Escape Rates for Multidimensional Shift Self-similar Additive Sequences
First the relation between shift self-similar additive sequences and stationary sequences of Ornstein–Uhlenbeck type (OU type) on R d is shown, and then the rates of escape for shift self-similar additive sequences are discussed. As a corollary, fundamental problems on recurrence of stationary seque...
Saved in:
| Published in | Journal of theoretical probability Vol. 29; no. 3; pp. 896 - 921 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
01.09.2016
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
Cover
Loading…
| Abstract | First the relation between shift self-similar additive sequences and stationary sequences of Ornstein–Uhlenbeck type (OU type) on
R
d
is shown, and then the rates of escape for shift self-similar additive sequences are discussed. As a corollary, fundamental problems on recurrence of stationary sequences of OU type are solved. Some applications to laws of the iterated logarithm for strictly stable Lévy processes on
R
d
and independent Brownian motions are given. |
|---|---|
| AbstractList | First the relation between shift self-similar additive sequences and stationary sequences of Ornstein–Uhlenbeck type (OU type) on
R
d
is shown, and then the rates of escape for shift self-similar additive sequences are discussed. As a corollary, fundamental problems on recurrence of stationary sequences of OU type are solved. Some applications to laws of the iterated logarithm for strictly stable Lévy processes on
R
d
and independent Brownian motions are given. First the relation between shift self-similar additive sequences and stationary sequences of Ornstein–Uhlenbeck type (OU type) on R d is shown, and then the rates of escape for shift self-similar additive sequences are discussed. As a corollary, fundamental problems on recurrence of stationary sequences of OU type are solved. Some applications to laws of the iterated logarithm for strictly stable Lévy processes on R d and independent Brownian motions are given. |
| Author | Watanabe, Toshiro |
| Author_xml | – sequence: 1 givenname: Toshiro surname: Watanabe fullname: Watanabe, Toshiro email: t-watanb@u-aizu.ac.jp organization: Center for Mathematical Sciences, Univ. of Aizu |
| BookMark | eNp1kE1LAzEQhoNUsK3-AG8LnqOTbLZJjqXUVqgIVs8h5kNTtrs1sxX8925ZD148DQzv887wTMioaZtAyDWDWwYg75CBrjQFVlGotKbyjIxZJTnVvIQRGYPSgmol4IJMEHcAoDXAmKyW6OwhFM-2C1jENhePx7pLPu1Dg6ltbF1sP1Lsim2oI8W0T7XNxdz71KWv0G8_j6FxAS_JebQ1hqvfOSWv98uXxZpunlYPi_mGOj5THeXMycC5tyC8lpUAwcCxUipRMRFFKWEWZyEKpxiP0SuImgOXb54rD16Fckpuht5DbvvT2Jlde8z9m2iYUqCkLkH3KTakXG4Rc4jmkNPe5m_DwJx8mcGX6X2Zky8je4YPDPbZ5j3kP83_Qj9P-G4e |
| Cites_doi | 10.1007/BF01199896 10.1214/aop/1176994945 10.1007/978-3-642-49742-1 10.1214/009117906000000629 10.1023/A:1007739010953 10.1023/A:1016267815166 10.1007/BF01213685 10.1214/aop/1024404286 10.1090/S0002-9947-1958-0104296-5 10.1214/aop/1176990626 10.1215/kjm/1250283698 10.1016/S0304-4149(02)00098-4 10.1112/S0024610704005319 10.1023/A:1021621926463 10.1007/BF00534909 10.1007/BF02214658 10.1007/BF01198788 |
