Download or read book Stochastic Exponential Growth and Lattice Gases written by Dan Pirjol and published by Springer Nature. This book was released on 2022-09-01 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book discusses a class of discrete time stochastic growth processes for which the growth rate is proportional to the exponential of a Gaussian Markov process. These growth processes appear naturally in problems of mathematical finance as discrete time approximations of stochastic volatility models and stochastic interest rates models such as the Black-Derman-Toy and Black-Karasinski models. These processes can be mapped to interacting one-dimensional lattice gases with long-range interactions. The book gives a detailed discussion of these statistical mechanics models, including new results not available in the literature, and their implication for the stochastic growth models. The statistical mechanics analogy is used to understand observed non-analytic dependence of the Lyapunov exponents of the stochastic growth processes considered, which is related to phase transitions in the lattice gas system. The theoretical results are applied to simulations of financial models and are illustrated with Mathematica code. The book includes a general introduction to exponential stochastic growth with examples from biology, population dynamics and finance. The presentation does not assume knowledge of mathematical finance. The new results on lattice gases can be read independently of the rest of the book. The book should be useful to practitioners and academics studying the simulation and application of stochastic growth models.
Download or read book Cellular Automaton Modeling of Biological Pattern Formation written by Andreas Deutsch and published by Springer Science & Business Media. This book was released on 2007-12-26 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on a challenging application field of cellular automata: pattern formation in biological systems, such as the growth of microorganisms, dynamics of cellular tissue and tumors, and formation of pigment cell patterns. These phenomena, resulting from complex cellular interactions, cannot be deduced solely from experimental analysis, but can be more easily examined using mathematical models, in particular, cellular automaton models. While there are various books treating cellular automaton modeling, this interdisciplinary work is the first one covering biological applications. The book is aimed at researchers, practitioners, and students in applied mathematics, mathematical biology, computational physics, bioengineering, and computer science interested in a cellular automaton approach to biological modeling.
Download or read book The Statistical Mechanics of Lattice Gases written by Barry Simon and published by . This book was released on 1993 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stochastic Processes in Astrophysics written by J. Robert Buchler and published by . This book was released on 1993 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Convexity in the Theory of Lattice Gases written by Robert B. Israel and published by . This book was released on with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lattice Gas Methods for Partial Differential Equations written by Gary Doolen and published by CRC Press. This book was released on 2021-03-13 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of the directions that lattice gas research has taken from 1986 to early 1989. It shows potential users and lattice gas scientists what research has been completed and gives some indication of the utility and limitations of lattice gas models.
Download or read book Energy Research Abstracts written by and published by . This book was released on 1989 with total page 1332 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Diffusion and Defect Data written by and published by . This book was released on 1990 with total page 968 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Stochastic Spatial Processes written by Petre Tautu and published by Springer. This book was released on 2006-11-14 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of a Conference held in Heidelberg, September 10 - 14, 1984
Download or read book Stochastic Processes in Physics Chemistry and Biology written by Jan A. Freund and published by Springer. This book was released on 2008-01-11 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of stochastic processes originally grew out of efforts to describe Brownian motion quantitatively. Today it provides a huge arsenal of methods suitable for analyzing the influence of noise on a wide range of systems. The credit for acquiring all the deep insights and powerful methods is due ma- ly to a handful of physicists and mathematicians: Einstein, Smoluchowski, Langevin, Wiener, Stratonovich, etc. Hence it is no surprise that until - cently the bulk of basic and applied stochastic research was devoted to purely mathematical and physical questions. However, in the last decade we have witnessed an enormous growth of results achieved in other sciences - especially chemistry and biology - based on applying methods of stochastic processes. One reason for this stochastics boom may be that the realization that noise plays a constructive rather than the expected deteriorating role has spread to communities beyond physics. Besides their aesthetic appeal these noise-induced, noise-supported or noise-enhanced effects sometimes offer an explanation for so far open pr- lems (information transmission in the nervous system and information p- cessing in the brain, processes at the cell level, enzymatic reactions, etc.). They may also pave the way to novel technological applications (noise-- hanced reaction rates, noise-induced transport and separation on the na- scale, etc.). Key words to be mentioned in this context are stochastic r- onance, Brownian motors or ratchets, and noise-supported phenomena in excitable systems.
