Estimates on moments of the solutions to stochastic differential equations with respect to martingales in the plane

Let M = { M z , z ϵ R 2 +} be a two-parameter strong martingale, A be a two-parameter increasing process on R 2 + = [0, + ∞) × [0, + ∞). Consider the following stochastic differential equations in the plane: X z = X 0 + ∞ R z a(ξ,X) dM ξ + ∞ R z b(ξ,X) dA ξ for z ϵ R 2 +. Under some assumptions on t...

Full description

Saved in:
Bibliographic Details
Published inStochastic processes and their applications Vol. 62; no. 2; pp. 263 - 276
Main Authors Liang, Zong-xia, Zheng, Ming-li
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.07.1996
Elsevier
SeriesStochastic Processes and their Applications
Subjects
Online AccessGet full text

Cover

Loading…
Abstract Let M = { M z , z ϵ R 2 +} be a two-parameter strong martingale, A be a two-parameter increasing process on R 2 + = [0, + ∞) × [0, + ∞). Consider the following stochastic differential equations in the plane: X z = X 0 + ∞ R z a(ξ,X) dM ξ + ∞ R z b(ξ,X) dA ξ for z ϵ R 2 +. Under some assumptions on the coefficients a, b and the integrators M, A, we prove the existence and uniqueness of solutions for the equations, and obtain some estimates on moments of solution.
AbstractList Let M = {Mz, z [epsilon] R2+} be a two-parameter strong martingale, A be a two-parameter increasing process on R2+ = [0, + [infinity]) x [0, + [infinity]). Consider the following stochastic differential equations in the plane: for z [epsilon] R2+. Under some assumptions on the coefficients a, b and the integrators M, A, we prove the existence and uniqueness of solutions for the equations, and obtain some estimates on moments of solution.
Let M = { M z , z ϵ R 2 +} be a two-parameter strong martingale, A be a two-parameter increasing process on R 2 + = [0, + ∞) × [0, + ∞). Consider the following stochastic differential equations in the plane: X z = X 0 + ∞ R z a(ξ,X) dM ξ + ∞ R z b(ξ,X) dA ξ for z ϵ R 2 +. Under some assumptions on the coefficients a, b and the integrators M, A, we prove the existence and uniqueness of solutions for the equations, and obtain some estimates on moments of solution.
Author Liang, Zong-xia
Zheng, Ming-li
Author_xml – sequence: 1
  givenname: Zong-xia
  surname: Liang
  fullname: Liang, Zong-xia
– sequence: 2
  givenname: Ming-li
  surname: Zheng
  fullname: Zheng, Ming-li
BackLink http://econpapers.repec.org/article/eeespapps/v_3a62_3ay_3a1996_3ai_3a2_3ap_3a263-276.htm$$DView record in RePEc
BookMark eNp9UE1PHSEUJY1N-rT-Axcs62IqMAzz2JgYo62NiZs26Y7w4NJHMwMjoMZ_3zt9jcsu7gc355xwzjE5SjkBIWecfeaMqwvWM9lJLvUnrc4ZY8PY6Xdkw7ej7gTTP4_I5g3ygRzX-htBXAi-IfWmtjjbBpXmROc8Q2q4Btr2QGuenlrMqdKWaW3Z7S2iHfUxBCiIjHai8PhkD6CX2Pa0QF3AtZUx29Ji-mUnFI_pr-Iy2QQfyftgpwqn_-YJ-XF78_36a3f_8OXu-uq-c_3IW-dHraxmw-C2Xim983x0A3fOSWk940PvHOMexFaADmqnVBBB-AByJ-XAhO1PiDzoupJrLRDMUtBreTWcmTU4s6Zi1lSMxscanNFI-3agFUAnbxwAdGaXpZpn01slsL1icY3U3kas9bSsU_VGjMrs24xilwcxQKPPEYqpLkJy4GPBmIzP8f-_-QO6OZLu
CitedBy_id crossref_primary_10_1016_j_jmaa_2019_123773
crossref_primary_10_1016_S0304_4149_01_00088_6
crossref_primary_10_1007_s11118_007_9038_4
crossref_primary_10_1016_S0304_4149_99_00040_X
crossref_primary_10_1515_156939703771891851
crossref_primary_10_1080_07362990008809693
crossref_primary_10_1007_BF02580407
crossref_primary_10_1080_07362994_2014_970277
crossref_primary_10_1080_07362994_2022_2144890
crossref_primary_10_1080_07362994_2015_1089516
Cites_doi 10.1016/0304-4149(78)90031-5
10.1214/aop/1176996028
10.2140/pjm.1981.97.217
10.1007/BF02392100
10.1214/aop/1176995718
10.1214/aop/1176993510
ContentType Journal Article
Copyright 1996
Copyright_xml – notice: 1996
DBID 6I.
