Topic
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.
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TL;DR: LAMPERTI as mentioned in this paper is a pseudonym for John Lamperti, et al.'s book as mentioned in this paper, which is published in 1998, 1998.http://www.journals.com.
Abstract: JOHN LAMPERTI
221 citations
TL;DR: A numerical method based on Wiener Chaos expansion is proposed and applied to solve the stochastic Burgers and Navier-Stokes equations driven by Brownian motion and it is demonstrated that for short time solutions the numerical methods are more efficient and accurate than those based on the Monte Carlo simulations.
221 citations
TL;DR: This paper investigates the problem of fault detection for Takagi-Sugeno (T-S) fuzzy systems with intermittent measurements and designs a fuzzy fault detection filter such that, for all data missing conditions, the residual system is stochastically stable and preserves a guaranteed performance.
Abstract: This paper investigates the problem of fault detection for Takagi-Sugeno (T-S) fuzzy systems with intermittent measurements. The communication links between the plant and the fault detection filter are assumed to be imperfect (i.e., data packet dropouts occur intermittently, which appear typically in a network environment), and a stochastic variable satisfying the Bernoulli random binary distribution is utilized to model the unreliable communication links. The aim is to design a fuzzy fault detection filter such that, for all data missing conditions, the residual system is stochastically stable and preserves a guaranteed performance. The problem is solved through a basis-dependent Lyapunov function method, which is less conservative than the quadratic approach. The results are also extended to T--S fuzzy systems with time-varying parameter uncertainties. All the results are formulated in the form of linear matrix inequalities, which can be readily solved via standard numerical software. Two examples are provided to illustrate the usefulness and applicability of the developed theoretical results.
221 citations
TL;DR: The model proposed here provides an explanation of this experimental behavior in terms of “long-ranged” aggregation and “short-ranged" repulsion mechanisms among individuals, in addition to an individual random dispersal described by a Brownian motion.
Abstract: In this paper we investigate the stochastic modelling of a spatially structured biological population subject to social interaction. The biological motivation comes from the analysis of field experiments on a species of ants which exhibits a clear tendency to aggregate, still avoiding overcrowding. The model we propose here provides an explanation of this experimental behavior in terms of "long-ranged" aggregation and "short-ranged" repulsion mechanisms among individuals, in addition to an individual random dispersal described by a Brownian motion. Further, based on a "law of large numbers", we discuss the convergence, for large N, of a system of stochastic differential equations describing the evolution of N individuals (Lagrangian approach) to a deterministic integro-differential equation describing the evolution of the mean-field spatial density of the population (Eulerian approach).
221 citations
TL;DR: The proposed method provides accurate results for stochastic dimensionality as high as 500 even with large-input variability and the efficiency of the proposed method is examined by comparing with Monte Carlo (MC) simulation.
221 citations