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

Jump SDEs and the study of their den...

Kohatsu-Higa, Arturo.

Jump SDEs and the study of their densitiesa self-study book /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Jump SDEs and the study of their densitiesby Arturo Kohatsu-Higa, Atsushi Takeuchi.
其他題名:	a self-study book /
作者:	Kohatsu-Higa, Arturo.
其他作者:	Takeuchi, Atsushi.
出版者:	Singapore :Springer Singapore :2019.
面頁冊數:	xix, 355 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
標題:	Stochastic differential equations.
電子資源:	https://doi.org/10.1007/978-981-32-9741-8
ISBN:	9789813297418$q(electronic bk.)

Jump SDEs and the study of their densitiesa self-study book /
Kohatsu-Higa, Arturo.

Jump SDEs and the study of their densitiesa self-study book /[electronic resource] :by Arturo Kohatsu-Higa, Atsushi Takeuchi. - Singapore :Springer Singapore :2019. - xix, 355 p. :ill., digital ;24 cm. - Universitext,0172-5939. - Universitext..

Review of some basic concepts of probability theory -- Simple Poisson process and its corresponding SDEs -- Compound Poisson process and its associated stochastic calculus -- Construction of Levy processes and their corresponding SDEs: The finite variation case -- Construction of Levy processes and their corresponding SDEs: The infinite variation case -- Multi-dimensional Levy processes and their densities -- Flows associated with stochastic differential equations with jumps -- Overview -- Techniques to study the density -- Basic ideas for integration by parts formulas -- Sensitivity formulas -- Integration by parts: Norris method -- A non-linear example: The Boltzmann equation -- Further hints for the exercises.

The present book deals with a streamlined presentation of Levy processes and their densities. It is directed at advanced undergraduates who have already completed a basic probability course. Poisson random variables, exponential random variables, and the introduction of Poisson processes are presented first, followed by the introduction of Poisson random measures in a simple case. With these tools the reader proceeds gradually to compound Poisson processes, finite variation Levy processes and finally one-dimensional stable cases. This step-by-step progression guides the reader into the construction and study of the properties of general Levy processes with no Brownian component. In particular, in each case the corresponding Poisson random measure, the corresponding stochastic integral, and the corresponding stochastic differential equations (SDEs) are provided. The second part of the book introduces the tools of the integration by parts formula for jump processes in basic settings and first gradually provides the integration by parts formula in finite-dimensional spaces and gives a formula in infinite dimensions. These are then applied to stochastic differential equations in order to determine the existence and some properties of their densities. As examples, instances of the calculations of the Greeks in financial models with jumps are shown. The final chapter is devoted to the Boltzmann equation.

ISBN: 9789813297418$q(electronic bk.)

Standard No.: 10.1007/978-981-32-9741-8doiSubjects--Topical Terms:

185784
Stochastic differential equations.

LC Class. No.: QA274.23 / .K64 2019

Dewey Class. No.: 519.22

Jump SDEs and the study of their densitiesa self-study book /
LDR:03233nmm a2200349 a 4500 001 587224
003 DE-He213
005 20200629174144.0
006 m d
007 cr nn 008maaau
008 210326s2019 si s 0 eng d
020 $a 9789813297418$q(electronic bk.)
020 $a 9789813297401$q(paper)
024 7 $a 10.1007/978-981-32-9741-8 $2 doi
035 $a 978-981-32-9741-8
040 $a GP $c GP
041 0 $a eng
050 4 $a QA274.23 $b .K64 2019
072 7 $a PBT $2 bicssc
072 7 $a MAT029000 $2 bisacsh
072 7 $a PBT $2 thema
072 7 $a PBWL $2 thema
082 0 4 $a 519.22 $2 23
090 $a QA274.23 $b .K79 2019
100 1 $a Kohatsu-Higa, Arturo. $3 522751
245 1 0 $a Jump SDEs and the study of their densities $h [electronic resource] : $b a self-study book / $c by Arturo Kohatsu-Higa, Atsushi Takeuchi.
260 $a Singapore : $b Springer Singapore : $b Imprint: Springer, $c 2019.
300 $a xix, 355 p. : $b ill., digital ; $c 24 cm.
490 1 $a Universitext, $x 0172-5939
505 0 $a Review of some basic concepts of probability theory -- Simple Poisson process and its corresponding SDEs -- Compound Poisson process and its associated stochastic calculus -- Construction of Levy processes and their corresponding SDEs: The finite variation case -- Construction of Levy processes and their corresponding SDEs: The infinite variation case -- Multi-dimensional Levy processes and their densities -- Flows associated with stochastic differential equations with jumps -- Overview -- Techniques to study the density -- Basic ideas for integration by parts formulas -- Sensitivity formulas -- Integration by parts: Norris method -- A non-linear example: The Boltzmann equation -- Further hints for the exercises.
520 $a The present book deals with a streamlined presentation of Levy processes and their densities. It is directed at advanced undergraduates who have already completed a basic probability course. Poisson random variables, exponential random variables, and the introduction of Poisson processes are presented first, followed by the introduction of Poisson random measures in a simple case. With these tools the reader proceeds gradually to compound Poisson processes, finite variation Levy processes and finally one-dimensional stable cases. This step-by-step progression guides the reader into the construction and study of the properties of general Levy processes with no Brownian component. In particular, in each case the corresponding Poisson random measure, the corresponding stochastic integral, and the corresponding stochastic differential equations (SDEs) are provided. The second part of the book introduces the tools of the integration by parts formula for jump processes in basic settings and first gradually provides the integration by parts formula in finite-dimensional spaces and gives a formula in infinite dimensions. These are then applied to stochastic differential equations in order to determine the existence and some properties of their densities. As examples, instances of the calculations of the Greeks in financial models with jumps are shown. The final chapter is devoted to the Boltzmann equation.
650 0 $a Stochastic differential equations. $3 185784
650 0 $a Levy processes. $3 205891
650 1 4 $a Probability Theory and Stochastic Processes. $3 274061
650 2 4 $a Functional Analysis. $3 274845
650 2 4 $a Partial Differential Equations. $3 274075
700 1 $a Takeuchi, Atsushi. $3 878786
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer Nature eBook
830 0 $a Universitext. $3 558272
856 4 0 $u https://doi.org/10.1007/978-981-32-9741-8
950 $a Mathematics and Statistics (SpringerNature-11649)