AAFTH
DKI
X2L
AAYXX
CITATION
DOI 10.1016/0304-4149(96)00057-9
DatabaseName ScienceDirect Open Access Titles
Elsevier:ScienceDirect:Open Access
RePEc IDEAS
RePEc
CrossRef
DatabaseTitle CrossRef
DatabaseTitleList

Database_xml – sequence: 1
  dbid: DKI
  name: RePEc IDEAS
  url: http://ideas.repec.org/
  sourceTypes: Index Database
DeliveryMethod fulltext_linktorsrc
Discipline Mathematics
EISSN 1879-209X
EndPage 276
ExternalDocumentID 10_1016_0304_4149_96_00057_9
eeespapps_v_3a62_3ay_3a1996_3ai_3a2_3ap_3a263_276_htm
0304414996000579
GroupedDBID --K
--M
-~X
.~1
0R~
123
1B1
1OL
1RT
1~.
1~5
29Q
3R3
4.4
457
4G.
5VS
63O
6I.
7-5
71M
8P~
9JN
9JO
AAAKF
AABNK
AACTN
AAEDT
AAEDW
AAFTH
AAIAV
AAIKJ
AAKOC
AALRI
AAOAW
AAQFI
AAQXK
AARIN
AAXUO
ABAOU
ABEFU
ABFNM
ABFRF
ABJNI
ABMAC
ABUCO
ABVKL
ABXDB
ABYKQ
ACAZW
ACDAQ
ACGFO
ACGFS
ACRLP
ADBBV
ADEZE
ADIYS
ADMUD
AEBSH
AEFWE
AEKER
AENEX
AEXQZ
AFKWA
AFTJW
AGHFR
AGUBO
AGYEJ
AHHHB
AIEXJ
AIGVJ
AIKHN
AITUG
AJBFU
AJOXV
ALMA_UNASSIGNED_HOLDINGS
AMFUW
AMRAJ
APLSM
ARUGR
ASPBG
AVWKF
AXJTR
AZFZN
BKOJK
BLXMC
CS3
DU5
E3Z
EBS
EFJIC
EFLBG
EJD
EO8
EO9
EP2
EP3
FDB
FEDTE
FGOYB
FIRID
FNPLU
FYGXN
G-2
G-Q
GBLVA
HAMUX
HVGLF
HX~
HZ~
IHE
IXB
J1W
KOM
LY1
M26
M41
MHUIS
MO0
N9A
NCXOZ
O-L
O9-
OAUVE
OHT
OK1
OZT
P-8
P-9
P2P
PC.