| ContentType | Journal Article |
| Copyright | Springer Science+Business Media New York 2015 Copyright Springer Science & Business Media 2016 |
| Copyright_xml | – notice: Springer Science+Business Media New York 2015 – notice: Copyright Springer Science & Business Media 2016 |
| DBID | AAYXX CITATION |
| DOI | 10.1007/s10959-015-0599-7 |
| DatabaseName | CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Statistics Mathematics |
| EISSN | 1572-9230 |
| EndPage | 921 |
| ExternalDocumentID | 10_1007_s10959_015_0599_7 |
| GroupedDBID | -52 -5D -5G -BR -EM -Y2 -~C -~X .86 .VR 06D 0R~ 0VY 199 1N0 1SB 2.D 203 29L 2J2 2JN 2JY 2KG 2KM 2LR 2P1 2VQ 2~H 30V 4.4 406 408 409 40D 40E 5GY 5QI 5VS 67Z 6NX 78A 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AABYN AAFGU AAHNG AAIAL AAJKR AANZL AARHV AARTL AATNV AATVU AAUYE AAWCG AAYFA AAYIU AAYQN AAYTO ABBBX ABBXA ABDZT ABECU ABFGW ABFTV ABHLI ABHQN ABJNI ABJOX ABKAS ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABWNU ABXPI ACBMV ACBRV ACBXY ACBYP ACGFS ACHSB ACHXU ACIGE ACIPQ ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACSNA ACTTH ACVWB ACWMK ADHHG ADHIR ADIMF ADINQ ADKNI ADKPE ADMDM ADOXG ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEEQQ AEFIE AEFTE AEGAL AEGNC AEJHL AEJRE AEKMD AENEX AEOHA AEPOP AEPYU AESKC AESTI AETLH AEVLU AEVTX AEXYK AFDYV AFEXP AFGCZ AFLOW AFMKY AFNRJ AFQWF AFWTZ AFZKB AGAYW AGDGC AGGBP AGGDS AGJBK AGMZJ AGPAZ AGQMX AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AHYZX AIAKS AIIXL AILAN AIMYW AITGF AJBLW AJDOV AJRNO AJZVZ AKQUC ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN B-. BA0 BAPOH BBWZM BDATZ BGNMA CAG COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP DU5 EBLON EBS EIOEI EJD ESBYG FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GQ6 GQ7 GQ8 GXS HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ I09 IHE IJ- IKXTQ ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ KDC KOV KOW LAK LLZTM M4Y MA- N2Q N9A NB0 NDZJH NPVJJ NQJWS NU0 O9- O93 O9G O9I O9J OAM OVD P19 P2P P9R PF- PT4 PT5 QOK QOS R4E R89 R9I RHV RNI RNS ROL RPX RSV RZC RZE RZK S16 S1Z S26 S27 S28 S3B SAP SCLPG SDD SDH SDM SHX SISQX SJYHP SMT SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 T16 TEORI TSG TSK TSV TUC U2A UG4 UNUBA UOJIU UTJUX UZXMN VC2 VFIZW W23 W48 WH7 WK8 YLTOR Z45 Z7R Z7U Z7X Z81 Z83 Z88 Z8R Z8W Z92 ZMTXR ZWQNP ~EX AACDK AAEOY AAJBT AASML AAYXX ABAKF ACAOD ACDTI ACZOJ AEARS AEFQL AEMSY AFBBN AGQEE AGRTI AIGIU CITATION H13 |
| ID | FETCH-LOGICAL-c268t-21c7e22da04d97540410c13784514f43706f6ef4c812ffd80f92027bd28d0d8e3 |
| IEDL.DBID | U2A |
| ISSN | 0894-9840 |
| IngestDate | Thu Oct 10 16:48:05 EDT 2024 Thu Sep 12 17:36:49 EDT 2024 Sat Dec 16 12:19:35 EST 2023 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 3 |
| Keywords | Stationary sequence of OU type 60G10 60G18 Shift self-similar additive sequence Decomposable distribution 60G50 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c268t-21c7e22da04d97540410c13784514f43706f6ef4c812ffd80f92027bd28d0d8e3 |
