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From Elementary Probability To Stochastic Differential Equations With Mapler
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Book Synopsis From Elementary Probability to Stochastic Differential Equations with MAPLE® by : Sasha Cyganowski
Download or read book From Elementary Probability to Stochastic Differential Equations with MAPLE® written by Sasha Cyganowski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introduction to probabilistic and statistical concepts necessary to understand the basic ideas and methods of stochastic differential equations. Based on measure theory, which is introduced as smoothly as possible, it provides practical skills in the use of MAPLE in the context of probability and its applications. It offers to graduates and advanced undergraduates an overview and intuitive background for more advanced studies.
Book Synopsis From Elementary Probability to Stochastic Differential Equations with Maple(r) by : Sasha Cyganowski
Download or read book From Elementary Probability to Stochastic Differential Equations with Maple(r) written by Sasha Cyganowski and published by . This book was released on 2001-11-20 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Elementary Applications of Probability Theory by : Henry C. Tuckwell
Download or read book Elementary Applications of Probability Theory written by Henry C. Tuckwell and published by Routledge. This book was released on 2018-02-06 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a clear and straightforward introduction to applications of probability theory with examples given in the biological sciences and engineering. The first chapter contains a summary of basic probability theory. Chapters two to five deal with random variables and their applications. Topics covered include geometric probability, estimation of animal and plant populations, reliability theory and computer simulation. Chapter six contains a lucid account of the convergence of sequences of random variables, with emphasis on the central limit theorem and the weak law of numbers. The next four chapters introduce random processes, including random walks and Markov chains illustrated by examples in population genetics and population growth. This edition also includes two chapters which introduce, in a manifestly readable fashion, the topic of stochastic differential equations and their applications.
Book Synopsis Elementary Applications of Probability Theory by :
Download or read book Elementary Applications of Probability Theory written by and published by . This book was released on 1995 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Random Differential Equations in Scientific Computing by : Tobias Neckel
Download or read book Random Differential Equations in Scientific Computing written by Tobias Neckel and published by Walter de Gruyter. This book was released on 2013-12-17 with total page 650 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a holistic and self-contained treatment of the analysis and numerics of random differential equations from a problem-centred point of view. An interdisciplinary approach is applied by considering state-of-the-art concepts of both dynamical systems and scientific computing. The red line pervading this book is the two-fold reduction of a random partial differential equation disturbed by some external force as present in many important applications in science and engineering. First, the random partial differential equation is reduced to a set of random ordinary differential equations in the spirit of the method of lines. These are then further reduced to a family of (deterministic) ordinary differential equations. The monograph will be of benefit, not only to mathematicians, but can also be used for interdisciplinary courses in informatics and engineering.
Book Synopsis Theory and Numerics of Differential Equations by : James Blowey
Download or read book Theory and Numerics of Differential Equations written by James Blowey and published by Springer Science & Business Media. This book was released on 2001-08-28 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: A compilation of detailed lecture notes on six topics at the forefront of current research in numerical analysis and applied mathematics. Each set of notes presents a self-contained guide to a current research area and has an extensive bibliography. In addition, most of the notes contain detailed proofs of the key results. The notes start from a level suitable for first year graduate students in applied mathematics, mathematical analysis or numerical analysis, and proceed to current research topics. The reader should therefore be able to quickly gain an insight into the important results and techniques in each area without recourse to the large research literature. Current (unsolved) problems are also described and directions for future research is given.
Book Synopsis Elementary Applications of Probability Theory, Second Edition by : Henry C. Tuckwell
Download or read book Elementary Applications of Probability Theory, Second Edition written by Henry C. Tuckwell and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book provides a clear and straightforward introduction to applications of probability theory with examples given in the biological sciences and engineering. The first chapter contains a summary of basic probability theory. Chapters two to five deal with random variables and their applications. Topics covered include geometric probability, estimation of animal and plant populations, reliability theory and computer simulation. Chapter six contains a lucid account of the convergence of sequences of random variables, with emphasis on the central limit theorem and the weak law of numbers. The next four chapters introduce random processes, including random walks and Markov chains illustrated by examples in population genetics and population growth. This edition also includes two chapters which introduce, in a manifestly readable fashion, the topic of stochastic differential equations and their applications."--Provided by publisher.