Q38
R2-
RIG
RNS
ROL
RPZ
SDF
SDG
SES
SEW
SPC
SPCBC
SSB
SSD
SSW
SSZ
T5K
TN5
UNMZH
WH7
WUQ
XFK
XPP
ZMT
~G-
0R
1
8P
ADACO
ADALY
DKI
G-
HX
HZ
IPNFZ
K
M
STF
X
X2L
0SF
AAXKI
AAYXX
ADVLN
AFJKZ
AKRWK
CITATION
ID FETCH-LOGICAL-c371t-d796a9055c8d669bd17c51ccc44ad0153cc01de282e9f6b66f2f2dfe4b44502a3
IEDL.DBID .~1
ISSN 0304-4149
IngestDate Thu Sep 26 18:04:58 EDT 2024
Wed Aug 18 03:10:07 EDT 2021
Fri Feb 23 02:21:04 EST 2024
IsDoiOpenAccess true
IsOpenAccess true
IsPeerReviewed true
IsScholarly true
Issue 2
Keywords 60H20
Two-parameter Ito's formula
Two-parameter stochastic differential equation
60H15
Gronwall's inequality
Two-parameter strong martingale
Language English
License http://www.elsevier.com/open-access/userlicense/1.0
LinkModel DirectLink
MergedId FETCHMERGED-LOGICAL-c371t-d796a9055c8d669bd17c51ccc44ad0153cc01de282e9f6b66f2f2dfe4b44502a3
OpenAccessLink https://www.sciencedirect.com/science/article/pii/0304414996000579
PageCount 14
ParticipantIDs crossref_primary_10_1016_0304_4149_96_00057_9
repec_primary_eeespapps_v_3a62_3ay_3a1996_3ai_3a2_3ap_3a263_276_htm
elsevier_sciencedirect_doi_10_1016_0304_4149_96_00057_9
PublicationCentury 1900
PublicationDate 1996-07-01
PublicationDateYYYYMMDD 1996-07-01
PublicationDate_xml – month: 07
  year: 1996
  text: 1996-07-01
  day: 01
PublicationDecade 1990
PublicationSeriesTitle Stochastic Processes and their Applications
PublicationTitle Stochastic processes and their applications
PublicationYear 1996
Publisher Elsevier B.V
Elsevier
Publisher_xml – name: Elsevier B.V
– name: Elsevier
References Reid (BIB6) 1983; 11
Chevalier (BIB2) 1982; 106
Nie (BIB4) 1987; 2
Wong, Zakai (BIB8) 1977; 5
Merzbach, Zakai (BIB5) 1980; 53
Wong, Zakai (BIB9) 1978; 6
Yeh (BIB10) 1981; 97
Ikeda, Watanabe (BIB3) 1981
Cairoli, Walsh (BIB1) 1975; 134
Wong, Zakai (BIB7) 1976; 4
Yeh (10.1016/0304-4149(96)00057-9_BIB10) 1981; 97
Wong (10.1016/0304-4149(96)00057-9_BIB7) 1976; 4
Merzbach (10.1016/0304-4149(96)00057-9_BIB5) 1980; 53
Wong (10.1016/0304-4149(96)00057-9_BIB8) 1977; 5
Chevalier (10.1016/0304-4149(96)00057-9_BIB2) 1982; 106
Reid (10.1016/0304-4149(96)00057-9_BIB6) 1983; 11
Ikeda (10.1016/0304-4149(96)00057-9_BIB3) 1981
Cairoli (10.1016/0304-4149(96)00057-9_BIB1) 1975; 134
Nie (10.1016/0304-4149(96)00057-9_BIB4) 1987; 2
Wong (10.1016/0304-4149(96)00057-9_BIB9) 1978; 6
References_xml – volume: 134
  start-page: 111
  year: 1975
  end-page: 183
  ident: BIB1
  article-title: Stochastic integral in the plane
  publication-title: Acta Math.
  contributor:
    fullname: Walsh
– year: 1981
  ident: BIB3
  article-title: Stochastic Differential Equations and Diffusion Processes
  contributor:
    fullname: Watanabe
– volume: 2
  start-page: 222
  year: 1987
  end-page: 227
  ident: BIB4
  article-title: The existence and uniqueness of solutions for S.D.E. in the plane
  publication-title: Appl. Math. J. Chinese Univ.
  contributor:
    fullname: Nie
– volume: 4
  start-page: 570
  year: 1976
  end-page: 586
  ident: BIB7
  article-title: Weak martingales and stochastic integrals in the plane
  publication-title: Ann. Probab.
  contributor:
    fullname: Zakai
– volume: 11
  start-page: 656
  year: 1983
  end-page: 668
  ident: BIB6
  article-title: Estimate on moments of the solutions to S.D.E. in the plane
  publication-title: Ann. Probab.
  contributor:
    fullname: Reid
– volume: 106
  start-page: 19
  year: 1982
  end-page: 62
  ident: BIB2
  article-title: Martingales continues a deux parametres
  publication-title: Bull.Sc.Math.
  contributor:
    fullname: Chevalier
– volume: 97
  start-page: 217
  year: 1981
  end-page: 247
  ident: BIB10
  article-title: Existence of strong solutions for stochastic differential equations in the plane
  publication-title: Pacific. J. Math.
  contributor:
    fullname: Yeh
– volume: 5
  start-page: 770
  year: 1977
  end-page: 778
  ident: BIB8
  article-title: An extension of stochastic integrals in the plane
  publication-title: Ann. Probab.
