Stochastic process

About: Stochastic process is a research topic. Over the lifetime, 31227 publications have been published within this topic receiving 898736 citations. The topic is also known as: random process & stochastic processes.

Statistical inference in a stochastic epidemic SEIR model with control intervention: Ebola as a case study.

Abstract: A stochastic discrete-time susceptible-exposed-infectious-recovered (SEIR) model for infectious diseases is developed with the aim of estimating parameters from daily incidence and mortality time series for an outbreak of Ebola in the Democratic Republic of Congo in 1995. The incidence time series exhibit many low integers as well as zero counts requiring an intrinsically stochastic modeling approach. In order to capture the stochastic nature of the transitions between the compartmental populations in such a model we specify appropriate conditional binomial distributions. In addition, a relatively simple temporally varying transmission rate function is introduced that allows for the effect of control interventions. We develop Markov chain Monte Carlo methods for inference that are used to explore the posterior distribution of the parameters. The algorithm is further extended to integrate numerically over state variables of the model, which are unobserved. This provides a realistic stochastic model that can be used by epidemiologists to study the dynamics of the disease and the effect of control interventions.

An Improved Exponential Model for Predicting Remaining Useful Life of Rolling Element Bearings

Abstract: The remaining useful life (RUL) prediction of rolling element bearings has attracted substantial attention recently due to its importance for the bearing health management. The exponential model is one of the most widely used methods for RUL prediction of rolling element bearings. However, two shortcomings exist in the exponential model: 1) the first predicting time (FPT) is selected subjectively; and 2) random errors of the stochastic process decrease the prediction accuracy. To deal with these two shortcomings, an improved exponential model is proposed in this paper. In the improved model, an adaptive FPT selection approach is established based on the $3\sigma$ interval, and particle filtering is utilized to reduce random errors of the stochastic process. In order to demonstrate the effectiveness of the improved model, a simulation and four tests of bearing degradation processes are utilized for the RUL prediction. The results show that the improved model is able to select an appropriate FPT and reduce random errors of the stochastic process. Consequently, it performs better in the RUL prediction of rolling element bearings than the original exponential model.

Markovian Representation of Stochastic Processes and Its Application to the Analysis of Autoregressive Moving Average Processes

Abstract: The problem of identifiability of a multivariate autoregressive moving average process is considered and a complete solution is obtained by using the Markovian representation of the process. The maximum likelihood procedure for the fitting of the Markovian representation is discussed. A practical procedure for finding an initial guess of the representation is introduced and its feasibility is demonstrated with numerical examples.

Random Trees, Levy Processes and Spatial Branching Processes

Abstract: 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 stochastic process called the height process, which is itself constructed as a local time functional of a Levy process with no negative jumps. We present a detailed study of the height process and of an associated measure-valued process called the exploration process, which plays a key role in most applications. Under suitable assumptions, we prove that whenever a sequence of rescaled Galton-Watson processes converges in distribution, their genealogies also converge to the continuous branching structure coded by the appropriate height process. We apply this invariance principle to various asymptotics for Galton-Watson trees. We then use the duality properties of the exploration process to compute explicitly the distribution of the reduced tree associated with Poissonnian marks in the height process, and the finite-dimensional marginals of the so-called stable continuous tree. This last calculation generalizes to the stable case a result of Aldous for the Brownian continuum random tree. Finally, we combine the genealogical structure with an independent spatial motion to develop a new approach to superprocesses with a general branching mechanism. In this setting, we derive certain explicit distributions, such as the law of the spatial reduced tree in a domain, consisting of the collection of all historical paths that hit the boundary.