Stochastic Exponential Growth And Lattice Gases

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Stochastic Exponential Growth And Lattice Gases

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Author : Dan Pirjol
language : en
Publisher:
Release Date : 2022

Stochastic Exponential Growth And Lattice Gases written by Dan Pirjol and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022 with categories.

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.

Stochastic Exponential Growth And Lattice Gases

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Author : Dan Pirjol
language : en
Publisher: Springer Nature
Release Date : 2022-09-01

Stochastic Exponential Growth And Lattice Gases written by Dan Pirjol and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-01 with Mathematics categories.

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.

Cellular Automaton Modeling Of Biological Pattern Formation

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Author : Andreas Deutsch
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-26

Cellular Automaton Modeling Of Biological Pattern Formation written by Andreas Deutsch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-26 with Science categories.

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.

Stochastic Processes In Astrophysics

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Author : J. Robert Buchler
language : en
Publisher:
Release Date : 1993

Stochastic Processes In Astrophysics written by J. Robert Buchler and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.

Energy Research Abstracts

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Author :
language : en
Publisher:
Release Date : 1989

Energy Research Abstracts written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Power resources categories.

Diffusion And Defect Data

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Author :
language : en
Publisher:
Release Date : 1990

Diffusion And Defect Data written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Crystals categories.

Stochastic Spatial Processes

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Author : Petre Tautu
language : en
Publisher: Springer
Release Date : 2006-11-14

Stochastic Spatial Processes written by Petre Tautu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

Proceedings of a Conference held in Heidelberg, September 10 - 14, 1984

Polygons Polyominoes And Polycubes

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Author : A. J. Guttmann
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-05-18

Polygons Polyominoes And Polycubes written by A. J. Guttmann and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-05-18 with Science categories.

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.

Dissertation Abstracts International

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Author :
language : en
Publisher:
Release Date : 2004

Dissertation Abstracts International written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Dissertations, Academic categories.

Large Deviations And Metastability

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Author : Enzo Olivieri
language : en
Publisher: Cambridge University Press
Release Date : 2005-02-21

Large Deviations And Metastability written by Enzo Olivieri 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 2005-02-21 with Mathematics categories.

The book provides a general introduction to the theory of large deviations and a wide overview of the metastable behaviour of stochastic dynamics. With only minimal prerequisites, the book covers all the main results and brings the reader to the most recent developments. Particular emphasis is given to the fundamental Freidlin-Wentzell results on small random perturbations of dynamical systems. Metastability is first described on physical grounds, following which more rigorous approaches to its description are developed. Many relevant examples are considered from the point of view of the so-called pathwise approach. The first part of the book develops the relevant tools including the theory of large deviations which are then used to provide a physically relevant dynamical description of metastability. Written to be accessible to graduate students, this book provides an excellent route into contemporary research.