Related papers: Local time penalizations with various clocks for o…
We prove several limit theorems for a simple class of partially hyperbolic fast-slow systems. We start with some well know results on averaging, then we give a substantial refinement of known large (and moderate) deviation results and…
In this work we revisit the Salecker-Wigner-Peres clock formalism and show that it can be directly applied to the phenomenon of tunneling. Then we apply this formalism to the determination of the tunneling time of a non relativistic…
We consider the determination of the optimal stationary singular stochastic control of a linear diffusion for a class of average cumulative cost minimization problems arising in various financial and economic applications of stochastic…
The reflection and transmission Salecker-Wigner-Peres clock times averaged over the post-selected reflected and transmitted sub-ensembles, respectively, are investigated for the one dimensional scattering of a localized wave packet through…
We study general random dynamical systems of continuous maps on some compact metric space. Assuming a local contraction condition and uniqueness of the stationary measure, we establish probabilistic limit laws such as the central limit…
We propose a general expression for the probability distribution of real-valued tunneling times of a localized particle, as measured by the Salecker-Wigner-Peres quantum clock. This general expression is used to obtain the distribution of…
The possibility of detecting the gravitomagnetic clock effect using artificial Earth satellites provides the incentive to develop a more intuitive approach to its derivation. We first consider two test electric charges moving on the same…
Estimation in generalized linear models (GLM) is complicated by the presence of constraints. One can handle constraints by maximizing a penalized log-likelihood. Penalties such as the lasso are effective in high dimensions, but often lead…
Being able to measure time, whether directly or indirectly, is a significant advantage for an organism. It allows for the timely reaction to regular or predicted events, reducing the pressure for fast processing of sensory input. Thus,…
Learning rate is a critical component of reinforcement learning (RL). This work uses global and local clocks to distinguish two types of learning rates. The former is of the standard form $\alpha_t$ that depends only on the time step $t$…
We discuss a family of time-inhomogeneous two-dimensional diffusions, defined over a finite time interval $[0,T]$, having transition density functions that are expressible in terms of the integral kernels for negative exponentials of the…
Diffusion-mediated surface phenomena are crucial for human life and industry, with examples ranging from oxygen capture by lung alveolar surface to heterogeneous catalysis, gene regulation, membrane permeation and filtration processes.…
A limit theorem for a sequence of diffusion processes on graphs is proved in a case when vary both parameters of the processes (the drift and diffusion coefficients on every edge and the asymmetry coefficients in every vertex), and…
This paper investigates a new formalism to describe real time evolution of quantum systems at finite temperature. A time correlation function among subsystems will be derived which allows for a probabilistic interpretation. Our derivation…
The effective approach to quantum dynamics allows a reformulation of the Dirac quantization procedure for constrained systems in terms of an infinite-dimensional constrained system of classical type. For semiclassical approximations, the…
Clocks are a central part of many computing paradigms, and are mainly used to synchronise the delicate operation of switching, necessary to drive modern computational processes. Unfortunately, this synchronisation process is reaching a…
We prove the convergence of the law of grid-valued random walks, which can be seen as time-space Markov chains, to the law of a general diffusion process. This includes processes with sticky features, reflecting or absorbing boundaries and…
The current algorithms are based on linear model, for example, Precision Time Protocol (PTP) which requires frequent synchronization in order to handle the effects of clock frequency drift. This paper introduces a nonlinear approach to…
As well known, the generalized Langevin equation with a memory kernel decreasing at large times as an inverse power law of time describes the motion of an anomalously diffusing particle. Here, we focus attention on some new aspects of the…
In the probability theory limit distributions (or probability measures) are often characterized by some convolution equations (factorization properties) rather than by Fourier transforms (the characteristic functionals). In fact, usually…