Stochastic Exponential Growth And Lattice Gases
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Author | : Dan Pirjol |
Publisher | : Springer Nature |
Total Pages | : 138 |
Release | : 2022-09-01 |
Genre | : Mathematics |
ISBN | : 3031111435 |
Download Stochastic Exponential Growth and Lattice Gases Book in PDF, Epub and Kindle
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.
Author | : Andreas Deutsch |
Publisher | : Springer Science & Business Media |
Total Pages | : 331 |
Release | : 2007-12-26 |
Genre | : Science |
ISBN | : 0817644156 |
Download Cellular Automaton Modeling of Biological Pattern Formation Book in PDF, Epub and Kindle
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.
Author | : Barry Simon |
Publisher | : |
Total Pages | : |
Release | : 1993 |
Genre | : |
ISBN | : |
Download The Statistical Mechanics of Lattice Gases Book in PDF, Epub and Kindle
Author | : J. Robert Buchler |
Publisher | : |
Total Pages | : 224 |
Release | : 1993 |
Genre | : Mathematics |
ISBN | : |
Download Stochastic Processes in Astrophysics Book in PDF, Epub and Kindle
Author | : Robert B. Israel |
Publisher | : |
Total Pages | : 253 |
Release | : |
Genre | : |
ISBN | : 9780608066189 |
Download Convexity in the Theory of Lattice Gases Book in PDF, Epub and Kindle
Author | : Gary Doolen |
Publisher | : CRC Press |
Total Pages | : 582 |
Release | : 2021-03-13 |
Genre | : Differential equations, Partial |
ISBN | : 9780367152741 |
Download Lattice Gas Methods for Partial Differential Equations Book in PDF, Epub and Kindle
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.
Author | : Gary D. Doolen |
Publisher | : |
Total Pages | : 0 |
Release | : 1991 |
Genre | : Differential equations, Partial |
ISBN | : |
Download Lattice Gas Methods Book in PDF, Epub and Kindle
Author | : Dieter A. Wolf-Gladrow |
Publisher | : Springer |
Total Pages | : 320 |
Release | : 2004-10-19 |
Genre | : Mathematics |
ISBN | : 3540465863 |
Download Lattice-Gas Cellular Automata and Lattice Boltzmann Models Book in PDF, Epub and Kindle
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.
Author | : |
Publisher | : |
Total Pages | : 1332 |
Release | : 1989 |
Genre | : Power resources |
ISBN | : |
Download Energy Research Abstracts Book in PDF, Epub and Kindle
Author | : |
Publisher | : |
Total Pages | : 968 |
Release | : 1990 |
Genre | : Crystals |
ISBN | : |
Download Diffusion and Defect Data Book in PDF, Epub and Kindle