Related papers: Piecewise Constant Martingales and Lazy Clocks

In this article we study networks of coupled dynamical systems with time-delayed connections. If two such networks hold different delays on the connections it is in general possible that they exhibit different dynamical behavior as well. We…

We consider continuous-time Markov chains on integers which allow transitions to adjacent states only, with alternating rates. We give explicit formulas for probability generating functions, and also for means, variances and state…

We construct a zig-zag process targeting a posterior distribution defined on a hybrid state space consisting of both discrete and continuous variables. The construction does not require any assumptions on the structure among discrete…

As semiconductor devices continue to scale down, process vari- ations become more relevant for circuit design. Facing such variations, statistical static timing analysis is introduced to model variations more accurately so that the…

We consider a Markov jump process on a general state space to which we apply a time-dependent weak perturbation over a finite time interval. By martingale-based stochastic calculus, under a suitable exponential moment bound for the…

We propose a unified framework to study policy evaluation (PE) and the associated temporal difference (TD) methods for reinforcement learning in continuous time and space. We show that PE is equivalent to maintaining the martingale…

Let $X$ be the unique normal martingale such that $X_0=0$ and \[\mathrm{d}[X]_t=(1-t-X_{t-}) \mathrm{d}X_t+\mathrm{d}t\] and let $Y_t:=X_t+t$ for all $t\geq 0$; the semimartingale $Y$ arises in quantum probability, where it is the…

Piecewise Deterministic Markov Processes (PDMPs) such as the Bouncy Particle Sampler and the Zig-Zag Sampler, have gained attention as continuous-time counterparts of classical Markov chain Monte Carlo. We study their transient regime under…

We study the prospects of using the electric quadrupole transitions from the ground states of Cu, Ag and Au to the metastable state $^2{\rm D}_{5/2}$ as clock transitions in optical lattice clocks. We calculate lifetimes, transition rates,…

This article introduces the class of continuous time locally stationary wavelet processes. Continuous time models enable us to properly provide scale-based time series models for irregularly-spaced observations for the first time, while…

Temporal graphs represent graph evolution over time, and have been receiving considerable research attention. Work on expressing temporal graph patterns or discovering temporal motifs typically assumes relatively simple temporal…

Dynamic techniques are a scalable and effective way to analyze concurrent programs. Instead of analyzing all behaviors of a program, these techniques detect errors by focusing on a single program execution. Often a crucial step in these…

The aim of this paper is to represent any continuous local martingale as an almost sure limit of a nested sequence of simple, symmetric random walks, time changed by a discrete quadratic variation process. One basis of this is a similar…

Cellular Automata are discrete--time dynamical systems on a spatially extended discrete space which provide paradigmatic examples of nonlinear phenomena. Their stochastic generalizations, i.e., Probabilistic Cellular Automata, are discrete…

We consider specification and inference for the stochastic scale of discretely-observed pure-jump semimartingales with locally stable L\'{e}vy densities in the setting where both the time span of the data set increases, and the mesh of the…

In this paper, we present an iterative Model Predictive Control (MPC) design for piecewise nonlinear systems. We consider finite time control tasks where the goal of the controller is to steer the system from a starting configuration to a…

This paper proposes a flexible framework for inferring large-scale time-varying and time-lagged correlation networks from multivariate or high-dimensional non-stationary time series with piecewise smooth trends. Built on a novel and unified…

We present a constraint-based algorithm for learning causal structures from observational time-series data, in the presence of latent confounders. We assume a discrete-time, stationary structural vector autoregressive process, with both…

The Thermal Time Hypotheis (TTH) has been proposed as a general method for identifying a time variable from within background-free theories which do not come equipped with a pre-defined clock variable. Here, we explore some implications of…

We construct a new class of efficient Monte Carlo methods based on continuous-time piecewise deterministic Markov processes (PDMPs) suitable for inference in high dimensional sparse models, i.e. models for which there is prior knowledge…