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브라우니안 운동과 분수 브라우니안 운동 표본 경로의 정칙성에 관하여
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.advisor | 이기정 | - |
| dc.contributor.author | 박지현 | - |
| dc.date.accessioned | 2018-11-08T08:02:59Z | - |
| dc.date.available | 2018-11-08T08:02:59Z | - |
| dc.date.issued | 2012-02 | - |
| dc.identifier.other | 12179 | - |
| dc.identifier.uri | https://dspace.ajou.ac.kr/handle/2018.oak/9830 | - |
| dc.description | 학위논문(석사)아주대학교 일반대학원 :수학과,2012. 2 | - |
| dc.description.tableofcontents | 1 Introduction = 3 2 The path-regularity of Brownian motion = 5 2.1 Preliminaries = 5 2.2 Nowhere differentiability = 7 2.3 H¨older continuity = 11 2.4 The law of the iterated logarithm = 14 2.5 Nowhere H¨older continuity = 19 3 The path-regularity of fractional Brownian motion = 21 3.1 Preliminaries = 21 3.2 Nowhere differentiability = 23 3.3 H¨older continuity = 24 3.4 The law of the iterated logarithm = 24 3.5 Nowhere H¨older continuity = 36 | - |
| dc.language.iso | eng | - |
| dc.publisher | The Graduate School, Ajou University | - |
| dc.rights | 아주대학교 논문은 저작권에 의해 보호받습니다. | - |
| dc.title | 브라우니안 운동과 분수 브라우니안 운동 표본 경로의 정칙성에 관하여 | - |
| dc.type | Thesis | - |
| dc.contributor.affiliation | 아주대학교 일반대학원 | - |
| dc.contributor.department | 일반대학원 수학과 | - |
| dc.date.awarded | 2012. 2 | - |
| dc.description.degree | Master | - |
| dc.identifier.localId | 570284 | - |
| dc.identifier.url | http://dcoll.ajou.ac.kr:9080/dcollection/jsp/common/DcLoOrgPer.jsp?sItemId=000000012179 | - |
| dc.subject.keyword | path-regularity | - |
| dc.subject.keyword | Brownian motion | - |
| dc.subject.keyword | fractional Brownian motion | - |
| dc.subject.keyword | H？lder continuity | - |
| dc.subject.keyword | the law of the iterated logarithm | - |
| dc.description.alternativeAbstract | We survey and study the regularity of the sample paths of Brownian motion and fractional Brownian motion. They are the examples of the continuous, but nowhere differentiable Gaussian processes. We focus on the H？lder regularity of the sample paths. In the case of Brownian motion the H？lder exponent is less than 1/2. For fractional Brownian motion of Hurst parameter H the sample paths has the H？lder exponent is less than H. These follow from the Kolmogorov continuity criterion. On the other hand, the law of the iterated logarithm for Gaussian processes shows that the sample paths of Brownian motion and fractional Brownian motion are nowhere H？lder continuous when the H？lder exponent is greater than equal to 1/2 and H, respectively. | - |
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- Graduate School of Ajou University > Department of Mathematics > 3. Theses(Master)
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