東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Stochastic exponential growth and la...

Pirjol, Dan.

Linked to FindBook

Google Book

Amazon

博客來

Stochastic exponential growth and lattice gases = statistical mechanics of stochastic compounding processes /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Stochastic exponential growth and lattice gases/ by Dan Pirjol.
Reminder of title:	statistical mechanics of stochastic compounding processes /
Author:	Pirjol, Dan.
Published:	Cham :Springer International Publishing : : 2022.,
Description:	ix, 132 p. :ill. (chiefly color), digital ;24 cm.
[NT 15003449]:	Chapter 1. Introduction to stochastic exponential growth -- Chapter 2. Stochastic growth processes with exponential growth rates -- Chapter 3. Lattice gas analogy -- Chapter 4. One-dimensional lattice gases with linear interaction -- Chapter 5. One-dimensional lattice gas with exponential attractive potentials -- Chapter 6. Asymptotic growth rates for exponential stochastic growth processes -- Chapter 7. Applications.
Contained By:	Springer Nature eBook
Subject:	Markov processes. -
Online resource:	https://doi.org/10.1007/978-3-031-11143-3
ISBN:	9783031111433

Stochastic exponential growth and lattice gases = statistical mechanics of stochastic compounding processes /
Pirjol, Dan.

Stochastic exponential growth and lattice gasesstatistical mechanics of stochastic compounding processes /[electronic resource] :by Dan Pirjol. - Cham :Springer International Publishing :2022. - ix, 132 p. :ill. (chiefly color), digital ;24 cm. - SpringerBriefs in applied sciences and technology,2191-5318. - SpringerBriefs in applied sciences and technology..

Chapter 1. Introduction to stochastic exponential growth -- Chapter 2. Stochastic growth processes with exponential growth rates -- Chapter 3. Lattice gas analogy -- Chapter 4. One-dimensional lattice gases with linear interaction -- Chapter 5. One-dimensional lattice gas with exponential attractive potentials -- Chapter 6. Asymptotic growth rates for exponential stochastic growth processes -- Chapter 7. Applications.

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.

ISBN: 9783031111433

Standard No.: 10.1007/978-3-031-11143-3doiSubjects--Topical Terms:

532104
Markov processes.

LC Class. No.: QA274.7

Dewey Class. No.: 519.233

Stochastic exponential growth and lattice gases = statistical mechanics of stochastic compounding processes /
LDR:03000nmm a2200349 a 4500 001 2303444
003 DE-He213
005 20220901170944.0
007 cr nn 008maaau
008 230409s2022 sz s 0 eng d
020 $a 9783031111433 $q (electronic bk.)
020 $a 9783031111426 $q (paper)
024 7 $a 10.1007/978-3-031-11143-3 $2 doi
035 $a 978-3-031-11143-3
040 $a GP $c GP
041 0 $a eng
050 4 $a QA274.7
072 7 $a PBW $2 bicssc
072 7 $a K $2 bicssc
072 7 $a MAT003000 $2 bisacsh
072 7 $a PBW $2 thema
072 7 $a K $2 thema
082 0 4 $a 519.233 $2 23
090 $a QA274.7 $b .P668 2022
100 1 $a Pirjol, Dan. $3 3604736
245 1 0 $a Stochastic exponential growth and lattice gases $h [electronic resource] : $b statistical mechanics of stochastic compounding processes / $c by Dan Pirjol.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2022.
300 $a ix, 132 p. : $b ill. (chiefly color), digital ; $c 24 cm.
490 1 $a SpringerBriefs in applied sciences and technology, $x 2191-5318
505 0 $a Chapter 1. Introduction to stochastic exponential growth -- Chapter 2. Stochastic growth processes with exponential growth rates -- Chapter 3. Lattice gas analogy -- Chapter 4. One-dimensional lattice gases with linear interaction -- Chapter 5. One-dimensional lattice gas with exponential attractive potentials -- Chapter 6. Asymptotic growth rates for exponential stochastic growth processes -- Chapter 7. Applications.
520 $a 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.
650 0 $a Markov processes. $3 532104
650 1 4 $a Mathematics in Business, Economics and Finance. $3 3538573
650 2 4 $a Statistical Physics. $3 892398
650 2 4 $a Statistical Mechanics. $3 3593587
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a SpringerBriefs in applied sciences and technology. $3 1565541
856 4 0 $u https://doi.org/10.1007/978-3-031-11143-3
950 $a Mathematics and Statistics (SpringerNature-11649)