Second-order differential equations with random perturbations and small parameters
We consider boundary-value problems for differential equations of second order containing a Brownian motion (random perturbation) and a small parameter and prove a special existence and uniqueness theorem for random solutions. We study the asymptotic behaviour of these solutions as the small paramet...
Saved in:
| Published in | Proceedings of the Royal Society of Edinburgh. Section A. Mathematics Vol. 147; no. 4; pp. 763 - 779 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Edinburgh, UK
Royal Society of Edinburgh Scotland Foundation
01.08.2017
Cambridge University Press Royal Society of Edinburgh |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0308-2105 1473-7124 |
| DOI | 10.1017/S0308210516000354 |
Cover
Loading…
| Abstract | We consider boundary-value problems for differential equations of second order containing a Brownian motion (random perturbation) and a small parameter and prove a special existence and uniqueness theorem for random solutions. We study the asymptotic behaviour of these solutions as the small parameter goes to zero and show the stochastic averaging theorem for such equations. We find the explicit limits for the solutions as the small parameter goes to zero. |
|---|---|
| AbstractList | We consider boundary-value problems for differential equations of second order containing a Brownian motion (random perturbation) and a small parameter and prove a special existence and uniqueness theorem for random solutions. We study the asymptotic behaviour of these solutions as the small parameter goes to zero and show the stochastic averaging theorem for such equations. We find the explicit limits for the solutions as the small parameter goes to zero. |
| Author | Pergamenchtchikov, S. Quincampoix, M. Kamenskii, M. |
| Author_xml | – sequence: 1 givenname: M. surname: Kamenskii fullname: Kamenskii, M. email: mikhailkamenski@mail.ru organization: Voronezh State University, Universitetskay pl. 1, 394063 Voronezh, Russia (mikhailkamenski@mail.ru) – sequence: 2 givenname: S. surname: Pergamenchtchikov fullname: Pergamenchtchikov, S. email: serge.pergamenchtchikov@univ-rouen.fr organization: Laboratoire de Mathématiques Raphael Salem, CNRS–UMR 6085, Université de Rouen, Avenue de l'Université, BP.12, Technopôle du Madrillet F76801, Saint-Étienne-du-Rouvray, France (serge.pergamenchtchikov@univ-rouen.fr) and International Laboratory of Statistics of Stochastic Processes and Quantitative Finance, National Research Tomsk State University, Russia – sequence: 3 givenname: M. surname: Quincampoix fullname: Quincampoix, M. email: marc.quincampoix@univ-brest.fr organization: Laboratoire de Mathématiques de Bretagne Atlantique, CNRS–UMR 6205, Université de Bretagne Occidentale, 6 avenue Victor Le Gorgeu, CS 93837, 29238 Brest Cedex 3, France (marc.quincampoix@univ-brest.fr) |
| BackLink | https://hal.science/hal-02334875$$DView record in HAL |
| BookMark | eNp1kFFLwzAUhYMouE1_gG8Fn3yoJk2bZI9jqBMGgtPnkDQ3LqNtuqRV_Pe2bIggPl045zuHe-8UnTa-AYSuCL4lmPC7DaZYZAQXhGGMaZGfoAnJOU05yfJTNBntdPTP0TTG3cAwUfAJetlA6RuT-mAgJMZZCwGazqkqgX2vOuebmHy6bpsE1RhfJy2Erg_66AxaEmtVVUmrgqqhgxAv0JlVVYTL45yht4f71-UqXT8_Pi0X67SkOetSLTgoDqUocq2MZhQMplQbkXPGiCkzLMhccGEBrAZNrdZ2uEyXyipqxJzO0M2hd6sq2QZXq_AlvXJytVjLUcMZpbngxQcZ2OsD2wa_7yF2cuf70AzrSTLPCsw4o9lAkQNVBh9jAPtTS7Ac3yz_vHnI0GNG1To48w6_qv9NfQOA84Gg |
| ContentType | Journal Article |
| Copyright | Copyright © Royal Society of Edinburgh 2017 Distributed under a Creative Commons Attribution 4.0 International License |