Book Synopsis On Stochastic Differential Equations by : Various
Download or read book On Stochastic Differential Equations written by Various and published by Maurice Press. This book was released on 2007-03 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt: MEMOIRS O F T H i-AMERICAN MATHEMATICAL SOCIETY NLMBKR 4 ON STOCHASTIC DlFFliRL. NT. lAL LUAUONS KFYOSl 1TO PUBLISHED BY THh AMERICAN MATHEMATFCAL SCXJF1T 531 West 116th St., New York City ON STOCHASTIC DIFFERENTIAL EQUATIONS By KIYOSI ITO Let Xj. be a simple Markoff process with a continuous parameter t, and F t, s, E be the transition probability law of the process D F t, -s, E - Prfx E X.-3, where the right side means the probability of x a E under the condition x. f Hie differential of x. at t s is given by the transition probability law of x in an infinitesimal neighborhood of t s 2 FCs-A jjs E. W. Feller has discussed the case in which it has the following form 3 F s-A 2, JJS A E 1-p s, I yA 2 G s-A 2, j js A E yA 2 p s, j P s, 3, E o yA 2, where G s-Ag, 5 s A, j, E is a probability distribution as a function of E and satisfies 5 T- T f 1 2 J -j h-jl f 6 2 J, l-J G s-A 2, J js dn - b t, J, for A A and p s, J and P s, J, E is a probability distribution in E. The special case of M p s, J O 11 has already been treated by A, Kolmogoroff and S. Bernstein. 3 We shall introduce a somewhat general definition of the differential of the process x. Cf. 85. Let P A denote the conditional probability law L 8,5, 2 Mx-V E-3, A V A 2 0. If the 1 A -times convolution of P fl A tends to a probability law L with regard to Levys law-distance as A A 0, then L is called the I d S, J stochastic differential coefficient at s. L is clearly an infinitely divisible law. In the above Fellers case the logarithmic characteristic function Received by the editors March 29, 5 KIYOSI I TO V, L S of L f is given by 7 z, L ib s, j z - a s, j z p s, 5 f 03 e iu2 - 1 P s, J, du J . 6 8 j 7 - 00 A problem of stochastic differential equations is to construct a Markoff process whose stochastic differential coefficient L. - is given as a function of t, . 9 W. Feller has deduced the following integro-differential equation from 3, 4, 5 and 6 F t, J s, E - P t, j F t, J s, E p t, f F t, 7 s, E P t, J, dT 0. He has proved the J-oo existence and uniqueness of the solution of this equation under some conditions and has shown that the solution becomes a transition probability law, and satisfies 3, 4, 5 6. He has termed the case p t, j as continuous case and the case a t, J and b t, J as purely discontinuous case. It is true that we can construct a simple Markoff process from the transition probability law by introducing a probability distribution into the functional space RR by Kolmogoroff f s theorem, 7 but it is impossible to discuss the regularity of the ob tained process, for example measurability, continuity, discontinuity of the first kind etc, as was pointed out by J. L, Doob. 8 To discuss the measurability of the process for example, J, L. Doob has introduced a probability distribution on a subspace of RR and E, Slutsky has introduced a new concept tf measurable kernel 1,9 We shall in vestigate the sense of the term lf continuous case 11 and fl purely discontinuous case 11 used by W, Feller from the rigorous view-point of J. L. Doob and E. Slutsky. A recent research of J, L, Doob O concerning a simple Markoff process taking values in an en umerable set has been achieved from this view-point, A research of R. FortetH con cerning the above continuous case seems also to stand on the same idea but the author is not yet informed of the details . In his paper ON STOCHASTIC PROCESSES I 11 12 the author has deduced Levys canonical form of differential processes with no fixed discontinuities by making use of the rigorous scheme of J. L, Doob, Using the results of the above paper, we shall here construct the solution of the above stochastic differential equation in such a way that we may be able to discuss the regularity of the solution. For this purpose we transform the stochastic differential equation into a stochastic integral . equation...
Book Synopsis Informal Introduction to Stochastic Processes with Maple by : Jan Vrbik
Download or read book Informal Introduction to Stochastic Processes with Maple written by Jan Vrbik and published by Springer Science & Business Media. This book was released on 2012-12-02 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents an introduction to Stochastic Processes including Markov Chains, Birth and Death processes, Brownian motion and Autoregressive models. The emphasis is on simplifying both the underlying mathematics and the conceptual understanding of random processes. In particular, non-trivial computations are delegated to a computer-algebra system, specifically Maple (although other systems can be easily substituted). Moreover, great care is taken to properly introduce the required mathematical tools (such as difference equations and generating functions) so that even students with only a basic mathematical background will find the book self-contained. Many detailed examples are given throughout the text to facilitate and reinforce learning. Jan Vrbik has been a Professor of Mathematics and Statistics at Brock University in St Catharines, Ontario, Canada, since 1982. Paul Vrbik is currently a PhD candidate in Computer Science at the University of Western Ontario in London, Ontario, Canada. .
Book Synopsis Journal of the American Statistical Association by :
Download or read book Journal of the American Statistical Association written by and published by . This book was released on 2003 with total page 1148 pages. Available in PDF, EPUB and Kindle. Book excerpt: A scientific and educational journal not only for professional statisticians but also for economists, business executives, research directors, government officials, university professors, and others who are seriously interested in the application of statistical methods to practical problems, in the development of more useful methods, and in the improvement of basic statistical data.
