國立虎尾科技大學 |

Stochastic Exponential Growth and Lattice Gases = Statistical Mechanics of Stochastic Compounding Processes /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Stochastic Exponential Growth and Lattice Gases/ by Dan Pirjol.
其他題名:	Statistical Mechanics of Stochastic Compounding Processes /
作者:	Pirjol, Dan.
面頁冊數:	IX, 132 p. 34 illus., 32 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Social sciences—Mathematics. -
電子資源:	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. - 1st ed. 2022. - IX, 132 p. 34 illus., 32 illus. in color.online resource. - 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:

1365934
Social sciences—Mathematics.

LC Class. No.: H61.25

Dewey Class. No.: 519

Stochastic Exponential Growth and Lattice Gases = Statistical Mechanics of Stochastic Compounding Processes /
LDR:03353nam a22004215i 4500 001 1082737
003 DE-He213
005 20220901170944.0
007 cr nn 008mamaa
008 221228s2022 sz | s |||| 0|eng d
020 $a 9783031111433 $9 978-3-031-11143-3
024 7 $a 10.1007/978-3-031-11143-3 $2 doi
035 $a 978-3-031-11143-3
050 4 $a H61.25
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 $2 23
100 1 $a Pirjol, Dan. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1388514
245 1 0 $a Stochastic Exponential Growth and Lattice Gases $h [electronic resource] : $b Statistical Mechanics of Stochastic Compounding Processes / $c by Dan Pirjol.
250 $a 1st ed. 2022.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2022.
300 $a IX, 132 p. 34 illus., 32 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
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 Social sciences—Mathematics. $3 1365934
650 0 $a Statistical Physics. $3 670714
650 0 $a Statistical Mechanics. $3 1366342
650 1 4 $a Mathematics in Business, Economics and Finance. $3 1365935
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783031111426
776 0 8 $i Printed edition: $z 9783031111440
830 0 $a SpringerBriefs in Applied Sciences and Technology, $x 2191-530X $3 1253575
856 4 0 $u https://doi.org/10.1007/978-3-031-11143-3
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)