High-dimensional Nonlinear Diffusion Stochastic Processes - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook High-dimensional Nonlinear Diffusion Stochastic Processes write by Yevgeny Mamontov. This book was released on 2001. High-dimensional Nonlinear Diffusion Stochastic Processes available in PDF, EPUB and Kindle. This book is the first one devoted to high-dimensional (or large-scale) diffusion stochastic processes (DSPs) with nonlinear coefficients. These processes are closely associated with nonlinear Ito's stochastic ordinary differential equations (ISODEs) and with the space-discretized versions of nonlinear Ito's stochastic partial integro-differential equations. The latter models include Ito's stochastic partial differential equations (ISPDEs).The book presents the new analytical treatment which can serve as the basis of a combined, analytical-numerical approach to greater computational efficiency in engineering problems. A few examples discussed in the book include: the high-dimensional DSPs described with the ISODE systems for semiconductor circuits; the nonrandom model for stochastic resonance (and other noise-induced phenomena) in high-dimensional DSPs; the modification of the well-known stochastic-adaptive-interpolation method by means of bases of function spaces; ISPDEs as the tool to consistently model non-Markov phenomena; the ISPDE system for semiconductor devices; the corresponding classification of charge transport in macroscale, mesoscale and microscale semiconductor regions based on the wave-diffusion equation; the fully time-domain nonlinear-friction aware analytical model for the velocity covariance of particle of uniform fluid, simple or dispersed; the specific time-domain analytics for the long, non-exponential “tails” of the velocity in case of the hard-sphere fluid.These examples demonstrate not only the capabilities of the developed techniques but also emphasize the usefulness of the complex-system-related approaches to solve some problems which have not been solved with the traditional, statistical-physics methods yet. From this veiwpoint, the book can be regarded as a kind of complement to such books as “Introduction to the Physics of Complex Systems. The Mesoscopic Approach to Fluctuations, Nonlinearity and Self-Organization” by Serra, Andretta, Compiani and Zanarini, “Stochastic Dynamical Systems. Concepts, Numerical Methods, Data Analysis” and “Statistical Physics: An Advanced Approach with Applications” by Honerkamp which deal with physics of complex systems, some of the corresponding analysis methods and an innovative, stochastics-based vision of theoretical physics.To facilitate the reading by nonmathematicians, the introductory chapter outlines the basic notions and results of theory of Markov and diffusion stochastic processes without involving the measure-theoretical approach. This presentation is based on probability densities commonly used in engineering and applied sciences.
High-dimensional Nonlinear Diffusion Stochastic Processes
High-dimensional Nonlinear Diffusion Stochastic Processes - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook High-dimensional Nonlinear Diffusion Stochastic Processes write by Yevgeny Mamontov. This book was released on 2001. High-dimensional Nonlinear Diffusion Stochastic Processes available in PDF, EPUB and Kindle. Annotation This book is one of the first few devoted to high-dimensional diffusion stochastic processes with nonlinear coefficients. These processes are closely associated with large systems of Ito's stochastic differential equations and with discretized-in-the-parameter versions of Ito's stochastic differential equations that are nonlocally dependent on the parameter. The latter models include Ito's stochastic integro-differential, partial differential and partial integro-differential equations.The book presents the new analytical treatment which can serve as the basis of a combined, analytical -- numerical approach to greater computational efficiency. Some examples of the modelling of noise in semiconductor devices are provided
High-Dimensional Probability
High-Dimensional Probability - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook High-Dimensional Probability write by Roman Vershynin. This book was released on 2018-09-27. High-Dimensional Probability available in PDF, EPUB and Kindle. An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
Stochastic Differential Equations and Diffusion Processes
Stochastic Differential Equations and Diffusion Processes - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Stochastic Differential Equations and Diffusion Processes write by Nobuyuki Ikeda. This book was released on 1989. Stochastic Differential Equations and Diffusion Processes available in PDF, EPUB and Kindle. Being a systematic treatment of the modern theory of stochastic integrals and stochastic differential equations, the theory is developed within the martingale framework, which was developed by J.L. Doob and which plays an indispensable role in the modern theory of stochastic analysis.
Analysis and Data-Based Reconstruction of Complex Nonlinear Dynamical Systems
Analysis and Data-Based Reconstruction of Complex Nonlinear Dynamical Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Analysis and Data-Based Reconstruction of Complex Nonlinear Dynamical Systems write by M. Reza Rahimi Tabar. This book was released on 2019-07-04. Analysis and Data-Based Reconstruction of Complex Nonlinear Dynamical Systems available in PDF, EPUB and Kindle. This book focuses on a central question in the field of complex systems: Given a fluctuating (in time or space), uni- or multi-variant sequentially measured set of experimental data (even noisy data), how should one analyse non-parametrically the data, assess underlying trends, uncover characteristics of the fluctuations (including diffusion and jump contributions), and construct a stochastic evolution equation? Here, the term "non-parametrically" exemplifies that all the functions and parameters of the constructed stochastic evolution equation can be determined directly from the measured data. The book provides an overview of methods that have been developed for the analysis of fluctuating time series and of spatially disordered structures. Thanks to its feasibility and simplicity, it has been successfully applied to fluctuating time series and spatially disordered structures of complex systems studied in scientific fields such as physics, astrophysics, meteorology, earth science, engineering, finance, medicine and the neurosciences, and has led to a number of important results. The book also includes the numerical and analytical approaches to the analyses of complex time series that are most common in the physical and natural sciences. Further, it is self-contained and readily accessible to students, scientists, and researchers who are familiar with traditional methods of mathematics, such as ordinary, and partial differential equations. The codes for analysing continuous time series are available in an R package developed by the research group Turbulence, Wind energy and Stochastic (TWiSt) at the Carl von Ossietzky University of Oldenburg under the supervision of Prof. Dr. Joachim Peinke. This package makes it possible to extract the (stochastic) evolution equation underlying a set of data or measurements.
