國立高雄大學圖資館 |

語系: 繁體中文

說明(常見問題)

圖資館首頁

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

Stochastic numerics for mathematical...

Mil'stein, G. N.

Stochastic numerics for mathematical physics

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Stochastic numerics for mathematical physicsby Grigori N. Milstein, Michael V. Tretyakov.
作者:	Mil'stein, G. N.
其他作者:	Tretyakov, Michael V.
出版者:	Cham :Springer International Publishing :2021.
面頁冊數:	xxv, 736 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Stochastic differential equations.
電子資源:	https://doi.org/10.1007/978-3-030-82040-4
ISBN:	9783030820404$q(electronic bk.)

Stochastic numerics for mathematical physics
Mil'stein, G. N.

Stochastic numerics for mathematical physics[electronic resource] /by Grigori N. Milstein, Michael V. Tretyakov. - Second edition. - Cham :Springer International Publishing :2021. - xxv, 736 p. :ill., digital ;24 cm. - Scientific computation,2198-2589. - Scientific computation..

Mean-square Approximation for Stochastic Diﬀerential Equations -- Weak Approximation for Stochastic Diﬀerential Equations: Foundations -- Weak Approximation for Stochastic Diﬀerential Equations: Special Cases -- Numerical Methods for SDEs with Small Noise -- Geometric Integrators and Computing Ergodic Limits.

This book is a substantially revised and expanded edition reflecting major developments in stochastic numerics since the first edition was published in 2004. The new topics, in particular, include mean-square and weak approximations in the case of nonglobally Lipschitz coefficients of Stochastic Differential Equations (SDEs) including the concept of rejecting trajectories; conditional probabilistic representations and their application to practical variance reduction using regression methods; multi-level Monte Carlo method; computing ergodic limits and additional classes of geometric integrators used in molecular dynamics; numerical methods for FBSDEs; approximation of parabolic SPDEs and nonlinear filtering problem based on the method of characteristics. SDEs have many applications in the natural sciences and in finance. Besides, the employment of probabilistic representations together with the Monte Carlo technique allows us to reduce the solution of multi-dimensional problems for partial differential equations to the integration of stochastic equations. This approach leads to powerful computational mathematics that is presented in the treatise. Many special schemes for SDEs are presented. In the second part of the book numerical methods for solving complicated problems for partial differential equations occurring in practical applications, both linear and nonlinear, are constructed. All the methods are presented with proofs and hence founded on rigorous reasoning, thus giving the book textbook potential. An overwhelming majority of the methods are accompanied by the corresponding numerical algorithms which are ready for implementation in practice. The book addresses researchers and graduate students in numerical analysis, applied probability, physics, chemistry, and engineering as well as mathematical biology and financial mathematics.

ISBN: 9783030820404$q(electronic bk.)

Standard No.: 10.1007/978-3-030-82040-4doiSubjects--Topical Terms:

185784
Stochastic differential equations.

LC Class. No.: QA274.23 / .M55 2021

Dewey Class. No.: 519.22

Stochastic numerics for mathematical physics
LDR:03266nmm a2200349 a 4500 001 612453
003 DE-He213
005 20211203080728.0
006 m d
007 cr nn 008maaau
008 220526s2021 sz s 0 eng d
020 $a 9783030820404$q(electronic bk.)
020 $a 9783030820398$q(paper)
024 7 $a 10.1007/978-3-030-82040-4 $2 doi
035 $a 978-3-030-82040-4
040 $a GP $c GP
041 0 $a eng
050 4 $a QA274.23 $b .M55 2021
072 7 $a PDE $2 bicssc
072 7 $a COM014000 $2 bisacsh
072 7 $a PDE $2 thema
082 0 4 $a 519.22 $2 23
090 $a QA274.23 $b .M661 2021
100 1 $a Mil'stein, G. N. $3 910949
245 1 0 $a Stochastic numerics for mathematical physics $h [electronic resource] / $c by Grigori N. Milstein, Michael V. Tretyakov.
250 $a Second edition.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2021.
300 $a xxv, 736 p. : $b ill., digital ; $c 24 cm.
490 1 $a Scientific computation, $x 2198-2589
505 0 $a Mean-square Approximation for Stochastic Diﬀerential Equations -- Weak Approximation for Stochastic Diﬀerential Equations: Foundations -- Weak Approximation for Stochastic Diﬀerential Equations: Special Cases -- Numerical Methods for SDEs with Small Noise -- Geometric Integrators and Computing Ergodic Limits.
520 $a This book is a substantially revised and expanded edition reflecting major developments in stochastic numerics since the first edition was published in 2004. The new topics, in particular, include mean-square and weak approximations in the case of nonglobally Lipschitz coefficients of Stochastic Differential Equations (SDEs) including the concept of rejecting trajectories; conditional probabilistic representations and their application to practical variance reduction using regression methods; multi-level Monte Carlo method; computing ergodic limits and additional classes of geometric integrators used in molecular dynamics; numerical methods for FBSDEs; approximation of parabolic SPDEs and nonlinear filtering problem based on the method of characteristics. SDEs have many applications in the natural sciences and in finance. Besides, the employment of probabilistic representations together with the Monte Carlo technique allows us to reduce the solution of multi-dimensional problems for partial differential equations to the integration of stochastic equations. This approach leads to powerful computational mathematics that is presented in the treatise. Many special schemes for SDEs are presented. In the second part of the book numerical methods for solving complicated problems for partial differential equations occurring in practical applications, both linear and nonlinear, are constructed. All the methods are presented with proofs and hence founded on rigorous reasoning, thus giving the book textbook potential. An overwhelming majority of the methods are accompanied by the corresponding numerical algorithms which are ready for implementation in practice. The book addresses researchers and graduate students in numerical analysis, applied probability, physics, chemistry, and engineering as well as mathematical biology and financial mathematics.
650 0 $a Stochastic differential equations. $3 185784
650 0 $a Differential equations, Partial $x Numerical solutions. $3 185034
650 0 $a Mathematical physics. $3 190854
650 1 4 $a Computational Science and Engineering. $3 274685
650 2 4 $a Numerical and Computational Physics, Simulation. $3 758154
650 2 4 $a Math. Applications in Chemistry. $3 274138
650 2 4 $a Mathematical and Computational Engineering. $3 775095
650 2 4 $a Mathematical and Computational Biology. $3 514442
650 2 4 $a Financial Mathematics. $3 816035
700 1 $a Tretyakov, Michael V. $3 910950
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Scientific computation. $3 561432
856 4 0 $u https://doi.org/10.1007/978-3-030-82040-4
950 $a Physics and Astronomy (SpringerNature-11651)