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In this paper, we propose a class of stochastic exponential discrete gradient schemes for SDEs with linear and gradient components in the coefficients. The root mean-square errors of the schemes are analyzed, and the structure-preserving…
This work proposes a detectability condition for linear time-varying systems based on the exponential dichotomy spectrum. The condition guarantees the existence of an observer, whose gain is determined only by the unstable modes of the…
In this paper, we study quasi-stationary distributions of nonlinearly perturbed semi-Markov processes in discrete time. This type of distributions is of interest for the analysis of stochastic systems which have finite lifetimes, but are…
We derive sufficient conditions for exponential decay of solutions of the delay negative feedback equation with distributed delay. The conditions are written in terms of exponential moments of the distribution. Our method only uses…
This paper deals with the problem of finite-time learning for unknown discrete-time nonlinear systems' dynamics, without the requirement of the persistence of excitation. Two finite-time concurrent learning methods are presented to…
We consider a class of continuous-time stochastic growth models on $d$-dimensional lattice with non-negative real numbers as possible values per site. We remark that the diffusive scaling limit proven in our previous work [Nagahata, Y.,…
In the present work, we revisit the topic of translational eigenmodes in discrete models. We focus on the prototypical example of the discrete nonlinear Schr{\"o}dinger equation, although the methodology presented is quite general. We…
We study linear time dispersive and dissipative systems. Very often such systems are not conservative and the standard spectral theory can not be applied. We develop a mathematically consistent framework allowing (i) to constructively…
For a general discrete dynamics on a Banach and Hilbert spaces we give a necessary and sufficient conditions of the existence of bounded solutions under assumption that the homogeneous difference equation admits an exponential dichotomy on…
An external description for nonperiodically sampled multivariable linear systems has been developed. Emphasis is on the sampling period sequence, included among the variables to be handled. The computational procedure is simple and no use…
In this paper, it is proved that, in a dual context, asymptotic expansions of ordinary linear time-differential equations which possess limiting equations to their limiting equations might be obtained by first discretizing them and then…
We study some sufficient conditions imposed on the sequence of martingale differences (m.d.) in the separable Banach spaces of continuous functions defined on the metric compact set for the Central Limit Theorem in this space. We taking…
Problem for the first order differential equation with an unbounded operator coefficient in Banach space and integral nonlocal condition is considered. An exponentially convergent algorithm is proposed and justified for the numerical…
We give a new scale of completeness conditions for exponential systems in two types of functional spaces on subsets of the complex plane. The first is the Banach spaces of functions that are continuous on a compact and simultaneously…
We obtain the quite exact exponential bounds for tails of distributions of sums of Banach space valued random variables uniformly over the number of summands under natural for the Law of Iterated Logarithm (LIL) norming. We study especially…
We introduce a category of vector spaces modelling full propositional linear logic, similar to probabilistic coherence spaces and to Koethe sequences spaces. Its objects are {\it rigged sequences spaces}, Banach spaces of sequences, with…
In this work, a new concept of nonself total asymptotically nonexpansive mapping is introduced and an iterative process is considered for two nonself totally asymptotically nonexpansive mappings. Weak and strong convergence theorems for…
We establish the existence of local stable manifolds for semiflows generated by nonlinear perturbations of nonautonomous ordinary linear differential equations in Banach spaces, assuming the existence of a general type of nonuniform…
Explicit formulas expressing the solution to non-autonomous differential equations are of great importance in many application domains such as control theory or numerical operator splitting. In particular, intrinsic formulas allowing to…
The structural invariant subspaces of the discrete-time singular Hamiltonian system are used in 1] to give an analytic nonrecursive expression of all the admissible trajectories. A deeper insight into the features of these subspaces,…