相关论文: Nonlinear asymptotic mean value characterizations …
Methods were initiated by Mark Kac and Richard Feynman to evaluate random functionals of the form $\int^t_0V(X_s)ds$ for a nonnegative $V$ and a Markov process $X_t$. Their results evolved into the well known Feynman Kac formula.…
We consider the Cauchy problem in ${\bf R}^{n}$ for heat and damped wave equations. We derive asymptotic profiles to those solutions with weighted $L^{1,1}({\bf R}^{n})$ data by presenting a simple method.
In this paper we continue our earlier investigations into the asymptotic behaviour of infinite systems of coupled differential equations. Under the mild assumption that the so-called characteristic function of our system is completely…
The Cauchy problem for a quasi-linear parabolic equation with a small parameter at a higher derivative is considered. The initial step-like function contains another small parameter. Formal asymptotic solutions of the problem in small…
We investigate statistical properties of the optimal value of the Sample Average Approximation of stochastic programs, continuing the study in Kr\"atschmer (2023). Central Limit Theorem type results are derived for the optimal value. As a…
We consider the Cauchy problem for the nonlinear Schroedinger eqiation with initial data close to a sum of N decoupled solitons. Under some suitable assumptions on the spectral structure of the one soliton linearizations we prove that for…
In this paper, we will develop an iterative procedure to determine the detailed asymptotic behaviour of solutions of a certain class of nonlinear vector differential equations which approach a nonlinear sink as time tends to infinity. This…
Generally, natural scientific problems are so complicated that one has to establish some effective perturbation or nonperturbation theories with respect to some associated ideal models. In this Letter, a new theory that combines…
Nonlinear control-affine systems described by ordinary differential equations with bounded measurable input functions are considered. The solvability of general boundary value problems for these systems is formulated in the sense of…
While the identification of nonlinear dynamical systems is a fundamental building block of model-based reinforcement learning and feedback control, its sample complexity is only understood for systems that either have discrete states and…
We study asymptotic behaviour of stochastic approximation procedures with three main characteristics: truncations with random moving bounds, a matrix valued random step-size sequence, and a dynamically changing random regression function.…
This paper reports on recent work to compute the asymptotic solution of a n-th order ordinary differential equation. Symbolic methods are used to compute the asymptotics over a large region. Application is made to the computation of the…
We introduce a new model of the nonlocal wave equations with a logarithmic damping mechanism. We consider the Cauchy poroblem for the new model in the whole space. We study the asymptotic profile and optimal decay and blowup rates of…
The coefficient sequences of multivariate rational functions appear in many areas of combinatorics. Their diagonal coefficient sequences enjoy nice arithmetic and asymptotic properties, and the field of analytic combinatorics in several…
Nonlinear dynamics and pattern formation in the systems with quadratic nonlinearity is computed symbolically by specially developed MATHEMATICA package. A Web interface for the presented methods is developed, which turns the implementations…
We consider the problem of predicting a real random variable from a functional explanatory variable. The problem is attacked by mean of nonparametric kernel approach which has been recently adapted to this functional context. We derive…
Analytic combinatorics studies the asymptotic behaviour of sequences through the analytic properties of their generating functions. This article provides effective algorithms required for the study of analytic combinatorics in several…
The standard approach to analyzing the asymptotic complexity of probabilistic programs is based on studying the asymptotic growth of certain expected values (such as the expected termination time) for increasing input size. We argue that…
In this paper, we obtain several asymptotic profiles of solutions to the Cauchy problem for structurally damped wave equations $\partial_{t}^{2} u - \Delta u + \nu (-\Delta)^{\sigma} \partial_{t} u=0$, where $\nu >0$ and $0< \sigma \le1$.…
In this lectures various methods which give a possibility to extend an area of applicability of perturbation series and hence to omit their local character are analysed. While applying asymptotic methods as a rule the following situation…