| PQID | 1880879309 |
| PQPubID | 2043769 |
| PageCount | 26 |
| ParticipantIDs | proquest_journals_1880879309 crossref_primary_10_1007_s10959_015_0599_7 springer_journals_10_1007_s10959_015_0599_7 |
| PublicationCentury | 2000 |
| PublicationDate | 2016-09-01 |
| PublicationDateYYYYMMDD | 2016-09-01 |
| PublicationDate_xml | – month: 09 year: 2016 text: 2016-09-01 day: 01 |
| PublicationDecade | 2010 |
| PublicationPlace | New York |
| PublicationPlace_xml | – name: New York |
| PublicationTitle | Journal of theoretical probability |
| PublicationTitleAbbrev | J Theor Probab |
| PublicationYear | 2016 |
| Publisher | Springer US Springer Nature B.V |
| Publisher_xml | – name: Springer US – name: Springer Nature B.V |
| References | JeanblancMPitmanJYorMSelf-similar processes with independent increments associated with Lévy and BesselStoch. Process. Appl.2002100223231191961410.1016/S0304-4149(02)00098-41059.60052 WatanabeTShift self-similar additive random sequences associated with supercritical branching processesJ. Theor. Probab.200215631665192244110.1023/A:10162678151661011.60068 MaejimaMSatoKSemi-selfsimilar processesJ. Theor. Probab.199912347373168474810.1023/A:10216219264630932.60043 Dvoretzky, A., Erdös, P.: Some problems on random walk in space. In: Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 1950, pp. 353–367. University of California Press, Berkeley and Los Angeles (1951) WatanabeTExact packing measure on the boundary of a Galton–Watson treeJ. Lond. Math. Soc.200469801816205004710.1112/S00246107040053191057.60079 WatanabeTYamamuroKLimsup behaviors of multi-dimensional selfsimilar processes with independent incrementsALEA Lat. Am. J. Probab. Math. Stat.201077911626518221276.60044 KhintchineAAsymptotische Gesetze der Wahrschenlichkeitsrechnung1933BerlinSpringer10.1007/978-3-642-49742-159.1153.01 SatoKLévy Processes and Infinitely Divisible Distributions. Cambridge Studies in Advanced Mathematics, 681999CambridgeCambridge University Press TakeuchiJWatanabeSSpitzer’s test for the Cauchy process on the lineZ. Wahrscheinlichkeitstheorie und Verw. Gebiete1964320421017232610.1007/BF005349090146.38004 SatoKSelf-similar processes with independent incrementsProbab. Theory Relat. Fields199189285300111322010.1007/BF011987880725.60034 FristedtBThe behavior of increasing stable processes for both small and large timesJ. Math. Mech.1964138498561680090126.33403 MaejimaMSatoKSemi-Lévy processes, semi-selfsimilar additive processes, and semi-stationary Ornstein–Uhlenbeck type processesJ. Math. Kyoto Univ.20034360963920286701066.60050 BreimanLProbability1968ReadingAddison-Wesley Publishing Company0174.48801 WatanabeTContinuity properties of distributions with some decomposabilityJ. Theor. Probab.200013169192174498710.1023/A:10077390109530949.60037 SpitzerFSome theorems concerning 2-dimensional Brownian motionTrans. Am. Math. Soc.1958871871971042960089.13601 WatanabeTExact Hausdorff measure