Stochastic Versus Deterministic Systems Of Differential Equations
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Stochastic Versus Deterministic Systems Of Differential Equations
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Author : G. S. Ladde
language : en
Publisher: CRC Press
Release Date : 2003-12-05
Stochastic Versus Deterministic Systems Of Differential Equations written by G. S. Ladde and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-12-05 with Mathematics categories.
This peerless reference/text unfurls a unified and systematic study of the two types of mathematical models of dynamic processes-stochastic and deterministic-as placed in the context of systems of stochastic differential equations. Using the tools of variational comparison, generalized variation of constants, and probability distribution as its met
Stochastic Ordinary And Stochastic Partial Differential Equations
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Author : Peter Kotelenez
language : en
Publisher: Springer
Release Date : 2014-09-18
Stochastic Ordinary And Stochastic Partial Differential Equations written by Peter Kotelenez and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-18 with Mathematics categories.
Stochastic Partial Differential Equations analyzes mathematical models of time-dependent physical phenomena on microscopic, macroscopic and mesoscopic levels. It provides a rigorous derivation of each level from the preceding one and examines the resulting mesoscopic equations in detail. Coverage first describes the transition from the microscopic equations to the mesoscopic equations. It then covers a general system for the positions of the large particles.
Deterministic Versus Stochastic Modelling In Biochemistry And Systems Biology
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Author : Paola Lecca
language : en
Publisher: Elsevier
Release Date : 2013-04-09
Deterministic Versus Stochastic Modelling In Biochemistry And Systems Biology written by Paola Lecca and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-09 with Mathematics categories.
Stochastic kinetic methods are currently considered to be the most realistic and elegant means of representing and simulating the dynamics of biochemical and biological networks. Deterministic versus stochastic modelling in biochemistry and systems biology introduces and critically reviews the deterministic and stochastic foundations of biochemical kinetics, covering applied stochastic process theory for application in the field of modelling and simulation of biological processes at the molecular scale. Following an overview of deterministic chemical kinetics and the stochastic approach to biochemical kinetics, the book goes onto discuss the specifics of stochastic simulation algorithms, modelling in systems biology and the structure of biochemical models. Later chapters cover reaction-diffusion systems, and provide an analysis of the Kinfer and BlenX software systems. The final chapter looks at simulation of ecodynamics and food web dynamics. - Introduces mathematical concepts and formalisms of deterministic and stochastic modelling through clear and simple examples - Presents recently developed discrete stochastic formalisms for modelling biological systems and processes - Describes and applies stochastic simulation algorithms to implement a stochastic formulation of biochemical and biological kinetics
Stochastic Versus Deterministic Systems Of Iterative Processes
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Author : Gangaram S Ladde
language : en
Publisher: World Scientific
Release Date : 2024-04-22
Stochastic Versus Deterministic Systems Of Iterative Processes written by Gangaram S Ladde and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-22 with Mathematics categories.
Continuous state dynamic models can be reformulated into discrete state processes. This process generates numerical schemes that lead theoretical iterative schemes. This type of method of stochastic modelling generates three basic problems. First, the fundamental properties of solution, namely, existence, uniqueness, measurability, continuous dependence on system parameters depend on mode of convergence. Second, the basic probabilistic and statistical properties, namely, the behavior of mean, variance, moments of solutions are described as qualitative/quantitative properties of solution process. We observe that the nature of probability distribution or density functions possess the qualitative/quantitative properties of iterative prosses as a special case. Finally, deterministic versus stochastic modelling of dynamic processes is to what extent the stochastic mathematical model differs from the corresponding deterministic model in the absence of random disturbances or fluctuations and uncertainties.Most literature in this subject was developed in the 1950s, and focused on the theory of systems of continuous and discrete-time deterministic; however, continuous-time and its approximation schemes of stochastic differential equations faced the solutions outlined above and made slow progress in developing problems. This monograph addresses these problems by presenting an account of stochastic versus deterministic issues in discrete state dynamic systems in a systematic and unified way.
Stochastic Versus Deterministic Systems Of Iterative Processes
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Author : Gangaram S Ladde
language : en
Publisher:
Release Date : 2024-06-06
Stochastic Versus Deterministic Systems Of Iterative Processes written by Gangaram S Ladde and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-06-06 with Mathematics categories.
State continuous dynamic models can be reformulated into discrete state processes. This process generates numerical schemes that lead theoretical iterative schemes. This type of method of stochastic modelling generates three basic problems. First, the fundamental properties of solution, namely, existence, uniqueness, measurability, continuous dependence on system parameters depend mode of convergence. Second, the basic probabilistic and statistical properties mean, variance, moments of qualitative/quantitative behaviour of solutions are directly described as concept of solution process or via probability distribution or density functions either. Finally, deterministic versus stochastic modelling of dynamic processes is to what extent the stochastic mathematical model differs from the corresponding deterministic model in the absence of random disturbances or fluctuations and uncertainties.Most literature in this subject was developed in the 1950s, and focussed on the theory of systems of continuous and discrete-time deterministic; however, continuous-time and its approximation schemes of stochastic differential equations faced the problems outlined above and made slow progress in developing problems as a result. This monograph addresses these problems by presenting an account of stochastic versus deterministic issues in discrete state dynamic systems in a systematic and unified way.
