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: In this paper, a new analytical approach for the derivation of fragility curves for masonry buildings is proposed, based on nonlinear stochastic analyses of building prototypes, where the mechanical properties of the prototypes are considered as random variables, assumed to vary within appropriate ranges of values.
218 citations
TL;DR: In this article, a generalized method of moments on the complex plane (GOMM) is proposed for the estimation of continuous-time stochastic models based on the characteristic function.
218 citations
TL;DR: An integrated approach is advocated which requires the use of both spectral method and random walk analysis, and the theoretical foundation of this approach is provided and the main ideas using examples are illustrated using examples.
Abstract: To assess whether a given time series can be modeled by a stochastic process possessing long range correlation, one usually applies one of two types of analysis methods: the spectral method and the random walk analysis. The first objective of this work is to show that each one of these methods used alone can be susceptible to producing false results. We thus advocate an integrated approach which requires the use of both methods in a consistent fashion. We provide the theoretical foundation of this approach and illustrate the main ideas using examples. The second objective relates to the observation of long range anticorrelation (Hurst exponent $Hl1/2)$ in real world time series data. The very peculiar nature of such processes is emphasized in light of the stringent condition under which such processes can occur. Using examples, we discuss the possible factors that could contribute to the false claim of long range anticorrelations, and demonstrate the particular importance of the integrated approach in this case.
218 citations
TL;DR: A unifying framework is proposed to design a dynamic output feedback control law, which drives the states to the origin almost surely while maintaining all the closed-loop signals bounded almost surely.
Abstract: This paper develops a unifying framework for output feedback regulation of stochastic nonlinear systems with more general stochastic inverse dynamics. The contributions of this work are characterized by the following novel features: (1) Motivated by the concept of integral input-to-state stability (iISS) in deterministic systems and stochastic input-to-state stability (SISS) using Lyapunov function in stochastic systems, a concept of stochastic integral input-to-state stability (SiISS) using Lyapunov function is first introduced, two important properties of SiISS are obtained: (i) SiISS is strictly weaker than SISS using Lyapunov function; (ii) SiISS is stronger than the minimum-phase property. However, only under the minimum-phase assumption, there is no dynamic output feedback control law for global stabilization in probability. (2) Almost sure boundedness, a reasonable and stronger concept than boundedness in probability, is introduced. The purpose of introducing the concept is to prove the boundedness and convergence of some signals in the closed-loop control system. (3) Some important mathematical tools which play an essential role in the boundedness and convergence analysis of the closed-loop system are established. (4) A unifying framework is proposed to design a dynamic output feedback control law, which drives the states to the origin almost surely while maintaining all the closed-loop signals bounded almost surely.
218 citations