Related papers: Asymptotics of Some Feynman-Kac Functionals
This paper is concerned with inference based on the mean function of a functional time series, which is defined as a collection of curves obtained by splitting a continuous time record, e.g. into daily or annual curves. We develop a normal…
We study a discrete time multitype branching random walk on a finite space with finite set of types. Particles follow a Markov chain on the spatial space whereas offspring distributions are given by a random field that is fixed throughout…
This paper is about vector autoregressive-moving average (VARMA) models with time-dependent coefficients to represent non-stationary time series. Contrarily to other papers in the univariate case, the coefficients depend on time but not on…
Different viewpoints on the asymptotic expansion of Feynman diagrams are reviewed. The relations between the field theoretic and diagrammatic approaches are sketched. The focus is on problems with large masses or large external momenta.…
We consider the asymptotic expansion for $x\to\pm\infty$ of the entire function \[F_{n,\sigma}(x;\mu)=\sum_{k=0}^\infty \frac{\sin\,(n\gamma_k)}{\sin \gamma_k}\,\frac{x^k}{k! \Gamma(\mu-\sigma k)},\quad \gamma_k=\frac{(k+1)\pi}{2n}\] for…
For affine stochastic differential equation with uniformly distributed time delay the local asymptotic properties of the likelihood function are studied. Local asymptotic normality, local asymptotic mixed normality, periodic local…
When the study variable is functional and storage capacities are limited or transmission costs are high, selecting with survey sampling techniques a small fraction of the observations is an interesting alternative to signal compression…
We determine the complete asymptotic behaviour of the work distribution in driven stochastic systems described by Langevin equations. Special emphasis is put on the calculation of the pre-exponential factor which makes the result free of…
We propose and study a certain discrete time counterpart of the classical Feynman--Kac semigroup with a confining potential in countable infinite spaces. For a class of long range Markov chains which satisfy the direct step property we…
General results on asymptotic expansions of Feynman diagrams in momenta and/or masses are reviewed. It is shown how they are applied for calculation of massive diagrams.
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…
This paper is a short overview of the main Abelian- and Tauberian-type results from [4, 14, 26] regarding the asymptotic analysis of different classes of generalized functions in terms of appropriate frames. The Tauberian-type results…
Asymptotic efficiency theory is one of the pillars in the foundations of modern mathematical statistics. Not only does it serve as a rigorous theoretical benchmark for evaluating statistical methods, but it also sheds light on how to…
Quantization and asymptotic behaviour of a variant of discrete random walk on integers are investigated. This variant, the $\epsilon_{V^{k}}$ walk, has the novel feature that it uses many identical quantum coins keeping at the same time…
The massless harmonic oscillator is a rare example of a system whose Feynman path integral can be explicitly computed and receives its main contributions from regions of the functional space that are far from the classical and semiclassical…
We consider the long-time behaviour of a branching random walk in random environment on the lattice $\Z^d$. The migration of particles proceeds according to simple random walk in continuous time, while the medium is given as a random…
Asymptotic properties of a vector of length power functionals of random geometric graphs are investigated. More precisely, its asymptotic covariance matrix is studied as the intensity of the underlying homogeneous Poisson point process…
We study piecewise polynomial functions $\gamma_k(c)$ that appear in the asymptotics of averages of the divisor sum in short intervals. Specifically, we express these polynomials as the inverse Fourier transform of a Hankel determinant that…
In a functional setting, we propose two test statistics to highlight the Poisson nature of a Cox process when n copies of the process are available. Our approach involves a comparison of the empirical mean and the empirical variance of the…
The main results of this paper comprise proofs of the following two related facts: (i) the Feynman--Kac formula is a functor $F_*$, namely, between a stochastic differential equation and a dynamical system on a statistical manifold, and…