| Copyright_xml | – notice: Copyright © Royal Society of Edinburgh 2017 – notice: Distributed under a Creative Commons Attribution 4.0 International License |
| DBID | AAYXX CITATION 3V. 7QF 7QQ 7SC 7SE 7SP 7SR 7TA 7TB 7U5 7XB 88I 8AL 8BQ 8FD 8FE 8FG 8FK ABJCF ABUWG AFKRA ARAPS AZQEC BENPR BGLVJ CCPQU DWQXO F28 FR3 GNUQQ H8D H8G HCIFZ JG9 JQ2 K7- KR7 L6V L7M L~C L~D M0N M2P M7S P5Z P62 PHGZM PHGZT PKEHL PQEST PQGLB PQQKQ PQUKI PRINS PTHSS Q9U 1XC VOOES |
| DOI | 10.1017/S0308210516000354 |
| DatabaseName | CrossRef ProQuest Central (Corporate) Aluminium Industry Abstracts Ceramic Abstracts Computer and Information Systems Abstracts Corrosion Abstracts Electronics & Communications Abstracts Engineered Materials Abstracts Materials Business File Mechanical & Transportation Engineering Abstracts Solid State and Superconductivity Abstracts ProQuest Central (purchase pre-March 2016) Science Database (Alumni Edition) Computing Database (Alumni Edition) METADEX Technology Research Database ProQuest SciTech Collection ProQuest Technology Collection ProQuest Central (Alumni) (purchase pre-March 2016) ProQuest SciTech Premium Collection Technology Collection Materials Science & Engineering Database ProQuest Central (Alumni) ProQuest Central UK/Ireland Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Central ProQuest Technology Collection ProQuest One ProQuest Central ANTE: Abstracts in New Technology & Engineering Engineering Research Database ProQuest Central Student Aerospace Database Copper Technical Reference Library SciTech Premium Collection Materials Research Database ProQuest Computer Science Collection Computer Science Database Civil Engineering Abstracts ProQuest Engineering Collection Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional Computing Database Science Database Engineering Database Advanced Technologies & Aerospace Database ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Premium ProQuest One Academic (New) ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic ProQuest One Academic UKI Edition ProQuest Central China Engineering Collection ProQuest Central Basic Hyper Article en Ligne (HAL) Hyper Article en Ligne (HAL) (Open Access) |
| DatabaseTitle | CrossRef Materials Research Database Computer Science Database ProQuest Central Student ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Computer Science Collection Computer and Information Systems Abstracts SciTech Premium Collection ProQuest Central China Materials Business File ProQuest One Applied & Life Sciences Engineered Materials Abstracts ProQuest Central (New) Engineering Collection ANTE: Abstracts in New Technology & Engineering Advanced Technologies & Aerospace Collection Engineering Database Aluminium Industry Abstracts ProQuest Science Journals (Alumni Edition) ProQuest One Academic Eastern Edition Electronics & Communications Abstracts ProQuest Technology Collection Ceramic Abstracts ProQuest One Academic UKI Edition Solid State and Superconductivity Abstracts Engineering Research Database ProQuest One Academic ProQuest One Academic (New) Technology Collection Technology Research Database Computer and Information Systems Abstracts – Academic ProQuest One Academic Middle East (New) Mechanical & Transportation Engineering Abstracts ProQuest Central (Alumni Edition) ProQuest One Community College ProQuest Central Aerospace Database Copper Technical Reference Library ProQuest Engineering Collection ProQuest Central Korea Advanced Technologies Database with Aerospace Civil Engineering Abstracts ProQuest Computing ProQuest Central Basic ProQuest Science Journals ProQuest Computing (Alumni Edition) ProQuest SciTech Collection METADEX Computer and Information Systems Abstracts Professional Advanced Technologies & Aerospace Database Materials Science & Engineering Collection Corrosion Abstracts ProQuest Central (Alumni) |
