相关论文: Multivariate stochastic delay differential equatio…

We compare two approaches to the predictive modeling of dynamical systems from partial observations at discrete times. The first is continuous in time, where one uses data to infer a model in the form of stochastic differential equations,…

We study the strong approximation of stochastic differential equations with discontinuous drift coefficients and (possibly) degenerate diffusion coefficients. To account for the discontinuity of the drift coefficient we construct an…

This paper proposes two distinct contributions to econometric analysis of large information sets and structural instabilities. First, it treats a regression model with time-varying coefficients, stochastic volatility and exogenous…

LSST is expected to yield ~10^7 light curves over the course of its mission, which will require a concerted effort in automated classification. Stochastic processes provide one means of quantitatively describing variability with the…

Auto-regressive moving-average (ARMA) models are ubiquitous forecasting tools. Parsimony in such models is highly valued for their interpretability and computational tractability, and as such the identification of model orders remains a…

We provide a novel method for large volatility matrix prediction with high-frequency data by applying eigen-decomposition to daily realized volatility matrix estimators and capturing eigenvalue dynamics with ARMA models. Given a sequence of…

We prove a stochastic averaging theorem for stochastic differential equations in which the slow and the fast variables interact. The approximate Markov fast motion is a family of Markov process with generator ${\mathcal L}_x$ for which we…

In the past four decades, research on count time series has made significant progress, but research on $\mathbb{Z}$-valued time series is relatively rare. Existing $\mathbb{Z}$-valued models are mainly of autoregressive structure, where the…

This paper proposes the beta binomial autoregressive moving average model (BBARMA) for modeling quantized amplitude data and bounded count data. The BBARMA model estimates the conditional mean of a beta binomial distributed variable…

We have developed a coarse-grained formulation for modeling the dynamic behavior of cells quantitatively, based on stochasticity and heterogeneity, rather than on biochemical reactions. We treat each reaction as a continuous-time stochastic…

A Poisson autoregressive (PAR) model accounting for discreteness and autocorrelation of count time series data is typically estimated in the state-space modelling framework through extended Kalman filter. However, because of the complex…

This paper presents the first sufficient conditions that guarantee the stability and almost sure convergence of multi-timescale stochastic approximation (SA) iterates. It extends the existing results on one-timescale and two-timescale SA…

We introduce a general approach for modeling the dynamic of multivariate time series when the data are of mixed type (binary/count/continuous). Our method is quite flexible and conditionally on past values, each coordinate at time $t$ can…

These notes survey some aspects of discrete-time chaotic calculus and its applications, based on the chaos representation property for i.i.d. sequences of random variables. The topics covered include the Clark formula and predictable…

We present time-constrained automata (TCA), a model for hard real-time computation in which agents behaviors are modeled by automata and constrained by time intervals. TCA actions can have multiple start time and deadlines, can be…

Multivariate time series classification is a task with increasing importance due to the proliferation of new problems in various fields (economy, health, energy, transport, crops, etc.) where a large number of information sources are…

We show that a substantial portion of stochastic calculus can be developed along similar lines to ordinary calculus, with derivative-based concepts driving the development. We define a notion of stopping derivative, which is a form of right…

In this note, we shall consider the existence of invariant measures for a class of infinite dimensional stochastic functional differential equations with delay whose driving semigroup is eventually norm continuous. The results obtained are…

This paper addresses the prediction of stationary functional time series. Existing contributions to this problem have largely focused on the special case of first-order functional autoregressive processes because of their technical…

We propose an approach for multiple sequence alignment (MSA) derived from the dynamic time warping viewpoint and recent techniques of curve synchronization developed in the context of functional data analysis. Starting from pairwise…