Stochastic Analysis and Nonlinear Filtering of Point Vortex Dynamics Subjected to Jump Noise PDF Download
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Author: Meng Xu
Publisher:
ISBN: 9781124886664
Category : Filters (Mathematics)
Languages : en
Pages : 111
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Book Description
In this thesis, we introduce a random vortex dynamics model described by stochastic differential equations. We first explore the existence and uniqueness of the solution. The nonlinear filtering problem for both continuous and jump noises are studied and an approximation of the associated solutions is discussed. We also study the absolute continuity of the law for the solution of our model using Malliavin calculus. The analysis of nonlinear filtering problem for our model is divided into two parts. For the case of continuous noise, we derive a numerical approximation for the nonlinear filtering equations of vortex dynamics in two dimensions using particle filter method. We prove the convergence of this scheme allowing the observation vector to be unbounded. The SDE driven by both continuous and jump noise is used to model stochastic Lagrangian particle dynamics with jumps for the three dimensional Navier-Stokes flow and the associated nonlinear filtering problem is also studied. We apply results from backward Kolmogorov integro-differential equation problem to prove uniqueness of solution to the Zakai equations of nonlinear filtering.
Author: Meng Xu
Publisher:
ISBN: 9781124886664
Category : Filters (Mathematics)
Languages : en
Pages : 111
Get Book Here
Book Description
In this thesis, we introduce a random vortex dynamics model described by stochastic differential equations. We first explore the existence and uniqueness of the solution. The nonlinear filtering problem for both continuous and jump noises are studied and an approximation of the associated solutions is discussed. We also study the absolute continuity of the law for the solution of our model using Malliavin calculus. The analysis of nonlinear filtering problem for our model is divided into two parts. For the case of continuous noise, we derive a numerical approximation for the nonlinear filtering equations of vortex dynamics in two dimensions using particle filter method. We prove the convergence of this scheme allowing the observation vector to be unbounded. The SDE driven by both continuous and jump noise is used to model stochastic Lagrangian particle dynamics with jumps for the three dimensional Navier-Stokes flow and the associated nonlinear filtering problem is also studied. We apply results from backward Kolmogorov integro-differential equation problem to prove uniqueness of solution to the Zakai equations of nonlinear filtering.
Author: Achintya Mukhopadhyay
Publisher: Springer Nature
ISBN: 9811505365
Category : Technology & Engineering
Languages : en
Pages : 526
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Book Description
This book presents recent advances in dynamics and control of different types of energy systems. It covers research on dynamics and control in energy systems from different aspects, namely, combustion, multiphase flow, nuclear, chemical and thermal. The chapters start from the basic concepts so that this book can be useful even for researchers with very little background in the area. A dedicated chapter provides an overview on the fundamental aspects of the dynamical systems approach. The book will be of use to researchers and professionals alike.
Author:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 1016
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Book Description
Author: Amarjit Budhiraja
Publisher: Springer
ISBN: 1493995790
Category : Mathematics
Languages : en
Pages : 574
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Book Description
This book presents broadly applicable methods for the large deviation and moderate deviation analysis of discrete and continuous time stochastic systems. A feature of the book is the systematic use of variational representations for quantities of interest such as normalized logarithms of probabilities and expected values. By characterizing a large deviation principle in terms of Laplace asymptotics, one converts the proof of large deviation limits into the convergence of variational representations. These features are illustrated though their application to a broad range of discrete and continuous time models, including stochastic partial differential equations, processes with discontinuous statistics, occupancy models, and many others. The tools used in the large deviation analysis also turn out to be useful in understanding Monte Carlo schemes for the numerical approximation of the same probabilities and expected values. This connection is illustrated through the design and analysis of importance sampling and splitting schemes for rare event estimation. The book assumes a solid background in weak convergence of probability measures and stochastic analysis, and is suitable for advanced graduate students, postdocs and researchers.
Author:
Publisher:
ISBN:
Category : Mechanics, Applied
Languages : en
Pages : 410
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Book Description
Author: Marian Wiercigroch
Publisher: Springer Science & Business Media
ISBN: 9400757425
Category : Technology & Engineering
Languages : en
Pages : 442
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Book Description
Nonlinear dynamics has been enjoying a vast development for nearly four decades resulting in a range of well established theory, with the potential to significantly enhance performance, effectiveness, reliability and safety of physical systems as well as offering novel technologies and designs. By critically appraising the state of the art, it is now time to develop design criteria and technology for new generation products/processes operating on principles of nonlinear interaction and in the nonlinear regime, leading to more effective, sensitive, accurate, and durable methods than what is currently available. This new approach is expected to radically influence the design, control and exploitation paradigms, in a magnitude of contexts. With a strong emphasis on experimentally calibrated and validated models, contributions by top-level international experts will foster future directions for the development of engineering technologies and design using robust nonlinear dynamics modelling and analysis.
Author:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 740
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Book Description
Author: Sergio Chibbaro
Publisher: Springer Science & Business Media
ISBN: 3709116228
Category : Technology & Engineering
Languages : en
Pages : 175
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Book Description
Since their first introduction in natural sciences through the work of Einstein on Brownian motion in 1905 and further works, in particular by Langevin, Smoluchowski and others, stochastic processes have been used in several areas of science and technology. For example, they have been applied in chemical studies, or in fluid turbulence and for combustion and reactive flows. The articles in this book provide a general and unified framework in which stochastic processes are presented as modeling tools for various issues in engineering, physics and chemistry, with particular focus on fluid mechanics and notably dispersed two-phase flows. The aim is to develop what can referred to as stochastic modeling for a whole range of applications.
Author: Harvey H. Hubbard
Publisher:
ISBN:
Category : Aerodynamic noise
Languages : en
Pages : 620
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Book Description
Author: P.S Landa
Publisher: Springer Science & Business Media
ISBN: 9401587639
Category : Mathematics
Languages : en
Pages : 550
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Book Description
A rich variety of books devoted to dynamical chaos, solitons, self-organization has appeared in recent years. These problems were all considered independently of one another. Therefore many of readers of these books do not suspect that the problems discussed are divisions of a great generalizing science - the theory of oscillations and waves. This science is not some branch of physics or mechanics, it is a science in its own right. It is in some sense a meta-science. In this respect the theory of oscillations and waves is closest to mathematics. In this book we call the reader's attention to the present-day theory of non-linear oscillations and waves. Oscillatory and wave processes in the systems of diversified physical natures, both periodic and chaotic, are considered from a unified poin t of view . The relation between the theory of oscillations and waves, non-linear dynamics and synergetics is discussed. One of the purposes of this book is to convince reader of the necessity of a thorough study popular branches of of the theory of oscillat ions and waves, and to show that such science as non-linear dynamics, synergetics, soliton theory, and so on, are, in fact , constituent parts of this theory. The primary audiences for this book are researchers having to do with oscillatory and wave processes, and both students and post-graduate students interested in a deep study of the general laws and applications of the theory of oscillations and waves.
