Related papers: Discrete-time trawl processes with long memory
Gradient-based learning in multi-layer neural networks displays a number of striking features. In particular, the decrease rate of empirical risk is non-monotone even after averaging over large batches. Long plateaus in which one observes…
We obtain general lower estimates of transition densities of jump L\'evy processes. We use them for processes with L\'evy measures having bounded support, processes with exponentially decaying L\'evy measures for large times and for…
We consider random walks on dynamical networks where edges appear and disappear during finite time intervals. The process is grounded on three independent stochastic processes determining the walker's waiting-time, the up-time and down-time…
Imposing some flexible sampling scheme we provide some discretization of continuous time discrete scale invariant (DSI) processes which is a subsidiary discrete time DSI process. Then by introducing some simple random measure we provide a…
The dynamical discrete web (DyDW),introduced in recent work of Howitt and Warren, is a system of coalescing simple symmetric one-dimensional random walks which evolve in an extra continuous dynamical time parameter \tau. The evolution is by…
This paper investigates the problem of forecasting multivariate aggregated human mobility while preserving the privacy of the individuals concerned. Differential privacy, a state-of-the-art formal notion, has been used as the privacy…
We have studied experimentally transport properties in a slowly driven granular system which recently was shown to display self-organized criticality [Frette {\em et al., Nature} {\bf 379}, 49 (1996)]. Tracer particles were added to a pile…
Time series data that are not measured at regular intervals are commonly discretized as a preprocessing step. For example, data about customer arrival times might be simplified by summing the number of arrivals within hourly intervals,…
In this work, we investigate the large-scale transport properties of a passive scalar advected by a turbulent fluid, modelled as a superposition of divergence-free vector fields, each weighted by an independent symmetric…
L\'evy walks are continuous time random walks with spatio-temporal coupling of jump lengths and waiting times, often used to model superdiffusive spreading processes such as animals searching for food, tracer motion in weakly chaotic…
Efficiency of search for randomly distributed targets is a prominent problem in many branches of the sciences. For the stochastic process of L\'evy walks, a specific range of optimal efficiencies was suggested under variation of search…
We investigate the genealogical structure of general critical or subcritical continuous-state branching processes. Analogously to the coding of a discrete tree by its contour function, this genealogical structure is coded by a real-valued…
The time that waves spend inside 1D random media with the possibility of performing L\'evy walks is experimentally and theoretically studied. The dynamics of quantum and classical wave diffusion has been investigated in canonical disordered…
We give a complete classification of scaling limits of randomly trapped random walks and associated clock processes on $\mathbb Z^d$, $d\ge 2$. Namely, under the hypothesis that the discrete skeleton of the randomly trapped random walk has…
We characterise the convergence of a certain class of discrete time Markov processes toward locally Feller processes in terms of convergence of associated operators. The theory of locally Feller processes is applied to L\'evy-type processes…
One-dimensional run-and-tumble processes may converge towards some localized non-equilibrium steady state when the two velocities and/or the two switching rates are space-dependent. A long dynamical trajectory can be then analyzed via the…
How do large deviation events in a stationary process cluster? The answer depends not only on the type of large deviations, but also on the length of memory in the process. Somewhat unexpectedly, it may also depend on the tails of the…
First, we present some results about the H\"older continuity of the sample paths of so called dilatively stable processes which are certain infinitely divisible processes having a more general scaling property than self-similarity. As a…
The project aims to research on combining deep learning specifically Long-Short Memory (LSTM) and basic statistics in multiple multistep time series prediction. LSTM can dive into all the pages and learn the general trends of variation in a…
The characterization of record events is considered for a discrete-time random walk model with long-term memory arising from correlations between successive steps. An important feature is that the correlations are strong enough to give rise…