語系:
繁體中文
English
說明(常見問題)
登入
回首頁
切換:
標籤
|
MARC模式
|
ISBD
Analytic Theory of Itô-Stochastic Differential Equations with Non-smooth Coefficients
紀錄類型:
書目-語言資料,印刷品 : Monograph/item
正題名/作者:
Analytic Theory of Itô-Stochastic Differential Equations with Non-smooth Coefficients/ by Haesung Lee, Wilhelm Stannat, Gerald Trutnau.
作者:
Lee, Haesung.
其他作者:
Trutnau, Gerald.
面頁冊數:
XV, 126 p. 1 illus.online resource. :
Contained By:
Springer Nature eBook
標題:
Functional Analysis. -
電子資源:
https://doi.org/10.1007/978-981-19-3831-3
ISBN:
9789811938313
Analytic Theory of Itô-Stochastic Differential Equations with Non-smooth Coefficients
Lee, Haesung.
Analytic Theory of Itô-Stochastic Differential Equations with Non-smooth Coefficients
[electronic resource] /by Haesung Lee, Wilhelm Stannat, Gerald Trutnau. - 1st ed. 2022. - XV, 126 p. 1 illus.online resource. - SpringerBriefs in Probability and Mathematical Statistics,2365-4341. - SpringerBriefs in Probability and Mathematical Statistics,.
Chapter 1. Introduction -- Chapter 2. The abstract Cauchy problem in Lr-spaces with weights -- Chapter 3.Stochastic differential equations -- Chapter 4. Conclusion and outlook.
This book provides analytic tools to describe local and global behavior of solutions to Itô-stochastic differential equations with non-degenerate Sobolev diffusion coefficients and locally integrable drift. Regularity theory of partial differential equations is applied to construct such solutions and to obtain strong Feller properties, irreducibility, Krylov-type estimates, moment inequalities, various types of non-explosion criteria, and long time behavior, e.g., transience, recurrence, and convergence to stationarity. The approach is based on the realization of the transition semigroup associated with the solution of a stochastic differential equation as a strongly continuous semigroup in the Lp-space with respect to a weight that plays the role of a sub-stationary or stationary density. This way we obtain in particular a rigorous functional analytic description of the generator of the solution of a stochastic differential equation and its full domain. The existence of such a weight is shown under broad assumptions on the coefficients. A remarkable fact is that although the weight may not be unique, many important results are independent of it. Given such a weight and semigroup, one can construct and further analyze in detail a weak solution to the stochastic differential equation combining variational techniques, regularity theory for partial differential equations, potential, and generalized Dirichlet form theory. Under classical-like or various other criteria for non-explosion we obtain as one of our main applications the existence of a pathwise unique and strong solution with an infinite lifetime. These results substantially supplement the classical case of locally Lipschitz or monotone coefficients. We further treat other types of uniqueness and non-uniqueness questions, such as uniqueness and non-uniqueness of the mentioned weights and uniqueness in law, in a certain sense, of the solution.
ISBN: 9789811938313
Standard No.: 10.1007/978-981-19-3831-3doiSubjects--Topical Terms:
672166
Functional Analysis.
LC Class. No.: QA273.A1-274.9
Dewey Class. No.: 519.2
Analytic Theory of Itô-Stochastic Differential Equations with Non-smooth Coefficients
LDR
:03606nam a22004215i 4500
001
1082494
003
DE-He213
005
20220827090711.0
007
cr nn 008mamaa
008
221228s2022 si | s |||| 0|eng d
020
$a
9789811938313
$9
978-981-19-3831-3
024
7
$a
10.1007/978-981-19-3831-3
$2
doi
035
$a
978-981-19-3831-3
050
4
$a
QA273.A1-274.9
072
7
$a
PBT
$2
bicssc
072
7
$a
PBWL
$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
Lee, Haesung.
$e
author.
$4
aut
$4
http://id.loc.gov/vocabulary/relators/aut
$3
1388183
245
1 0
$a
Analytic Theory of Itô-Stochastic Differential Equations with Non-smooth Coefficients
$h
[electronic resource] /
$c
by Haesung Lee, Wilhelm Stannat, Gerald Trutnau.
250
$a
1st ed. 2022.
264
1
$a
Singapore :
$b
Springer Nature Singapore :
$b
Imprint: Springer,
$c
2022.
300
$a
XV, 126 p. 1 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
SpringerBriefs in Probability and Mathematical Statistics,
$x
2365-4341
505
0
$a
Chapter 1. Introduction -- Chapter 2. The abstract Cauchy problem in Lr-spaces with weights -- Chapter 3.Stochastic differential equations -- Chapter 4. Conclusion and outlook.
520
$a
This book provides analytic tools to describe local and global behavior of solutions to Itô-stochastic differential equations with non-degenerate Sobolev diffusion coefficients and locally integrable drift. Regularity theory of partial differential equations is applied to construct such solutions and to obtain strong Feller properties, irreducibility, Krylov-type estimates, moment inequalities, various types of non-explosion criteria, and long time behavior, e.g., transience, recurrence, and convergence to stationarity. The approach is based on the realization of the transition semigroup associated with the solution of a stochastic differential equation as a strongly continuous semigroup in the Lp-space with respect to a weight that plays the role of a sub-stationary or stationary density. This way we obtain in particular a rigorous functional analytic description of the generator of the solution of a stochastic differential equation and its full domain. The existence of such a weight is shown under broad assumptions on the coefficients. A remarkable fact is that although the weight may not be unique, many important results are independent of it. Given such a weight and semigroup, one can construct and further analyze in detail a weak solution to the stochastic differential equation combining variational techniques, regularity theory for partial differential equations, potential, and generalized Dirichlet form theory. Under classical-like or various other criteria for non-explosion we obtain as one of our main applications the existence of a pathwise unique and strong solution with an infinite lifetime. These results substantially supplement the classical case of locally Lipschitz or monotone coefficients. We further treat other types of uniqueness and non-uniqueness questions, such as uniqueness and non-uniqueness of the mentioned weights and uniqueness in law, in a certain sense, of the solution.
650
2 4
$a
Functional Analysis.
$3
672166
650
2 4
$a
Real Functions.
$3
672094
650
2 4
$a
Analysis.
$3
669490
650
1 4
$a
Probability Theory.
$3
1366244
650
0
$a
Functional analysis.
$3
527706
650
0
$a
Functions of real variables.
$3
792248
650
0
$a
Mathematical analysis.
$3
527926
650
0
$a
Probabilities.
$3
527847
700
1
$a
Trutnau, Gerald.
$e
editor.
$4
aut
$4
http://id.loc.gov/vocabulary/relators/aut
$3
1280600
700
1
$a
Stannat, Wilhelm.
$e
editor.
$4
aut
$4
http://id.loc.gov/vocabulary/relators/aut
$3
1280599
710
2
$a
SpringerLink (Online service)
$3
593884
773
0
$t
Springer Nature eBook
776
0 8
$i
Printed edition:
$z
9789811938306
776
0 8
$i
Printed edition:
$z
9789811938320
830
0
$a
SpringerBriefs in Probability and Mathematical Statistics,
$x
2365-4333
$3
1264581
856
4 0
$u
https://doi.org/10.1007/978-981-19-3831-3
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)
筆 0 讀者評論
多媒體
評論
新增評論
分享你的心得
Export
取書館別
處理中
...
變更密碼[密碼必須為2種組合(英文和數字)及長度為10碼以上]
登入