Related papers: Invariance principles for fractionally integrated …
We propose certain conditions which are sufficient for the functional law of the iterated logarithm (the Strassen invariance principle) for some general class of non-stationary Markov-Feller chains. This class may be briefly specified by…
We establish almost sure invariance principles (ASIP), a strong form of approximation by Brownian motion, for non-stationary time series arising as observations on sequential maps possessing an indifferent fixed point. These transformations…
This work leverages recent advances in probabilistic machine learning to discover conservation laws expressed by parametric linear equations. Such equations involve, but are not limited to, ordinary and partial differential,…
In this article, we will first introduce a class of Gaussian processes, and prove the quasi-invariant theorem with respect to the Gaussian Wiener measure, which is the law of the associated Gaussian process. In particular, it includes the…
Invariance-based randomization tests -- such as permutation tests, rotation tests, or sign changes -- are an important and widely used class of statistical methods. They allow drawing inferences under weak assumptions on the data…
In this paper, we introduce two new non-singular kernel fractional derivatives and present a class of other fractional derivatives derived from the new formulations. We present some important results of uniformly convergent sequences of…
In this paper, we obtain some uniform laws of large numbers and functional central limit theorems for sequential empirical measure processes indexed by classes of product functions satisfying appropriate Vapnik-Chervonenkis properties.
Our first result is a stochastic sewing lemma with quantitative estimates for mild incremental processes, with which we study SPDEs driven by fractional Brownian motions in a random environment. We obtain uniform $L^p$-bounds. Our second…
Fractional dynamics of relativistic particle is discussed. Derivatives of fractional orders with respect to proper time describe long-term memory effects that correspond to intrinsic dissipative processes. Relativistic particle subjected to…
Motivated by recent developments in Hamiltonian variational principles, Hamiltonian variational integrators, and their applications such as to optimization and control, we present a new Type II variational approach for Hamiltonian systems,…
We study a limit behavior of a sequence of Markov processes (or Markov chains) such that their distributions outside of any neighborhood of a "singular" point attract to some probability law. In any neighborhood of this point the behavior…
We study a continuous time random walk $X$ in an environment of i.i.d. random conductances $\mu_e\in[1,\infty)$. We obtain heat kernel bounds and prove a quenched invariance principle for $X$. This holds even when…
A novel principle is presented which allows for the proof of bounded weak solutions to a class of physically relevant, strongly coupled parabolic systems exhibiting a formal gradient-flow structure. The main feature of these systems is that…
We prove large deviation principles for two versions of fractional Poisson processes. Firstly we consider the main version which is a renewal process; we also present large deviation estimates for the ruin probabilities of an insurance…
In this note we consider generalized diffusion equations in which the diffusivity coefficient is not necessarily constant in time, but instead it solves a nonlinear fractional differential equation involving fractional Riemann-Liouville…
We study the impact of the recently introduced underspread/overspread classificationon the spectra of processes with square-integrable covariance functions. We briefly review the most prominent definitions of a time-varying power spectrum…
Galilean invariance is a cornerstone of classical mechanics. It states that for closed systems the equations of motion of the microscopic degrees of freedom do not change under Galilean transformations to different inertial frames. However,…
This paper presents some asymptotic results for statistics of Brownian semi-stationary (BSS) processes. More precisely, we consider power variations of BSS processes, which are based on high frequency (possibly higher order) differences of…
This work is concerned with the large deviation principle for a family of slow-fast systems perturbed by infinite-dimensional mixed fractional Brownian motion with Hurst parameter $H\in(\frac12,1)$. We adopt the weak convergence method…
The stochastic trajectories of molecules in living cells, as well as the dynamics in many other complex systems, often exhibit memory in their path over long periods of time. In addition, these systems can show dynamic heterogeneities due…