Related papers: Periodic trawl processes: Simulation, statistical …
Single-particle traces of the diffusive motion of molecules, cells, or animals are by-now routinely measured, similar to stochastic records of stock prices or weather data. Deciphering the stochastic mechanism behind the recorded dynamics…
Temporal point processes are the dominant paradigm for modeling sequences of events happening at irregular intervals. The standard way of learning in such models is by estimating the conditional intensity function. However, parameterizing…
We give conditions to prove the existence of an Extremal Index for general stationary stochastic processes by detecting the presence of one or more underlying periodic phenomena. This theory, besides giving general useful tools to identify…
In the study of dynamical processes on networks, there has been intense focus on network structure -- i.e., the arrangement of edges and their associated weights -- but the effects of the temporal patterns of edges remains poorly…
We propose a new class of univariate nonstationary time series models, using the framework of modulated time series, which is appropriate for the analysis of rapidly-evolving time series as well as time series observations with missing…
Integer-valued trawl processes are a class of serially correlated, stationary and infinitely divisible processes that Ole E. Barndorff-Nielsen has been working on in recent years. In this Chapter, we provide the first analysis of likelihood…
This paper is concerned with asymptotic behavior of a variety of functionals of increments of continuous semimartingales. Sampling times are assumed to follow a rather general discretization scheme. If an underlying semimartingale is…
A class of stochastic processes strongly related to random sums plays an important role in network and in finance. In this paper we study this kind of stochastic process discuss an overtime unchanged parameter and reveal its asymptotic…
The main purpose of this chapter is to present some theoretical aspects of parametric estimation of L\'evy processes based on high-frequency sampling, with a focus on infinite activity pure-jump models. Asymptotics for several classes of…
Earlier we proposed the stochastic point process model, which reproduces a variety of self-affine time series exhibiting power spectral density S(f) scaling as power of the frequency f and derived a stochastic differential equation with the…
Mounting empirical evidence suggests that the observed extreme prices within a trading period can provide valuable information about the volatility of the process within that period. In this paper we define a class of stochastic volatility…
In real-world scenario, many phenomena produce a collection of events that occur in continuous time. Point Processes provide a natural mathematical framework for modeling these sequences of events. In this survey, we investigate…
Classical particles driven through periodically modulated potential energy landscapes are predicted to follow a Devil's staircase hierarchy of commensurate trajectories depending on the orientation of the driving force. Recent experiments…
Aperiodic variability is a characteristic feature of young stars, massive stars, and active galactic nuclei. With the recent proliferation of time domain surveys, it is increasingly essential to develop methods to quantify and analyze…
Stochastic processes generated by non-stationary distributions are difficult to represent with conventional models such as Gaussian processes. This work presents Recurrent Autoregressive Flows as a method toward general stochastic process…
Random walks are basic diffusion processes on networks and have applications in, for example, searching, navigation, ranking, and community detection. Recent recognition of the importance of temporal aspects on networks spurred studies of…
This paper is devoted to the analysis of the finite-dimensional distributions and asymptotic behavior of extremal Markov processes connected to the Kendall convolution. In particular, based on its stochastic representation, we provide…
Many real-world objects can be modeled as a stream of events on the nodes of a graph. In this paper, we propose a class of graphical event models named temporal point process graphical models for representing the temporal dependencies among…
We consider random variables observed at arrival times of a renewal process, which possibly depends on those observations and has regularly varying steps with infinite mean. Due to the dependence and heavy tailed steps, the limiting…
We introduce a class of discrete time stationary trawl processes taking real or integer values and written as sums of past values of independent `seed' processes on shrinking intervals (`trawl heights'). Related trawl processes in…