on the boundary of a Galton–Watson treeAnn. Probab.20073510071038231971410.1214/0091179060000006291127.60083 WatanabeTSample function behavior of increasing processes of class LProbab. Theory Relat. Fields1996104349374137634210.1007/BF012136850849.60036 GruetJCShiZThe occupation time of Brownian motion in a ballJ. Theor. Probab.19969429445138540610.1007/BF022146580870.60072 WatanabeTLimit theorems for shift selfsimilar additive random sequencesOsaka J. Math.20023956160319322821022.60028 PruittWEThe rate of escape of random walkAnn. Probab.19901814171461107180310.1214/aop/11769906260715.60087 KhoshnevisanDEscape rates for Lévy processesStud. Sci. Math. Hung.19973317718314541090910.60061 GetoorRKThe Brownian escape processAnn. Probab.1979786486754213610.1214/aop/11769949450416.60086 KhoshnevisanDLewisTMLiWVOn the future infima of some transient processesProbab. Theory Relat. Fields199499337360128311610.1007/BF011998960801.60066 TaylorSJSample path properties of a transient stable processJ. Math. Mech.196716122912462086840178.19301 BungeJNested classes of C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C$$\end{document}-decomposable lawsAnn. Probab.199725215229142850710.1214/aop/10244042860873.60005 L Breiman (599_CR1) 1968 SJ Taylor (599_CR18) 1967; 16 WE Pruitt (599_CR13) 1990; 18 599_CR3 J Bunge (599_CR2) 1997; 25 D Khoshnevisan (599_CR10) 1994; 99 T Watanabe (599_CR23) 2004; 69 K Sato (599_CR14) 1991; 89 B Fristedt (599_CR4) 1964; 13 K Sato (599_CR15) 1999 T Watanabe (599_CR25) 2010; 7 T Watanabe (599_CR21) 2002; 39 JC Gruet (599_CR6) 1996; 9 M Maejima (599_CR12) 2003; 43 D Khoshnevisan (599_CR9) 1997; 33 T Watanabe (599_CR20) 2000; 13 T Watanabe (599_CR24) 2007; 35 M Maejima (599_CR11) 1999; 12 F Spitzer (599_CR16) 1958; 87 T Watanabe (599_CR19) 1996; 104 M Jeanblanc (599_CR7) 2002; 100 T Watanabe (599_CR22) 2002; 15 A Khintchine (599_CR8) 1933 J Takeuchi (599_CR17) 1964; 3 RK Getoor (599_CR5) 1979; 7 |
| References_xml | – volume: 99 start-page: 337 year: 1994 ident: 599_CR10 publication-title: Probab. Theory Relat. Fields doi: 10.1007/BF01199896 contributor: fullname: D Khoshnevisan – volume: 7 start-page: 864 year: 1979 ident: 599_CR5 publication-title: Ann. Probab. doi: 10.1214/aop/1176994945 contributor: fullname: RK Getoor – volume-title: Asymptotische Gesetze der Wahrschenlichkeitsrechnung year: 1933 ident: 599_CR8 doi: 10.1007/978-3-642-49742-1 contributor: fullname: A Khintchine – volume: 35 start-page: 1007 year: 2007 ident: 599_CR24 publication-title: Ann. Probab. doi: 10.1214/009117906000000629 contributor: fullname: T Watanabe – volume: 13 start-page: 169 year: 2000 ident: 599_CR20 publication-title: J. Theor. Probab. doi: 10.1023/A:1007739010953 contributor: fullname: T Watanabe – volume: 39 start-page: 561 year: 2002 ident: 599_CR21 publication-title: Osaka J. Math. contributor: fullname: T Watanabe – volume: 15 start-page: 631 year: 2002 ident: 599_CR22 publication-title: J. Theor. Probab. doi: 10.1023/A:1016267815166 contributor: