Related papers: Asymptotic expansion of Markov random evolution
We analyze asymptotically a differential-difference equation, that arises in a Markov-modulated fluid model. We use singular perturbation methods to analyze the problem with appropriate scalings of the two state variables. In particular,…
We study the asymptotic behavior of complex discrete evolution equations of Ginzburg- Landau type. Depending on the nonlinearity and the data of the problem, we find different dynamical behavior ranging from global existence of solutions…
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…
An operator form of asymptotic expansions for Markov chains is established. Coefficients are given explicitly. Such expansions require a certain modification of the classical spectral method. They prove to be extremely useful within the…
An asymptotic expansion with respect to a small parameter of a singularly perturbed system of hyperbolic equations, describing vibrations of two rigidly connected strings is constructed. Under certain conditions imposed on these problems,…
We consider time-inhomogeneous ODEs whose parameters are governed by an underlying ergodic Markov process. When this underlying process is accelerated by a factor $\varepsilon^{-1}$, an averaging phenomenon occurs and the solution of the…
We consider a discrete time semi-Markov process where the characteristics defining the process depend on a small perturbation parameter. It is assumed that the state space consists of one finite communicating class of states and, in…
We develop a general method for extending Markov processes to a larger state space such that the added points form a polar set. The so obtained extension is an improvement on the standard trivial extension in which case the process is made…
We analyze asymptotic scaling properties of a model class of anomalous reaction-diffusion (ARD) equations. Numerical experiments show that solutions to these have, for large $t$, well defined scaling properties. We suggest a general…
The growth-fragmentation equation describes a system of growing and dividing particles, and arises in models of cell division, protein polymerisation and even telecommunications protocols. Several important questions about the equation…
This paper investigates the asymptotic behaviour of solutions of periodic evolution equations. Starting with a general result concerning the quantified asymptotic behaviour of periodic evolution families we go on to consider a special class…
Asymptotic expansions are derived for the tail distribution of the product of two correlated normal random variables with non-zero means and arbitrary variances, and more generally the sum of independent copies of such random variables.…
We calculate asymptotic expansions for the moments of number of comparisons used by the randomized quick sort algorithm using the singularity analysis of certain generating functions.
We define a type of generalized asymptotic series called $v$-asymptotic. We show that every function with moderate growth at infinity has a $v$-asymptotic expansion. We also describe the set of $v$-asymptotic series, where a given function…
The asymptotic variance is an important criterion to evaluate the performance of Markov chains, especially for the central limit theorems. We give the variational formulas for the asymptotic variance of discrete-time (non-reversible) Markov…
In this paper, our main goal is to achieve the high-order asymptotic expansion of solutions to $\sigma$-evolution equations with different damping types in the $L^2$ framework. Throughout this, we observe the influence of parabolic like…
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…
In this paper we consider asymptotic expansions for a class of sequences of symmetric functions of many variables. Applications to classical and free probability theory are discussed.
We study diffusion-type equations supported on structures that are randomly varying in time. After settling the issue of well-posedness, we focus on the asymptotic behavior of solutions: our main result gives sufficient conditions for…
Markov branching systems form a fundamental class of stochastic models that are extensively applied in biology, physics, finance, and other domains. These systems are distinguished by their continuous-time evolution and inherent branching…