Book Synopsis Topics in Stochastic Processes by : Robert B. Ash
Download or read book Topics in Stochastic Processes written by Robert B. Ash and published by Academic Press. This book was released on 2014-06-20 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topics in Stochastic Processes covers specific processes that have a definite physical interpretation and that explicit numerical results can be obtained. This book contains five chapters and begins with the L2 stochastic processes and the concept of prediction theory. The next chapter discusses the principles of ergodic theorem to real analysis, Markov chains, and information theory. Another chapter deals with the sample function behavior of continuous parameter processes. This chapter also explores the general properties of Martingales and Markov processes, as well as the one-dimensional Brownian motion. The aim of this chapter is to illustrate those concepts and constructions that are basic in any discussion of continuous parameter processes, and to provide insights to more advanced material on Markov processes and potential theory. The final chapter demonstrates the use of theory of continuous parameter processes to develop the Itô stochastic integral. This chapter also provides the solution of stochastic differential equations. This book will be of great value to mathematicians, engineers, and physicists.
Book Synopsis An Introduction to Stochastic Modeling by : Mark Pinsky
Download or read book An Introduction to Stochastic Modeling written by Mark Pinsky and published by Academic Press. This book was released on 2011 with total page 585 pages. Available in PDF, EPUB and Kindle. Book excerpt: Serving as the foundation for a one-semester course in stochastic processes for students familiar with elementary probability theory and calculus, Introduction to Stochastic Modeling, Fourth Edition, bridges the gap between basic probability and an intermediate level course in stochastic processes. The objectives of the text are to introduce students to the standard concepts and methods of stochastic modeling, to illustrate the rich diversity of applications of stochastic processes in the applied sciences, and to provide exercises in the application of simple stochastic analysis to realistic problems. New to this edition: Realistic applications from a variety of disciplines integrated throughout the text, including more biological applications Plentiful, completely updated problems Completely updated and reorganized end-of-chapter exercise sets, 250 exercises with answers New chapters of stochastic differential equations and Brownian motion and related processes Additional sections on Martingale and Poisson process Realistic applications from a variety of disciplines integrated throughout the text Extensive end of chapter exercises sets, 250 with answers Chapter 1-9 of the new edition are identical to the previous edition New! Chapter 10 - Random Evolutions New! Chapter 11- Characteristic functions and Their Applications
Book Synopsis Stochastic Calculus by : Richard Durrett
Download or read book Stochastic Calculus written by Richard Durrett and published by Chapman & Hall. This book was released on 2013-06-01 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text focuses on the parts of stochastic theory that are particularly relevant to applications. It begins with a description of Brownian motion and the associated stochastic calculus, including the relationship to partial differential equations. It then solves stochastic differential equations by a variety of methods. The author also studies in detail the one-dimensional case. The book concludes with a treatment of semigroups and generators, applying the theory of Harris chains to diffusions as well as weak convergence of Markov chains to diffusions.
Book Synopsis New Software for Mathematical Package Maple of Releases 6, 7 and 8 by : Victor Aladjev
Download or read book New Software for Mathematical Package Maple of Releases 6, 7 and 8 written by Victor Aladjev and published by . This book was released on 2002 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stochastic Analysis and Applications by : Mark A. Pinsky
Download or read book Stochastic Analysis and Applications written by Mark A. Pinsky and published by CRC Press. This book was released on 2020-10-14 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume attempts to exhibit current research in stochastic integration, stochastic differential equations, stochastic optimization and stochastic problems in physics and biology. It includes information on the theory of Dirichlet forms, Feynman integration and the Schrodinger's equation.
Book Synopsis Algebraic Geometry by : Daniel Perrin
Download or read book Algebraic Geometry written by Daniel Perrin and published by . This book was released on 2008 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed primarily at graduate students and beginning researchers, this book provides an introduction to algebraic geometry that is particularly suitable for those with no previous contact with the subject; it assumes only the standard background of undergraduate algebra. The book starts with easily-formulated problems with non-trivial solutions and uses these problems to introduce the fundamental tools of modern algebraic geometry: dimension; singularities; sheaves; varieties; and cohomology. A range of exercises is provided for each topic discussed, and a selection of problems and exam papers are collected in an appendix to provide material for further study.
Book Synopsis Stochastic Differential Equations by : Bernt Oksendal
Download or read book Stochastic Differential Equations written by Bernt Oksendal and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes are based on a postgraduate course I gave on stochastic differential equations at Edinburgh University in the spring 1982. No previous knowledge about the subject was assumed, but the presen tation is based on some background in measure theory. There are several reasons why one should learn more about stochastic differential equations: They have a wide range of applica tions outside mathematics, there are many fruitful connections to other mathematical disciplines and the subject has a rapidly develop ing life of its own as a fascinating research field with many interesting unanswered questions. Unfortunately most of the literature about stochastic differential equations seems to place so much emphasis on rigor and complete ness that is scares many nonexperts away. These notes are an attempt to approach the subject from the nonexpert point of view: Not knowing anything (except rumours, maybe) about a subject to start with, what would I like to know first of all? My answer would be: 1) In what situations does the subject arise? 2) What are its essential features? 3) What are the applications and the connections to other fields? I would not be so interested in the proof of the most general case, but rather in an easier proof of a special case, which may give just as much of the basic idea in the argument. And I would be willing to believe some basic results without proof (at first stage, anyway) in order to have time for some more basic applications.
