Related papers: Application of boundary functionals of random proc…
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…
The bifurcation theory of ordinary differential equations (ODEs), and its application to deterministic population models, are by now well established. In this article, we begin to develop a complementary theory for diffusion-like…
We study random dynamical systems of certain continuous functions on the unit interval. We use bounded variation to provide sufficient conditions for unique ergodicity of these systems. Several classes of examples are provided.
The aim of the present article is to establish the connection between the existence of the limit along the normal and an admissible limit at a fixed boundary point for holomorphic functions of several complex variables.
Statistical divergences are important tools in data analysis, information theory, and statistical physics, and there exist well known inequalities on their bounds. However, in many circumstances involving temporal evolution, one needs…
We study well-posedness of sweeping processes with stochastic perturbations generated by a fractional Brownian motion and convergence of associated numerical schemes. To this end, we first prove new existence, uniqueness and approximation…
Spatial process models are widely used for modeling point-referenced variables arising from diverse scientific domains. Analyzing the resulting random surface provides deeper insights into the nature of latent dependence within the studied…
We consider a family of random locations, called intrinsic location functionals, of periodic stationary processes. This family includes but is not limited to the location of the path supremum and first/last hitting times. We first show that…
Temporal logics provide a formalism for expressing complex system specifications. A large body of literature has addressed the verification and the control synthesis problem for deterministic systems under such specifications. For…
We consider a multidimensional random walk in a product random environment with bounded steps, transience in some spatial direction, and high enough moments on the regeneration time. We prove an invariance principle, or functional central…
The paper deals with the asymptotic behavior of the bridge of a Gaussian process conditioned to stay in $n$ fixed points at $n$ fixed past instants. In particular, functional large deviation results are stated for small time. Several…
A uniform dimensional result for normally reflected Brownian motion (RBM) in a large class of non-smooth domains is established. Exact Hausdorff dimensions for the boundary occupation time and the boundary trace of RBM are given. Extensions…
Selection of descent direction at a point plays an important role in numerical optimization for minimizing a real valued function. In this article, a descent sequence is generated for the functions with bounded parameters to obtain a…
Fractional Brownian motion is a non-Markovian Gaussian process indexed by the Hurst exponent $H\in [0,1]$, generalising standard Brownian motion to account for anomalous diffusion. Functionals of this process are important for practical…
The study of first passage times for diffusing particles reaching target states is foundational in various practical applications, including diffusion-controlled reactions. In this work, we present a bi-scaling theory for the probability…
We survey some geometrical properties of trajectories of $d$-dimensional random walks via the application of functional limit theorems. We focus on the functional law of large numbers and functional central limit theorem (Donsker's…
We present examples of holomorphic functions that vanish to in- finite order at points at the boundary of their domain of definition. They give rise to examples of Dirichlet minimizing Q-valued functions indicating that "higher"-regularity…
Different change-point type models encountered in statistical inference for stochastic processes give rise to different limiting likelihood ratio processes. In this paper we consider two such likelihood ratios. The first one is an…
We consider the behaviour of holomorphic functions on a bounded open subset of the plane, satisfying a Lipschitz condition with exponent $\alpha$, with $0<\alpha<1$, in the vicinity of an exceptional boundary point where all such functions…
We study the problem of empirical minimization for variance-type functionals over functional classes. Sharp non-asymptotic bounds for the excess variance are derived under mild conditions. In particular, it is shown that under some…