PDEs). The key idea of this…

We present a general method for studying long time asymptotics of nonlinear parabolic partial differential equations. The method does not rely on a priori estimates such as the maximum principle. It applies to systems of coupled equations,…

Asymptotic expansions are derived for solutions of the parabolic cylinder and Weber differential equations. In addition the inhomogeneous versions of the equations are considered, for the case of polynomial forcing terms. The expansions…

We introduce an alternative to the method of matched asymptotic expansions. In the "traditional" implementation, approximate solutions, valid in different (but overlapping) regions are matched by using "intermediate" variables. Here we…

Local expansion exponents for nonequilibrium dynamical systems, described by partial differential equations, are introduced. These exponents show whether the system phase volume expands, contracts, or is conserved in time. The ways of…

In this paper we apply techniques from nonstandard analysis to study expansive dynamical systems. Among other results, we provide a necessary and sufficient condition for an expansive homeomorphism on a compact metric space to admit…

The renormalization method based on the Taylor expansion for asymptotic analysis of differential equations is generalized to difference equations. The proposed renormalization method is based on the Newton-Maclaurin expansion. Several basic…