相关论文: Time change approach to generalized excursion meas…

We analyze the question whether sliding window time averages applied to stationary increment processes converge to a limit in probability. The question centers on averages, correlations, and densities constructed via time averages of the…

In this paper excursions of a stationary diffusion in stationary state are studied. In particular, we compute the joint distribution of the occupation times $I^{(+)}_t$ and $I^{(-)}_t$ above and below, respectively, the observed level at…

General relativity allows for the existence of closed time-like curves, along which a material object could travel back in time and interact with its past self. This possibility raises the question whether certain initial conditions, or…

We consider random walks with independent but not necessarily identical distributed increments. Assuming that the increments satisfy the well-known Lindeberg condition, we investigate the asymptotic behaviour of first-passage times over…

The primary purpose of this article is to prove a tightness of skew random walks. The tightness result implies, in particular, that the skew Brownian motion can be constructed as the scaling limit of such random walks. Our proof of…

Non-linear renewal theory is extended to include random walks perturbed by both a slowly changing sequence and a stationary one. Main results include a version of the Key Renewal Theorem, a derivation of the limiting distribution of the…

We consider the model of Brownian motion indexed by the Brownian tree, which has appeared in a variety of different contexts in probability, statistical physics and combinatorics. For this model, the total occupation measure is known to…

Diffeomorphism-induced symmetry transformations and time evolution are distinct operations in generally covariant theories formulated in phase space. Time is not frozen. Diffeomorphism invariants are consequently not necessarily constants…

Assuming that a threshold Ornstein-Uhlenbeck process is observed at discrete time instants, we propose generalized moment estimators to estimate the parameters. Our theoretical basis is the celebrated ergodic theorem. To use this theorem we…

The Benjamin-Ono equation describes the propagation of internal waves in a stratified fluid. In the present work, we study large time dynamics of its regular solutions via some probabilistic point of view. We prove the existence of an…

As a continuation of our previous work on the subject, we prove new measure invariance results for the Benjamin-Ono equation. The measures are associated with conservation laws whose leading term is a fractional Sobolev norm of order larger…

For a random walk defined for a doubly infinite sequence of times, we let the time parameter itself be an integer-valued process, and call the orginal process a random walk at random time. We find the scaling limit which generalizes the…

Limit theorems for the volumes of excursion sets of weakly and strongly dependent heavy-tailed random fields are proved. Some generalizations to sojourn measures above moving levels and for cross-correlated scenarios are presented. Special…

Considering a minimal number of assumptions and in the context of the timeless formalism, conditional probabilities are derived for subsequent measurements in the non-relativistic regime. Only unitary transformations are considered with…

The theory of relativity associates a proper time with each moving object via its world line. In quantum theory however, such well-defined trajectories are forbidden. After introducing a general characterisation of quantum clocks, we…

We derive the conditions that the coupling constants of the Generalized Thirring Model have to satisfy in order for the model to admit an infinite number of commuting classical conserved quantities. Our treatment uses the bosonized version…

Consider p independent Brownian motions in R^d, each running up to its first exit time from an open domain B, and their intersection local time l as a measure on B. We give a sharp criterion for the finiteness of exponential moments,…

Quintino et. al. (Phys. Rev. Lett. 113, 160402 (2014)) and Uola et. al. (Phys. Rev. Lett. 113, 160403 (2014)) have recently established an intrinsic relation between non-joint measurability and Einstein-Podolsky- Rosen steering. They showed…

We prove a version of a general transfer theorem for random sequences with independent random indexes in the double array limit setting under relaxed conditions. We also prove its partial inverse providing the necessary and sufficient…

In this note we investigate the behaviour of Brownian motion conditioned on a growth constraint of its local time which has been previously investigated by Berestycki and Benjamini. For a class of non-decreasing positive functions $f(t);…