| DatabaseTitleList | CrossRef Materials Research Database |
| Database_xml | – sequence: 1 dbid: 8FG name: ProQuest Technology Collection url: https://search.proquest.com/technologycollection1 sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Sciences (General) Mathematics |
| DocumentTitleAlternate | M. Kamenskii, S. Pergamenchtchikov and M. Quincampoix Randomly perturbed second-order differential equations |
| EISSN | 1473-7124 |
| EndPage | 779 |
| ExternalDocumentID | oai_HAL_hal_02334875v1 10_1017_S0308210516000354 |
| GroupedDBID | -2P -2V -E. -~X .FH 09C 09E 0E1 0R~ 123 29P 3V. 4.4 5VS 6TJ 74X 74Y 7~V 88I 8FE 8FG 8R4 8R5 AAAZR AABES AABWE AACJH AAEED AAGFV AAKTX AANRG AARAB AASVR AAUKB ABBXD ABBZL ABITZ ABJCF ABJNI ABKKG ABMWE ABMYL ABQTM ABROB ABUWG ABXAU ABZCX ACBMC ACCHT ACETC ACGFS ACGOD ACIMK ACIWK ACQFJ ACQPF ACREK ACUIJ ACUYZ ACWGA ACYZP ACZBM ACZUX ACZWT ADCGK ADDNB ADFEC ADGEJ ADKIL ADOCW ADOVH ADOVT ADVJH AEBAK AEBPU AEHGV AEMTW AENCP AENGE AEYYC AFFUJ AFKQG AFKRA AFLOS AFLVW AFUTZ AGABE AGBYD AGJUD AGLWM AGOOT AHQXX AHRGI AIGNW AIHIV AIOIP AISIE AJ7 AJCYY AJPFC AJQAS AKZCZ ALMA_UNASSIGNED_HOLDINGS ALVPG ALWZO AQJOH ARABE ARAPS ARZZG ATUCA AUXHV AYIQA AZQEC BBLKV BCGOX BENPR BESQT BGHMG BGLVJ BJBOZ BLZWO BMAJL BPHCQ BQFHP C0O CAG CBIIA CCPQU CCQAD CCUQV CFAFE CFBFF CGQII CHEAL CJCSC COF CS3 DC4 DOHLZ DWQXO EBS EGQIC EJD GNUQQ HCIFZ HG- HST HZ~ I.6 I.7 I.9 IH6 IOEEP IOO IS6 I~P J36 J38 J3A JHPGK JQKCU K6V K7- KAFGG KCGVB KFECR L6V L98 LHUNA LW7 M-V M0N M2P M7S M7~ M8. NIKVX NZEOI O9- P2P P62 PQQKQ PROAC PTHSS PYCCK Q2X RAMDC RCA ROL RR0 S10 S6U SAAAG T9M UT1 WFFJZ WH7 WQ3 WXU WXY WYP XFK YNT ZDLDU ZJOSE ZMEZD ZYDXJ ~V1 AATMM AAYXX ABGDZ ABVKB ABVZP ABXHF ACDLN ACRPL ADNMO AEMFK AFZFC AGQPQ AKMAY CITATION PHGZM PHGZT 7QF 7QQ 7SC 7SE 7SP 7SR 7TA 7TB 7U5 7XB 8AL 8BQ 8FD 8FK F28 FR3 H8D H8G JG9 JQ2 KR7 L7M L~C L~D PKEHL PQEST PQGLB PQUKI PRINS Q9U 1XC AAXMD PUEGO VOOES |
| ID | FETCH-LOGICAL-c346t-b87ea7ec854badb63ed033bd847661dc20819878feefbeb3fbbf003bcafa3d893 |
| IEDL.DBID | BENPR |
| ISSN | 0308-2105 |
| IngestDate | Thu Sep 04 07:24:48 EDT 2025 Fri Jul 25 19:40:21 EDT 2025 Tue Jul 01 00:43:19 EDT 2025 Wed Mar 13 05:52:17 EDT 2024 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 4 |
| Keywords | 34D15 34B05 34B27 boundary-value problems 60J60 Green functions stochastic averaging method Primary 60H10 58J37 34C29 Green functions AMS 2000 Subject Classifications: Primary: 60H10 Boundary value problems |
| Language | English |
| License | https://www.cambridge.org/core/terms Distributed under a Creative Commons Attribution 4.0 International License: http://creativecommons.org/licenses/by/4.0 |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c346t-b87ea7ec854badb63ed033bd847661dc20819878feefbeb3fbbf003bcafa3d893 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| OpenAccessLink | https://hal.science/hal-02334875 |
| PQID | 1925067632 |
| PQPubID | 39415 |
| PageCount | 17 |
| ParticipantIDs | hal_primary_oai_HAL_hal_02334875v1 proquest_journals_1925067632 crossref_primary_10_1017_S0308210516000354 cambridge_journals_10_1017_S0308210516000354 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2017-08-01 |
| PublicationDateYYYYMMDD | 2017-08-01 |
| PublicationDate_xml | – month: 08 year: 2017 text: 2017-08-01 day: 01 |
| PublicationDecade | 2010 |
