Related papers: Aggregation of autoregressive processes and long m…
Stationary ergodic processes with finite alphabets are estimated by finite memory processes from a sample, an n-length realization of the process, where the memory depth of the estimator process is also estimated from the sample using…
Given the observation of a high-dimensional Ornstein-Uhlenbeck (OU) process in continuous time, we proceed to the inference of the drift parameter under a row-sparsity assumption. Towards that aim, we consider the negative log-likelihood of…
Motivated by a variety of applications, high-dimensional time series have become an active topic of research. In particular, several methods and finite-sample theories for individual stable autoregressive processes with known lag have…
Convergence rate to the stationary distribution for continuous-time Markov processes can be studied using Lyapunov functions. Recent work by the author provided explicit rates of convergence in special case of a reflected jump-diffusion on…
This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…
The aim of this paper is to extend the aggregation convergence results given in (Dacunha-Castelle and Fermin 2005, Dacunha-Castelle and Fermin 2008) to doubly stochastic linear and nonlinear processes with weakly dependent innovations.…
We introduce the elliptical Ornstein-Uhlenbeck (OU) process, which is a generalisation of the well-known univariate OU process to bivariate time series. This process maps out elliptical stochastic oscillations over time in the complex…
Many active systems move in complex environments whose mechanical response is slow and history dependent. To address this regime, we study the collective dynamics of self-sustained active particles in non-Markovian media within a…
We propose a first-order autoregressive (i.e. AR(1)) model for dynamic network processes in which edges change over time while nodes remain unchanged. The model depicts the dynamic changes explicitly. It also facilitates simple and…
These lecture notes present some new concentration inequalities for Feynman-Kac particle processes. We analyze different types of stochastic particle models, including particle profile occupation measures, genealogical tree based evolution…
We investigate a generalized stochastic model with the property known as mean reversion, that is, the tendency to relax towards a historical reference level. Besides this property, the dynamics is driven by multiplicative and additive…
An integro-differential equation for the probability density of the generalized stochastic Ornstein-Uhlenbeck process with jump diffusion is considered. It is shown that for a certain ratio between the intensity of jumps and the speed of…
We derive recursions for the probability distribution of random sums by computer algebra. Unlike the well-known Panjer-type recursions, they are of finite order and thus allow for computation in linear time. This efficiency is bought by the…
This work shows how exponential concentration inequalities for additive functionals of stochastic processes over a finite time interval can be derived from concentration inequalities for martingales. The approach is entirely probabilistic…
Associative Memories like the famous Hopfield Networks are elegant models for describing fully recurrent neural networks whose fundamental job is to store and retrieve information. In the past few years they experienced a surge of interest…
We consider the correlations and the hydrodynamic description of random walkers with a general finite memory moving on a $d$ dimensional hypercubic lattice. We derive a drift-diffusion equation and identify a memory-dependent critical…
Long memory and volatility clustering are two stylized facts frequently related to financial markets. Traditionally, these phenomena have been studied based on conditionally heteroscedastic models like ARCH, GARCH, IGARCH and FIGARCH, inter…
We investigate how large deviations events cluster in the framework of an infinite moving average process with light-tailed noise and long memory. The long memory makes clusters larger, and the asymptotic behaviour of the size of the…
The modeling of time-varying graph signals as stationary time-vertex stochastic processes permits the inference of missing signal values by efficiently employing the correlation patterns of the process across different graph nodes and time…
n this paper we consider polynomial cointegrating relationships among stationary processes with long range dependence. We express the regression functions in terms of Hermite polynomials and we consider a form of spectral regression around…