相关论文: Geometric Deviation From L\'evy's Occupation Time …
Classical arcsine law states that fraction of occupation time on the positive or the negative side in Brownian motion does not converge to a constant but converges in distribution to the arcsine distribution. Here, we consider how a…
Occupation times quantify how long a stochastic process remains in a region, and their single-time statistics are famously given by the arcsine law for Brownian and L\'evy processes. By contrast, two-time occupation statistics, which…
Some analysis on the Lorentzian distance in a spacetime with controlled sectional (or Ricci) curvatures is done. In particular, we focus on the study of the restriction of such distance to a spacelike hypersurface satisfying the Omori-Yau…
We prove that the joint distribution of the occupation time ratios for ergodic transformations preserving an infinite measure converges to a multidimensional version of Lamperti's generalized arcsine distribution, in the sense of strong…
The random acceleration model is one of the simplest non-Markovian stochastic systems and has been widely studied in connection with applications in physics and mathematics. However, the occupation time and related properties are…
We consider the occupation area of spherical (fractional) Brownian motion, i.e. the area where the process is positive, and show that it is uniformly distributed. For the proof, we introduce a new simple combinatorial view on occupation…
In this paper we analyze the problem of uniqueness for spacelike hypersurfaces with constant higher order mean curvature in generalized Robertson-Walker spacetimes. We consider first the case of compact spacelike hypersurfaces, completing…
This paper looks at the splitting problem for globally hyperbolic spacetimes with timelike Ricci curvature bounded below containing a (spacelike, acausal, future causally complete) hypersurface with mean curvature bounded from above. For…
We establish large deviation estimates related to the Darling--Kac theorem and generalized arcsine laws for occupation and waiting times of ergodic transformations preserving an infinite measure, such as non-uniformly expanding interval…
Geometry is wavy: even at the purely geometric level (no particular theory chosen), curvature satisfies a covariant quasilinear wave equation. In Riemannian geometry equipped with the Levi-Civita connection, the Riemann curvature tensor…
We investigate occupation time statistics for random walks on a comb with ramified teeth. This is achieved through the relation between the occupation time and the first passage times. Statistics of occupation times in half space follows…
We study the existence problem for achronal hypersurfaces $M \hookrightarrow \overline{M}$ in a globally hyperbolic spacetime, whose mean curvature is a prescribed -- possibly singular -- source, and whose boundary is a given smooth…
This work investigates slant timelike-ruled surfaces and their evolute offsets in Minkowski 3-space $\mathbb{E}_{1}^{3}$. Using the symmetry of evolute curves, we derive a parametric formulation for skew timelike-ruled surfaces and…
We prove that any piece of a rotational hypersurface with prescribed mean curvature function in a Euclidean space can be uniquely extended infinitely, which generalizes the results by Euler and Delaunay for surfaces of revolution with…
In this paper we prove Hessian and Laplacian comparison theorems for the Lorentzian distance function in a spacetime with sectional (or Ricci) curvature bounded by a certain function by means of a comparison criterion for Riccati equations.…
The investigations presented in this study are directed at relativistic modifications of the uncertainty relation derived from the curvature of the background spacetime. These findings generalize previous work which is recovered in the…
We present a study of the distance between a Brownian motion and a submanifold of a complete Riemannian manifold. We include a variety of results, including an inequality for the Laplacian of the distance function derived from a Jacobian…
We obtain sharp estimates involving the mean curvatures of higher order of a complete bounded hypersurface immersed in a complete Riemannian manifold. Similar results are also given for complete spacelike hypersurfaces in Lorentzian ambient…
Let $f:M\ra \erre^{m+1}$ be an isometrically immersed hypersurface. In this paper, we exploit recent results due to the authors in \cite{bimari} to analyze the stability of the differential operator $L_r$ associated with the $r$-th Newton…
We give a sufficient condition under which the time-marginal law of $\mu$-reversible infinite interacting Brownian motions is characterised as the steepest gradient descent of the relative entropy in the Wasserstein space in the sense of…