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.

Finite-Horizon $H_{\infty} $ Filtering With Missing Measurements and Quantization Effects

Abstract: In this paper, a new H∞ filtering approach is developed for a class of discrete time-varying systems subject to missing measurements and quantization effects. The missing measurements are modeled via a diagonal matrix consisting of a series of mutually independent random variables satisfying certain probabilistic distributions on the interval [0,1] . The measured output is quantized by a logarithmic quantizer. Attention is focused on the design of a stochastic H∞ filter such that the H∞ estimation performance is guaranteed over a given finite-horizon in the simultaneous presence of probabilistic missing measurements, quantization effects as well as external non-Gaussian disturbances. A necessary and sufficient condition is first established for the existence of the desired time-varying filters in virtue of the solvability of certain coupled recursive Riccati difference equations (RDEs). Owing to its recursive nature, the proposed RDE approach is shown to be suitable for online application without the need of increasing the problem size. The simulation experiment is carried out for the mobile robot localization problem with non-Gaussian disturbances, missing measurements and quantization effects. The effectiveness of the proposed method is demonstrated in the numerical example.

Stochastic analysis of fractional brownian motions

Abstract: In this article some of the important ideas in ordinary stochastic analysis are applied to fractional Brownian motions (fBm's). First we give a simple and elementary proof of the fact that any fBm has zero quadratic variation. This fact leads to the non-semimartingale structure of fBm's. Another consequence is that we can integrate (in probability) the functionals of fBm's with fBm differentials. With the same integrator, we then develop the L2 integration theory of bounded sure processes based on of K. Bichteler's integral extension theory. Finally, we investigate the corresponding stochastic differential equations with fractional Brownian noise

Exponential families of stochastic processes

Abstract: Natural Exponential Families of Leevy Processes.- Definitions and Examples.- First Properties.- Random Time Transformations.- Exponential Families of Markov Processes.- The Envelope Families.- Likelihood Theory.- Linear Stochastic Differential Equations with Time Delay.- Sequential Methods.- The Semimartingale Approach.- Alternative Definitions.

Input–Output Stability of Networked Control Systems With Stochastic Protocols and Channels

Abstract: This paper introduces a new definition of stochastic protocols for networked control systems (NCS) and the stochastic analog of the notion of uniform persistency of excitation of protocols first presented in the Proceedings of the 44th IEEE Conference on Decision and Control. Our framework applies directly to common wireless and wireline NCS, including those built on carrier-sense multiple access (CSMA) style protocols, with Ethernet and 802.11a/b/g as prime examples of this class. We present conditions for a general class of nonlinear NCS with exogenous disturbances using stochastic protocols in the presence of packet dropouts, random packet transmission times and collisions that are sufficient for LP stability from exogenous disturbance to NCS state with a linear finite expected gain. Within the same framework, we extend the results of Nesic and Teel (see IEEE Trans. Autom. Control, vol. 49, no. 10, pp. 1650-1667, Oct. 2004) to provide an analysis of deterministic protocols, including try-once-discard (TOD), in the presence of random packet dropouts and intertransmission times and provide a stochastic analog of the Lyapunov-theoretic stability properties for network protocols introduced therein.

Dynamical pricing of weather derivatives

Abstract: The dynamics of temperature can be modelled by means of a stochastic process known as fractional Brownian motion. Based on this empirical observation, we characterize temperature dynamics by a fractional Ornstein–Uhlenbeck process. This model is used to price two types of contingent claims: one based on heating and cooling degree days, and one based on cumulative temperature. We derive analytic expressions for the expected discounted payoffs of such derivatives, and discuss the dependence of the results on the fractionality of the temperature dynamics.