fullname: T Watanabe – volume: 104 start-page: 349 year: 1996 ident: 599_CR19 publication-title: Probab. Theory Relat. Fields doi: 10.1007/BF01213685 contributor: fullname: T Watanabe – volume: 25 start-page: 215 year: 1997 ident: 599_CR2 publication-title: Ann. Probab. doi: 10.1214/aop/1024404286 contributor: fullname: J Bunge – volume: 13 start-page: 849 year: 1964 ident: 599_CR4 publication-title: J. Math. Mech. contributor: fullname: B Fristedt – volume-title: Lévy Processes and Infinitely Divisible Distributions. Cambridge Studies in Advanced Mathematics, 68 year: 1999 ident: 599_CR15 contributor: fullname: K Sato – volume: 87 start-page: 187 year: 1958 ident: 599_CR16 publication-title: Trans. Am. Math. Soc. doi: 10.1090/S0002-9947-1958-0104296-5 contributor: fullname: F Spitzer – volume: 16 start-page: 1229 year: 1967 ident: 599_CR18 publication-title: J. Math. Mech. contributor: fullname: SJ Taylor – volume: 18 start-page: 1417 year: 1990 ident: 599_CR13 publication-title: Ann. Probab. doi: 10.1214/aop/1176990626 contributor: fullname: WE Pruitt – volume: 43 start-page: 609 year: 2003 ident: 599_CR12 publication-title: J. Math. Kyoto Univ. doi: 10.1215/kjm/1250283698 contributor: fullname: M Maejima – ident: 599_CR3 – volume: 100 start-page: 223 year: 2002 ident: 599_CR7 publication-title: Stoch. Process. Appl. doi: 10.1016/S0304-4149(02)00098-4 contributor: fullname: M Jeanblanc – volume-title: Probability year: 1968 ident: 599_CR1 contributor: fullname: L Breiman – volume: 69 start-page: 801 year: 2004 ident: 599_CR23 publication-title: J. Lond. Math. Soc. doi: 10.1112/S0024610704005319 contributor: fullname: T Watanabe – volume: 12 start-page: 347 year: 1999 ident: 599_CR11 publication-title: J. Theor. Probab. doi: 10.1023/A:1021621926463 contributor: fullname: M Maejima – volume: 3 start-page: 204 year: 1964 ident: 599_CR17 publication-title: Z. Wahrscheinlichkeitstheorie und Verw. Gebiete doi: 10.1007/BF00534909 contributor: fullname: J Takeuchi – volume: 9 start-page: 429 year: 1996 ident: 599_CR6 publication-title: J. Theor. Probab. doi: 10.1007/BF02214658 contributor: fullname: JC Gruet – volume: 89 start-page: 285 year: 1991 ident: 599_CR14 publication-title: Probab. Theory Relat. Fields doi: 10.1007/BF01198788 contributor: fullname: K Sato – volume: 7 start-page: 79 year: 2010 ident: 599_CR25 publication-title: ALEA Lat. Am. J. Probab. Math. Stat. contributor: fullname: T Watanabe – volume: 33 start-page: 177 year: 1997 ident: 599_CR9 publication-title: Stud. Sci. Math. Hung. contributor: fullname: D Khoshnevisan |
| SSID | ssj0009900 |
| Score | 2.087599 |
| Snippet | First the relation between shift self-similar additive sequences and stationary sequences of Ornstein–Uhlenbeck type (OU type) on
R
d
is shown, and then the... First the relation between shift self-similar additive sequences and stationary sequences of Ornstein–Uhlenbeck type (OU type) on R d is shown, and then the... |
| SourceID | proquest crossref springer |