| PublicationPlace | Edinburgh, UK |
| PublicationPlace_xml | – name: Edinburgh, UK – name: Cambridge |
| PublicationTitle | Proceedings of the Royal Society of Edinburgh. Section A. Mathematics |
| PublicationTitleAlternate | Proceedings of the Royal Society of Edinburgh: Section A Mathematics |
| PublicationYear | 2017 |
| Publisher | Royal Society of Edinburgh Scotland Foundation Cambridge University Press Royal Society of Edinburgh |
| Publisher_xml | – name: Royal Society of Edinburgh Scotland Foundation – name: Cambridge University Press – name: Royal Society of Edinburgh |
| SSID | ssj0006857 |
| Score | 2.1055918 |
| Snippet | We consider boundary-value problems for differential equations of second order containing a Brownian motion (random perturbation) and a small parameter and... |
| SourceID | hal proquest crossref cambridge |
| SourceType | Open Access Repository Aggregation Database Index Database Publisher |
| StartPage | 763 |
| SubjectTerms | Asymptotic properties Boundary value problems Brownian motion Differential equations Existence theorems Mathematical analysis Mathematics Probability Probability theory Randomness Uniqueness theorems |
| Title | Second-order differential equations with random perturbations and small parameters |
| URI | https://www.cambridge.org/core/product/identifier/S0308210516000354/type/journal_article https://www.proquest.com/docview/1925067632 https://hal.science/hal-02334875 |
| Volume | 147 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV1LS8QwEB7c9aIH8YnriyAeVCx2N22aPYmK6yIq4gO8lUyS4mGfdvX3O2nT4gO8JoHCTDLfN8n0G4CDSHYTjZSpxqZDCUoW6kBiomgvq8gooRUX7kfhu3vRf4luXuNXf-GW-7LKKiYWgdqMtbsjPyUmElNkFbxzNpkGrmuUe131LTQaME8hWMZNmL-4un94rGOxkKXWJw9pPxCVqN41C9Fop9RCY21RvKdF39UVfqBU483VSP4K1QX-9JZhyRNHdl56egXm7GgVFu9q1dV8FVb8Qc3ZoVeTPlqDxyeX8pqg0NhkVT8UOtcDZqelznfO3G0sI9Qy4yGb2HeCIfQzNMbyoRoMmBMJH7rimXwdXnpXz5f9wDdSCDSPxCxAmViVWC3jCJVBwa0JOUdDyETwbHTH8QKZyMzaDCm7zhAzMglqlSluiNFsQHM0HtlNYKHGmByK7YzAHZNQoubdNmbEg7pSirgFJ7URU38c8rQsJUvSPzZvwXFl53RSymv8t3ifPFGvc8LY_fPb1I0R8-Au9fpst2CnctS379ebZ-v_6W1Y6DjcLir8dqA5e_-wu8Q6ZrgHDdm73vMb7Av4R9OK |
| linkProvider | ProQuest |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV3fTxQxEJ4gPKgPBlDjIUpjNFHjxr3tbrf3QAgi5JC7i0FIeFs7bTc83C_YU8I_5d_IzP4KasIbr-0mm0y_znzTTr8BeBvrXmqRMtXERZSg5KENNKaGsGxiZ5Q1UvFD4eFI9U_jb2fJ2RL8ad7CcFll4xNLR-1mls_IPxMTScizKhntzC8C7hrFt6tNC40KFkf--opStmL78Cut77soOtg_2esHdVeBwMpYLQLUqTeptzqJ0ThU0rtQSnTkpilWORtxkNSpzr3PkVLNHDEn6KM1uZFOs_gSufwVohk92kUrX_ZH349b3690pS0qQ8IfUZfmHrUUqWZlGBrrqvL-Lr6t5vBXVHxwzjWZ_4SGMt4drMKTmqiK3QpZa7Dkp-vweNiqvBbrsFY7hkK8r9WrPzyF4x-cYrug1PQUTf8V8iNj4S8qXfFC8OmvoCjpZhMx95cU9rCeoTFRTMx4LFiUfMLFOsUzOL0XEz-H5els6l-ACC0mBCDs5kQmMA01WtnrYk68q6e1SjrwqTViVm-_IqtK19LsP5t34GNj52xeyXnc9fEbWon2Oxbi7u8OMh4jpiM51fvd7cBms1C3_t-CdePu6S142D8ZDrLB4ejoJTyKmDOU1YWbsLy4_OVfEeNZ4OsaZgJ-3jeybwB6NhJ0 |
| 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=Second-order+differential+equations+with+random+perturbations+and+small+parameters&rft.jtitle=Proceedings+of+the+Royal+Society+of+Edinburgh.+Section+A.+Mathematics&rft.au=Kamenskii%2C+M.&rft.au=Pergamenchtchikov%2C+S.&rft.au=Quincampoix%2C+M.&rft.date=2017-08-01&rft.pub=Royal+Society+of+Edinburgh+Scotland+Foundation&rft.issn=0308-2105&rft.eissn=1473-7124&rft.volume=147&rft.issue=4&rft.spage=763&rft.epage=779&rft_id=info:doi/10.1017%2FS0308210516000354&rft.externalDocID=10_1017_S0308210516000354 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0308-2105&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0308-2105&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0308-2105&client=summon |