Stochastic Modelling Of Reaction Diffusion Processes
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Author : Radek Erban
language : en
Publisher: Cambridge University Press
Release Date : 2020-01-30
Stochastic Modelling Of Reaction Diffusion Processes written by Radek Erban and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-30 with Mathematics categories.
This practical introduction to stochastic reaction-diffusion modelling is based on courses taught at the University of Oxford. The authors discuss the essence of mathematical methods which appear (under different names) in a number of interdisciplinary scientific fields bridging mathematics and computations with biology and chemistry. The book can be used both for self-study and as a supporting text for advanced undergraduate or beginning graduate-level courses in applied mathematics. New mathematical approaches are explained using simple examples of biological models, which range in size from simulations of small biomolecules to groups of animals. The book starts with stochastic modelling of chemical reactions, introducing stochastic simulation algorithms and mathematical methods for analysis of stochastic models. Different stochastic spatio-temporal models are then studied, including models of diffusion and stochastic reaction-diffusion modelling. The methods covered include molecular dynamics, Brownian dynamics, velocity jump processes and compartment-based (lattice-based) models.
Strange Functions In Real Analysis Second Edition
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Author : Alexander Kharazishvili
language : en
Publisher: CRC Press
Release Date : 2005-12-20
Strange Functions In Real Analysis Second Edition written by Alexander Kharazishvili and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-20 with Mathematics categories.
Weierstrass and Blancmange nowhere differentiable functions, Lebesgue integrable functions with everywhere divergent Fourier series, and various nonintegrable Lebesgue measurable functions. While dubbed strange or "pathological," these functions are ubiquitous throughout mathematics and play an important role in analysis, not only as counterexamples of seemingly true and natural statements, but also to stimulate and inspire the further development of real analysis. Strange Functions in Real Analysis explores a number of important examples and constructions of pathological functions. After introducing the basic concepts, the author begins with Cantor and Peano-type functions, then moves to functions whose constructions require essentially noneffective methods. These include functions without the Baire property, functions associated with a Hamel basis of the real line, and Sierpinski-Zygmund functions that are discontinuous on each subset of the real line having the cardinality continuum. Finally, he considers examples of functions whose existence cannot be established without the help of additional set-theoretical axioms and demonstrates that their existence follows from certain set-theoretical hypotheses, such as the Continuum Hypothesis.
A First Graduate Course In Abstract Algebra
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Author : William Jennings Wickless
language : en
Publisher: CRC Press
Release Date : 2019-09-27
A First Graduate Course In Abstract Algebra written by William Jennings Wickless and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-27 with Mathematics categories.
Realizing the specific needs of first-year graduate students, this reference allows readers to grasp and master fundamental concepts in abstract algebra-establishing a clear understanding of basic linear algebra and number, group, and commutative ring theory and progressing to sophisticated discussions on Galois and Sylow theory, the structure of abelian groups, the Jordan canonical form, and linear transformations and their matrix representations.
Introduction To The Mathematics Of Operations Research With Mathematica
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Author : Kevin J. Hastings
language : en
Publisher: CRC Press
Release Date : 2018-10-24
Introduction To The Mathematics Of Operations Research With Mathematica written by Kevin J. Hastings and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-24 with Business & Economics categories.
The breadth of information about operations research and the overwhelming size of previous sources on the subject make it a difficult topic for non-specialists to grasp. Fortunately, Introduction to the Mathematics of Operations Research with Mathematica®, Second Edition delivers a concise analysis that benefits professionals in operations research and related fields in statistics, management, applied mathematics, and finance. The second edition retains the character of the earlier version, while incorporating developments in the sphere of operations research, technology, and mathematics pedagogy. Covering the topics crucial to applied mathematics, it examines graph theory, linear programming, stochastic processes, and dynamic programming. This self-contained text includes an accompanying electronic version and a package of useful commands. The electronic version is in the form of Mathematica notebooks, enabling you to devise, edit, and execute/reexecute commands, increasing your level of comprehension and problem-solving. Mathematica sharpens the impact of this book by allowing you to conveniently carry out graph algorithms, experiment with large powers of adjacency matrices in order to check the path counting theorem and Markov chains, construct feasible regions of linear programming problems, and use the "dictionary" method to solve these problems. You can also create simulators for Markov chains, Poisson processes, and Brownian motions in Mathematica, increasing your understanding of the defining conditions of these processes. Among many other benefits, Mathematica also promotes recursive solutions for problems related to first passage times and absorption probabilities.
Applied Stochastic Differential Equations
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Author : Simo Särkkä
language : en
Publisher: Cambridge University Press
Release Date : 2019-05-02
Applied Stochastic Differential Equations written by Simo Särkkä and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-02 with Business & Economics categories.
With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.