  contributor:
    fullname: Zakai
– volume: 6
  start-page: 339
  year: 1978
  end-page: 349
  ident: BIB9
  article-title: Differentiation formulas for stochastic integral in the plane
  publication-title: Stochastic Process. Appl.
  contributor:
    fullname: Zakai
– volume: 53
  start-page: 263
  year: 1980
  end-page: 269
  ident: BIB5
  publication-title: Predictable and dual predictable projections of two-parameter stochastic processes
  contributor:
    fullname: Zakai
– volume: 6
  start-page: 339
  year: 1978
  ident: 10.1016/0304-4149(96)00057-9_BIB9
  article-title: Differentiation formulas for stochastic integral in the plane
  publication-title: Stochastic Process. Appl.
  doi: 10.1016/0304-4149(78)90031-5
  contributor:
    fullname: Wong
– volume: 4
  start-page: 570
  year: 1976
  ident: 10.1016/0304-4149(96)00057-9_BIB7
  article-title: Weak martingales and stochastic integrals in the plane
  publication-title: Ann. Probab.
  doi: 10.1214/aop/1176996028
  contributor:
    fullname: Wong
– volume: 97
  start-page: 217
  year: 1981
  ident: 10.1016/0304-4149(96)00057-9_BIB10
  article-title: Existence of strong solutions for stochastic differential equations in the plane
  publication-title: Pacific. J. Math.
  doi: 10.2140/pjm.1981.97.217
  contributor:
    fullname: Yeh
– volume: 2
  start-page: 222
  year: 1987
  ident: 10.1016/0304-4149(96)00057-9_BIB4
  article-title: The existence and uniqueness of solutions for S.D.E. in the plane
  publication-title: Appl. Math. J. Chinese Univ.
  contributor:
    fullname: Nie
– volume: 134
  start-page: 111
  year: 1975
  ident: 10.1016/0304-4149(96)00057-9_BIB1
  article-title: Stochastic integral in the plane
  publication-title: Acta Math.
  doi: 10.1007/BF02392100
  contributor:
    fullname: Cairoli
– volume: 5
  start-page: 770
  year: 1977
  ident: 10.1016/0304-4149(96)00057-9_BIB8
  article-title: An extension of stochastic integrals in the plane
  publication-title: Ann. Probab.
  doi: 10.1214/aop/1176995718
  contributor:
    fullname: Wong
– volume: 11
  start-page: 656
  year: 1983
  ident: 10.1016/0304-4149(96)00057-9_BIB6
  article-title: Estimate on moments of the solutions to S.D.E. in the plane
  publication-title: Ann. Probab.
  doi: 10.1214/aop/1176993510
  contributor:
    fullname: Reid
– year: 1981
  ident: 10.1016/0304-4149(96)00057-9_BIB3
  contributor:
    fullname: Ikeda
– volume: 53
  start-page: 263
  year: 1980
  ident: 10.1016/0304-4149(96)00057-9_BIB5
  publication-title: Predictable and dual predictable projections of two-parameter stochastic processes
  contributor:
    fullname: Merzbach
– volume: 106
  start-page: 19
  year: 1982
  ident: 10.1016/0304-4149(96)00057-9_BIB2
  article-title: Martingales continues a deux parametres
  publication-title: Bull.Sc.Math.
  contributor:
    fullname: Chevalier
SSID ssj0001221
Score 1.5395364
Snippet Let M = { M z , z ϵ R 2 +} be a two-parameter strong martingale, A be a two-parameter increasing process on R 2 + = [0, + ∞) × [0, + ∞). Consider the following...
Let M = {Mz, z [epsilon] R2+} be a two-parameter strong martingale, A be a two-parameter increasing process on R2+ = [0, + [infinity]) x [0, + [infinity])....
