相关论文: Harris Processes
We study the problem of parameter estimation for reflected stochastic processes driven by a standard Brownian motion. The estimator is obtained using nonlinear least squares method based on discretely observed processes. Under some certain…
We develop a Bayesian non-parametric framework based on multi-task Gaussian processes, appropriate for temporal shrinkage. We focus on a particular class of dynamic hierarchical models to obtain evidence-based knowledge of infectious…
Stochastic processes have found numerous applications in science, as they are broadly used to model a variety of natural phenomena. Due to their intrinsic randomness and uncertainty, they are, however, difficult to characterize. Here, we…
In this paper, we analyze Gaussian processes using statistical mechanics. Although the input is originally multidimensional, we simplify our model by considering the input as one-dimensional for statistical mechanical analysis. Furthermore,…
The authors present a method of indicator random processes, applicable to constructing models of jump processes associated with diffusion process. Indicator random processes are processes that take only two values: 1 and 0, in accordance…
We consider a multidimensional time-homogeneous dynamical system and add a randomly perturbed time-dependent deterministic signal to some of its components, giving rise to a high-dimensional system of stochastic differential equations,…
We study the stationary states of variants of the noisy voter model, subject to fluctuating parameters or external environments. Specifically, we consider scenarios in which the herding-to-noise ratio switches randomly and on different time…
We propose a new model for nonstationary integer-valued time series which is particularly suitable for data with a strong trend. In contrast to popular Poisson-INGARCH models, but in line with classical GARCH models, we propose to pick the…
Stochastic processes can model many emerging phenomena on networks, like the spread of computer viruses, rumors, or infectious diseases. Understanding the dynamics of such stochastic spreading processes is therefore of fundamental interest.…
We consider two kinds of stochastic volatility models. Both kinds of models contain a stationary volatility process, the density of which, at a fixed instant in time, we aim to estimate. We discuss discrete time models where for instance a…
Different change-point type models encountered in statistical inference for stochastic processes give rise to different limiting likelihood ratio processes. In a previous paper of one of the authors it was established that one of these…
A defining feature of non-stationary systems is the time dependence of their statistical parameters. Measured time series may exhibit Gaussian statistics on short time horizons, due to the central limit theorem. The sample statistics for…
We develop correlated random measures, random measures where the atom weights can exhibit a flexible pattern of dependence, and use them to develop powerful hierarchical Bayesian nonparametric models. Hierarchical Bayesian nonparametric…
The literature on Bayesian methods for the analysis of discrete-time semi-Markov processes is sparse. In this paper, we introduce the semi-Markov beta-Stacy process, a stochastic process useful for the Bayesian non-parametric analysis of…
Existing methods for the estimation of stable distribution parameters, such as those based on sample quantiles, sample characteristic functions or maximum likelihood generally assume an independent sample. Little attention has been paid to…
We study the non-stationary Feller process with time varying coefficients. We obtain the exact probability distribution exemplified by its characteristic function and cumulants. In some particular cases we exactly invert the distribution…
We discuss a general Bayesian framework on modeling multidimensional function-valued processes by using a Gaussian process or a heavy-tailed process as a prior, enabling us to handle nonseparable and/or nonstationary covariance structure.…
This paper focuses on systems of nonlinear second-order stochastic differential equations with multi-scales. The motivation for our study stems from mathematical physics and statistical mechanics, for examples, Langevin dynamics and…
Point pattern data often exhibit features such as abrupt changes, hotspots and spatially varying dependence in local intensity. Under a Poisson process framework, these correspond to discontinuities and nonstationarity in the underlying…
We introduce a path sampling method for obtaining statistical properties of an arbitrary stochastic dynamics. The method works by decomposing a trajectory in time, estimating the probability of satisfying a progress constraint, modifying…