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Author: Daniel W. Stroock Publisher: Springer ISBN: 3540289992 Category : Mathematics Languages : en Pages : 338
Book Description
From the reviews: "This book is an excellent presentation of the application of martingale theory to the theory of Markov processes, especially multidimensional diffusions. [...] This monograph can be recommended to graduate students and research workers but also to all interested in Markov processes from a more theoretical point of view." Mathematische Operationsforschung und Statistik
Author: Daniel W. Stroock Publisher: Springer ISBN: 3540289992 Category : Mathematics Languages : en Pages : 338
Book Description
From the reviews: "This book is an excellent presentation of the application of martingale theory to the theory of Markov processes, especially multidimensional diffusions. [...] This monograph can be recommended to graduate students and research workers but also to all interested in Markov processes from a more theoretical point of view." Mathematische Operationsforschung und Statistik
Author: Nikola_ Ivanovich Portenko Publisher: American Mathematical Soc. ISBN: 9780821898260 Category : Mathematics Languages : en Pages : 200
Book Description
Diffusion processes serve as a mathematical model for the physical phenomenon of diffusion. One of the most important problems in the theory of diffusion processes is the development of methods for constructing these processes from a given diffusion matrix and a given drift vector. Focusing on the investigation of this problem, this book is intended for specialists in the theory of random processes and its applications. A generalized diffusion process (that is, a continuous Markov process for which the Kolmogorov local characteristics exist in the generalized sense) can serve as a model for diffusion in a medium moving in a nonregular way. The author constructs generalized diffusion processes under two assumptions: first, that the diffusion matrix is sufficiently regular; and second, that the drift vector is a function integrable to some power, or is a generalized function of the type of the derivative of a measure.
Author: Publisher: ISBN: Category : Languages : en Pages : 148
Book Description
In this dissertation we consider several limiting criteria forn-dimensional diffusion processes defined as solutions of stochasticdifferential equations. Our main interest is in criteria for polynomialand exponential rates of convergence to the steady state distributionin the total variation norm. Resulting criteria should place assumptionsonly on the coefficients of the elliptic differentialoperator governing the diffusion. Coupling of Harris chains is one of the main methods employed in thisdissertation.
Author: Jan Baldeaux Publisher: Springer Science & Business Media ISBN: 3319007475 Category : Mathematics Languages : en Pages : 432
Book Description
This research monograph provides an introduction to tractable multidimensional diffusion models, where transition densities, Laplace transforms, Fourier transforms, fundamental solutions or functionals can be obtained in explicit form. The book also provides an introduction to the use of Lie symmetry group methods for diffusions, which allows to compute a wide range of functionals. Besides the well-known methodology on affine diffusions it presents a novel approach to affine processes with applications in finance. Numerical methods, including Monte Carlo and quadrature methods, are discussed together with supporting material on stochastic processes. Applications in finance, for instance, on credit risk and credit valuation adjustment are included in the book. The functionals of multidimensional diffusions analyzed in this book are significant for many areas of application beyond finance. The book is aimed at a wide readership, and develops an intuitive and rigorous understanding of the mathematics underlying the derivation of explicit formulas for functionals of multidimensional diffusions.
Author: Merkel H. Jacobs Publisher: Springer Science & Business Media ISBN: 3642864147 Category : Science Languages : en Pages : 165
Book Description
A basic tenet of present day biophysics is that flows in biological systems are causally related to forces. A large and growing fraction of membrane biophysics is devoted to an exploration of the quantitative relationship between forces and flows in order to understand both the nature of biological membranes and the processes that take place on and in these membranes. This is why the discussion of the nature of diffusion is so important in any formal development of membrane bio physics. This was equally true twenty years ago when tracers were just beginning to be used for the measurement of m.
Author: Devendra Gupta Publisher: Springer Science & Business Media ISBN: 9780080947082 Category : Science Languages : en Pages : 552
Book Description
This new game book for understanding atoms at play aims to document diffusion processes and various other properties operative in advanced technological materials. Diffusion in functional organic chemicals, polymers, granular materials, complex oxides, metallic glasses, and quasi-crystals among other advanced materials is a highly interactive and synergic phenomenon. A large variety of atomic arrangements are possible. Each arrangement affects the performance of these advanced, polycrystalline multiphase materials used in photonics, MEMS, electronics, and other applications of current and developing interest. This book is written by pioneers in industry and academia for engineers, chemists, and physicists in industry and academia at the forefront of today's challenges in nanotechnology, surface science, materials science, and semiconductors.
Author: Publisher: ISBN: Category : Languages : en Pages :
Book Description
This thesis deals with the extreme behavior of multidimensional reversible diffusion processes. The partial maxima of the process, measured in a suitable norm, are considered up to the time horizon T>0. The fine tail asymptotics of the maxima is evaluated for fixed T>0 as well as the long time behavior in the sense of classical extreme value theory. The problem can be reduced to the analysis of spectral asymptotics for the generator of the process subject to Dirichlet boundary conditions on bounded domains which extend to the whole state space. The results are applied to multidimensional diffusion processes in financial mathematics. Multivariate short-rate models are presented and their extreme behavior is explicitly analyzed. In addition, goodness-of-fit tests are developed taking into account the extremes in the data.
Author: Daniel W. Stroock
Author: Daniel W. Stroock
Author: Nikola_ Ivanovich Portenko
Author: Guoliang Wu
Author: 
Author: Jan Baldeaux
Author: Merkel H. Jacobs
Author: Devendra Gupta
Author: 
Author: Andreas Kunz
Author: Kiyosi Itō