Download or read book Polygons Polyominoes and Polycubes written by A. J. Guttmann and published by Springer Science & Business Media. This book was released on 2009-05-18 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of counting the number of self-avoiding polygons on a square grid, - therbytheirperimeterortheirenclosedarea,is aproblemthatis soeasytostate that, at ?rst sight, it seems surprising that it hasn’t been solved. It is however perhaps the simplest member of a large class of such problems that have resisted all attempts at their exact solution. These are all problems that are easy to state and look as if they should be solvable. They include percolation, in its various forms, the Ising model of ferromagnetism, polyomino enumeration, Potts models and many others. These models are of intrinsic interest to mathematicians and mathematical physicists, but can also be applied to many other areas, including economics, the social sciences, the biological sciences and even to traf?c models. It is the widespread applicab- ity of these models to interesting phenomena that makes them so deserving of our attention. Here however we restrict our attention to the mathematical aspects. Here we are concerned with collecting together most of what is known about polygons, and the closely related problems of polyominoes. We describe what is known, taking care to distinguish between what has been proved, and what is c- tainlytrue,but has notbeenproved. Theearlierchaptersfocusonwhatis knownand on why the problems have not been solved, culminating in a proof of unsolvability, in a certain sense. The next chapters describe a range of numerical and theoretical methods and tools for extracting as much information about the problem as possible, in some cases permittingexactconjecturesto be made.
Download or read book Lattice Gas Cellular Automata and Lattice Boltzmann Models written by Dieter A. Wolf-Gladrow and published by Springer. This book was released on 2004-10-19 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lattice-gas cellular automata (LGCA) and lattice Boltzmann models (LBM) are relatively new and promising methods for the numerical solution of nonlinear partial differential equations. The book provides an introduction for graduate students and researchers. Working knowledge of calculus is required and experience in PDEs and fluid dynamics is recommended. Some peculiarities of cellular automata are outlined in Chapter 2. The properties of various LGCA and special coding techniques are discussed in Chapter 3. Concepts from statistical mechanics (Chapter 4) provide the necessary theoretical background for LGCA and LBM. The properties of lattice Boltzmann models and a method for their construction are presented in Chapter 5.
Download or read book Dissertation Abstracts International written by and published by . This book was released on 2004 with total page 820 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nuclear Science Abstracts written by and published by . This book was released on 1973 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Essentials of Stochastic Processes written by Richard Durrett and published by Springer. This book was released on 2016-11-07 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: Building upon the previous editions, this textbook is a first course in stochastic processes taken by undergraduate and graduate students (MS and PhD students from math, statistics, economics, computer science, engineering, and finance departments) who have had a course in probability theory. It covers Markov chains in discrete and continuous time, Poisson processes, renewal processes, martingales, and option pricing. One can only learn a subject by seeing it in action, so there are a large number of examples and more than 300 carefully chosen exercises to deepen the reader’s understanding. Drawing from teaching experience and student feedback, there are many new examples and problems with solutions that use TI-83 to eliminate the tedious details of solving linear equations by hand, and the collection of exercises is much improved, with many more biological examples. Originally included in previous editions, material too advanced for this first course in stochastic processes has been eliminated while treatment of other topics useful for applications has been expanded. In addition, the ordering of topics has been improved; for example, the difficult subject of martingales is delayed until its usefulness can be applied in the treatment of mathematical finance.
Download or read book Probabilistic Cellular Automata written by Pierre-Yves Louis and published by Springer. This book was released on 2018-02-21 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores Probabilistic Cellular Automata (PCA) from the perspectives of statistical mechanics, probability theory, computational biology and computer science. PCA are extensions of the well-known Cellular Automata models of complex systems, characterized by random updating rules. Thanks to their probabilistic component, PCA offer flexible computing tools for complex numerical constructions, and realistic simulation tools for phenomena driven by interactions among a large number of neighboring structures. PCA are currently being used in various fields, ranging from pure probability to the social sciences and including a wealth of scientific and technological applications. This situation has produced a highly diversified pool of theoreticians, developers and practitioners whose interaction is highly desirable but can be hampered by differences in jargon and focus. This book – just as the workshop on which it is based – is an attempt to overcome these difference and foster interest among newcomers and interaction between practitioners from different fields. It is not intended as a treatise, but rather as a gentle introduction to the role and relevance of PCA technology, illustrated with a number of applications in probability, statistical mechanics, computer science, the natural sciences and dynamical systems. As such, it will be of interest to students and non-specialists looking to enter the field and to explore its challenges and open issues.
Download or read book The Random Cluster Model written by Geoffrey R. Grimmett and published by Springer Science & Business Media. This book was released on 2006-12-13 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: The random-cluster model has emerged as a key tool in the mathematical study of ferromagnetism. It may be viewed as an extension of percolation to include Ising and Potts models, and its analysis is a mix of arguments from probability and geometry. The Random-Cluster Model contains accounts of the subcritical and supercritical phases, together with clear statements of important open problems. The book includes treatment of the first-order (discontinuous) phase transition.
