相关论文: Stopping times are hitting times: a natural repres…

When analysing time series an important issue is to decide whether the time series is stationary or a random walk. Relaxing these notions, we consider the problem to decide in favor of the I(0)- or I(1)-property. Fixed-sample statistical…

Sudden and abrupt changes can occur in a nonlinear system within many fields of science when such a system crosses a tipping point and rapid changes of the system occur in response to slow changes in an external forcing. These can occur…

In this paper we extend the definition of time conditional G-expectations $\mathbb{\hat{E}}_{t}[\cdot]$ to a larger domain on which the dynamical consistency still holds. In fact we can consistently define, by taking the limit, the time…

Last passage times arise in a number of areas of applied probability, including risk theory and degradation models. Such times are obviously not stopping times since they depend on the whole path of the underlying process. We consider the…

This document is focused on computing systems implemented in technologies that communicate and compute with temporal transients. Although described in general terms, implementations of spiking neural networks are of primary interest. As…

We base ourselves on the construction of the two-dimensional random interlacements [12] to define the one-dimensional version of the process. For this constructions we consider simple random walks conditioned on never hitting the origin,…

Since many real-world problems arising in the fields of compiler optimisation, automated software engineering, formal proof systems, and so forth are equivalent to the Halting Problem--the most notorious undecidable problem--there is a…

Most clinical prediction studies are developed from retrospective cohorts and reported as if all patient information were observed at once. In practice, clinicians face a more consequential question: \emph{when is there already enough…

We introduce a method which enables a recurrent dynamics model to be temporally abstract. Our approach, which we call Adaptive Skip Intervals (ASI), is based on the observation that in many sequential prediction tasks, the exact time at…

We briefly review two concepts of time - the usual time associated with "being" and more recent ideas, answering to the description of "becoming". The approximation involved in the former is examined. Finally we argue that it is…

The detailed behaviour of a system is often represented as a labelled transition system (LTS) and the abstract behaviour as a stuttering-insensitive semantic congruence. Numerous congruences have been presented in the literature. On the…

The determination of the time averages of continuous functions, or discrete time sequences is important for various problems in physics and engineering, and the generalized final-value theorems of the Laplace and z-transforms, relevant to…

Stochastic gradient Langevin dynamics (SGLD) is a fundamental algorithm in stochastic optimization. Recent work by Zhang et al. [2017] presents an analysis for the hitting time of SGLD for the first and second order stationary points. The…

This paper investigates the asymptotic behaviour of solutions to certain infinite systems of coupled recurrence relations. In particular, we obtain a characterisation of those initial values which lead to a convergent solution, and for…

We develop an approach for solving one-sided optimal stopping problems in discrete time for general underlying Markov processes on the real line. The main idea is to transform the problem into an auxiliary problem for the ladder height…

Hitting times are the average time it takes a walk to reach a given final vertex from a given starting vertex. The hitting time for a classical random walk on a connected graph will always be finite. We show that, by contrast, quantum walks…

This paper is concerned with the small time behaviour of a L\'{e}vy process $X$. In particular, we investigate the {\it stabilities} of the times, $\Tstarb(r)$ and $\Tbarb(r)$, at which $X$, started with $X_0=0$, first leaves the space-time…

This technical report is concerned with the convergence properties of what we call the split optimal policy iteration for coupled LQR problems; see section 3.1 in the manuscript. Interestingly, the iteration shows different convergence…

We consider random walks on the line given by a sequence of independent identically distributed jumps belonging to the strict domain of attraction of a stable distribution, and first determine the almost sure exponential divergence rate, as…

In reinforcement learning, it is common to let an agent interact for a fixed amount of time with its environment before resetting it and repeating the process in a series of episodes. The task that the agent has to learn can either be to…