SourceID crossref
repec
elsevier
SourceType Aggregation Database
Index Database
Publisher
StartPage 263
SubjectTerms 60H15
60H15 60H20 Two-parameter stochastic differential equation Two-parameter strong martingale Two-parameter Ito's formula Gronwall's inequality
60H20
Gronwall's inequality
Two-parameter Ito's formula
Two-parameter stochastic differential equation
Two-parameter strong martingale
Title Estimates on moments of the solutions to stochastic differential equations with respect to martingales in the plane
URI https://dx.doi.org/10.1016/0304-4149(96)00057-9
http://econpapers.repec.org/article/eeespapps/v_3a62_3ay_3a1996_3ai_3a2_3ap_3a263-276.htm
Volume 62
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1Lb9QwELZQe4ED4ilaoPKhBziYTeJH1sd2abXLthVCFO3NchxbXambpE1A4sJvZ8ZJlnJAlTjEIzl-aewZj5NvxoQcwqLhQWnJbKodEyErmdViyjhXVmSF1blEB-fzCzW_FJ9WcnXHFwZhlYPu73V61NZDzmTg5qRZryf4T0-AfQ8mePSoRAd2GWXzw68_KI80i65XWJhh6dF7LlWTbd47rd7HNpj-1-60e-sb7-7sPKdPyOPBZKRH_aiekge-ekYenW_jrbbPSXsCkrpBs5HWFd3U0W-N1oFCGbpdXbSrKdh67spicGY63o0CMn5N_U0f87ul-GWWwiEcXTCxxiYGGsCNpKXrKrbYIEL2Bbk8Pfk6m7PhOgXmeJ52rMy1sjqR0k1LpXRRprmTqXNOCFuCVcCdS9LSwxnM66AKpUIGUxe8KISQSWb5S7JT1ZV_Raj2skT5lVOwaELioIr3ydSrwBUPWbJH2MhG0_RRM8wIJ0O2G2S70YioA7YbvUfykdfmr9k3oNjvqTmLU7PtBgbS4hVprflhuFUZJD_hQbA1kDU8mNUgVdxkuTJX3Wb_v_t_TR72OG4E8L4hO93td_8WzJSuOIgL8YDsHh1_W54hnX05-4x0sZxfwNuPywWki9Xxb6MB6Ns
link.rule.ids 315,783,787,3515,4018,4511,24130,27583,27938,27939,45599,45677,45693,45888
linkProvider Elsevier
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1LT9wwELYKHAqHqqWgbp8-cICD2SR-ZH2sEGjbspxA4mY5ji1WYpOUBCQu_e2dcZItPaBKPTiRLL80Ho8_J9-MCTkApeFBaclsqh0TISuZ1WLGOFdWZIXVuUQH58WFml-J79fy-okvDNIqB9vf2_RorYec6SDNabNcTvGfngB8DxA8elRukC2B4bNAp49__aF5pFn0vcLSDIuP7nOpmq7zDrU6io0w_dz2tHXnG--ebD1nr8mrATPSr_2w3pAXvtolO4t1wNX2LWlPYamuEDfSuqKrOjqu0TpQKEPX6kW7mgLYczcWozPT8XIUWOS31P_sg363FD_NUjiFow8m1ljFSAO4k7R0WcUWG6TI7pGrs9PLkzkb7lNgjudpx8pcK6sTKd2sVEoXZZo7mTrnhLAlwALuXJKWHg5hXgdVKBUymLvgRSGETDLL98lmVVf-HaHayxIXsJwBpAmJgyreJzOvAlc8ZMmEsFGMpunDZpiRT4ZiNyh2o5FSB2I3ekLyUdbmr-k3YNn_UfMkTs26GxhIi3ektebBcKsyeDxCQrY1vJaQMKvBt-Imy5W56Vbv_7v_L-Tl_HJxbs6_Xfz4QLZ7UjeyeT-Sze7u3n8CzNIVn6NS_gbvLeVY
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Estimates+on+moments+of+the+solutions+to+stochastic+differential+equations+with+respect+to+martingales+in+the+plane&rft.jtitle=Stochastic+processes+and+their+applications&rft.au=Liang%2C+Zong-xia&rft.au=Zheng%2C+Ming-li&rft.date=1996-07-01&rft.pub=Elsevier+B.V&rft.issn=0304-4149&rft.eissn=1879-209X&rft.volume=62&rft.issue=2&rft.spage=263&rft.epage=276&rft_id=info:doi/10.1016%2F0304-4149%2896%2900057-9&rft.externalDocID=0304414996000579
thumbnail_l http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0304-4149&client=summon
thumbnail_m http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0304-4149&client=summon
thumbnail_s http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0304-4149&client=summon