| SourceType | Aggregation Database Publisher |
| StartPage | 896 |
| SubjectTerms | Brownian motion Mathematics Mathematics and Statistics Probability Theory and Stochastic Processes Self-similarity Statistics |
| Title | Escape Rates for Multidimensional Shift Self-similar Additive Sequences |
| URI | https://link.springer.com/article/10.1007/s10959-015-0599-7 https://www.proquest.com/docview/1880879309 |
| Volume | 29 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV27TsMwFL0q7VIGBAVEoVQZmEBGieP6MUaoD4FgoFQqU5T4ISqgIBL-HzuPtiAYyJhEHo4T3-N7zz0GOGNJKoydayRD7lI3_gAllEiUEk6DBCsW6MLt845OZuR6Ppg3AK9SF8vny7oiWSzUG71uLmNloxdyliKIbUHLcgfiZFwzHK2NdkXZdsIFQcLuXupK5m9DfI9Fa4L5oyZahJrRLuxUHNGLykndg4ZedmD7dmWwmnWg7Uhi6bG8D-Nh5mRM3r3jjZ5loV7RVquccX9puuFNnxYm96b6xaBs8bqw21kvUqrQDdm7lZr6AGaj4cPVBFUHJCCJKc8RDiTTGKvEJ0owy71I4MsgZJxYGmRIyHxqqDZE2ihujOK-ES7XkSrMla-4Dg-huXxb6iPwEkxTZZy3vuZEKCZMKpJA2ssdjy6TLpzXUMXvpQ9GvHY8drjGFtfY4RqzLvRqMOPql8hiZ_zG7Wrgiy5c1ABvPP5rsON_vX0CbUtpaKkC60Ez__jUp5Y25GkfWtH48WbYL76XL-8Fueo |
| link.rule.ids | 315,783,787,27938,27939,41095,41537,42164,42606,52125,52248 |
| linkProvider | Springer Nature |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV05T8MwFH6CdqAMHAVEoUAGJpCrJHVje6xQD-gx0FYqU5T4EBVQEEkXfj12DloqGJoxsazkPcfv8zu-B3BNgpAprWvE69S4buwGCjzMUYip5wSuII5M2D6HXneCH6aNaVbHHeXZ7nlIMtmpV4rdjMtKmy9kOEUQ2YYidjXaL0Cx2XnqtZZcuyytPKEMI6YPMHkw869JfpujJcZcC4sm1qa9D-P8PdMkk5faIg5r_GuNwnHDDzmAvQx9Ws10uRzClpyXYXfwQ90alaFk4GfK3nwEnVZkEqSsR4NILY1vraRgV5iWACmdhzV6nqnYGslXhaLZ20wflK2mEElGkr6b5Wkfw6TdGt91UdZ6AXHXozFyHU6k64rAxoIRjeqwY3OnTijWAEvhOrE95UmFucYHSglqK2a8KKFwqbAFlfUTKMzf5_IUrMD1QqEMa7-kmAnCVMgCh-vLNF7nQQVucg34HynDhr_kUjai8rWofCMqn1SgmuvIz362yDeUclTvMzarwG0u8pXH_012ttHoK9jpjgd9v38_7J1DSQMnL801q0Ih_lzICw1O4vAyW4zf8AnYhA |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LT8JAEJ4oJEYPPlAjitqDJ81CW5bu7pEoD0WJEUnwVNt9RKIiseXir3eXtoJED8Yet5tNO7PtfDuPbwBOSBAypXWNeJUa141dQ4GHOQox9ZzAFcSRU7bPrtfu46tBbZD2OY2ybPcsJJnUNBiWplFcGQtVmSt8M-4rbcqQ4RdBZBny2IzlIF9vPXQaM95dllShUIYR04eZLLD50yLfTdMMby6ESKeWp7kBj9kzJwknz-VJHJb5xwKd4z9eahPWU1Rq1ZNttAVLclSAtZsvSteoAKsGliasztvQakQmccq6M0jV0rjXmhbyCtMqIKH5sHpPQxVbPfmiUDR8HeoDtFUXYpqppEfT_O0d6Dcb9-dtlLZkQNz1aIxchxPpuiKwsWBEoz0tde5UCcUaeClcJbanPKkw17hBKUFtxYx3JRQuFbagsroLudHbSO6BFbheKJRh85cUM0GYClngcH2Zhuw8KMJppg1_nDBv-DOOZSMqX4vKN6LySRFKmb789COMfEM1R_X_x2ZFOMvEP3f7t8X2_zT7GFZuL5r-9WW3cwCrGk95SQpaCXLx-0QeaswSh0fpvvwEb6fhaA |
| 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=Escape+Rates+for+Multidimensional+Shift+Self-similar+Additive+Sequences&rft.jtitle=Journal+of+theoretical+probability&rft.au=Watanabe%2C+Toshiro&rft.date=2016-09-01&rft.issn=0894-9840&rft.eissn=1572-9230&rft.volume=29&rft.issue=3&rft.spage=896&rft.epage=921&rft_id=info:doi/10.1007%2Fs10959-015-0599-7&rft.externalDBID=n%2Fa&rft.externalDocID=10_1007_s10959_015_0599_7 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0894-9840&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0894-9840&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0894-9840&client=summon |