國立虎尾科技大學 |

Stochastic Flows and Jump-Diffusions

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Stochastic Flows and Jump-Diffusions/ by Hiroshi Kunita.
作者:	Kunita, Hiroshi.
面頁冊數:	XVII, 352 p. 145 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	Probabilities. -
電子資源:	https://doi.org/10.1007/978-981-13-3801-4
ISBN:	9789811338014

Stochastic Flows and Jump-Diffusions
Kunita, Hiroshi.

Stochastic Flows and Jump-Diffusions[electronic resource] /by Hiroshi Kunita. - 1st ed. 2019. - XVII, 352 p. 145 illus.online resource. - Probability Theory and Stochastic Modelling,922199-3130 ;. - Probability Theory and Stochastic Modelling,76.

Preface -- Introduction -- 1.Probability distributions and stochastic processes -- 2.Stochastic integrals based on Wiener processes and Poisson random measures -- 3.Stochastic differential equations and stochastic flows -- 4.Diffusions, jump-diffusions and heat equations -- 5.Malliavin calculus for Wiener processes and Poisson random measures -- 6.Smooth densities and heat kernels -- 7.Jump-diffusions on manifolds and smooth densities -- Bibliography -- Index.

This monograph presents a modern treatment of (1) stochastic differential equations and (2) diffusion and jump-diffusion processes. The simultaneous treatment of diffusion processes and jump processes in this book is unique: Each chapter starts from continuous processes and then proceeds to processes with jumps. In the first part of the book, it is shown that solutions of stochastic differential equations define stochastic flows of diffeomorphisms. Then, the relation between stochastic flows and heat equations is discussed. The latter part investigates fundamental solutions of these heat equations (heat kernels) through the study of the Malliavin calculus. The author obtains smooth densities for transition functions of various types of diffusions and jump-diffusions and shows that these density functions are fundamental solutions for various types of heat equations and backward heat equations. Thus, in this book fundamental solutions for heat equations and backward heat equations are constructed independently of the theory of partial differential equations. Researchers and graduate student in probability theory will find this book very useful.

ISBN: 9789811338014

Standard No.: 10.1007/978-981-13-3801-4doiSubjects--Topical Terms:

527847
Probabilities.

LC Class. No.: QA273.A1-274.9

Dewey Class. No.: 519.2

Stochastic Flows and Jump-Diffusions
LDR:03031nam a22004215i 4500 001 1007402
003 DE-He213
005 20200705142339.0
007 cr nn 008mamaa
008 210106s2019 si | s |||| 0|eng d
020 $a 9789811338014 $9 978-981-13-3801-4
024 7 $a 10.1007/978-981-13-3801-4 $2 doi
035 $a 978-981-13-3801-4
050 4 $a QA273.A1-274.9
050 4 $a QA274-274.9
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 519.2 $2 23
100 1 $a Kunita, Hiroshi. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1301162
245 1 0 $a Stochastic Flows and Jump-Diffusions $h [electronic resource] / $c by Hiroshi Kunita.
250 $a 1st ed. 2019.
264 1 $a Singapore : $b Springer Singapore : $b Imprint: Springer, $c 2019.
300 $a XVII, 352 p. 145 illus. $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 Probability Theory and Stochastic Modelling, $x 2199-3130 ; $v 92
505 0 $a Preface -- Introduction -- 1.Probability distributions and stochastic processes -- 2.Stochastic integrals based on Wiener processes and Poisson random measures -- 3.Stochastic differential equations and stochastic flows -- 4.Diffusions, jump-diffusions and heat equations -- 5.Malliavin calculus for Wiener processes and Poisson random measures -- 6.Smooth densities and heat kernels -- 7.Jump-diffusions on manifolds and smooth densities -- Bibliography -- Index.
520 $a This monograph presents a modern treatment of (1) stochastic differential equations and (2) diffusion and jump-diffusion processes. The simultaneous treatment of diffusion processes and jump processes in this book is unique: Each chapter starts from continuous processes and then proceeds to processes with jumps. In the first part of the book, it is shown that solutions of stochastic differential equations define stochastic flows of diffeomorphisms. Then, the relation between stochastic flows and heat equations is discussed. The latter part investigates fundamental solutions of these heat equations (heat kernels) through the study of the Malliavin calculus. The author obtains smooth densities for transition functions of various types of diffusions and jump-diffusions and shows that these density functions are fundamental solutions for various types of heat equations and backward heat equations. Thus, in this book fundamental solutions for heat equations and backward heat equations are constructed independently of the theory of partial differential equations. Researchers and graduate student in probability theory will find this book very useful.
650 0 $a Probabilities. $3 527847
650 0 $a Economics, Mathematical . $3 1253712
650 0 $a Partial differential equations. $3 1102982
650 1 4 $a Probability Theory and Stochastic Processes. $3 593945
650 2 4 $a Quantitative Finance. $3 669372
650 2 4 $a Partial Differential Equations. $3 671119
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9789811338007
776 0 8 $i Printed edition: $z 9789811338021
830 0 $a Probability Theory and Stochastic Modelling, $x 2199-3130 ; $v 76 $3 1254049
856 4 0 $u https://doi.org/10.1007/978-981-13-3801-4
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)