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브라우니안 운동과 분수 브라우니안 운동 표본 경로의 정칙성에 관하여
- Author(s)
- 박지현
- Advisor
- 이기정
- Department
- 일반대학원 수학과
- Publisher
- The Graduate School, Ajou University
- Publication Year
- 2012-02
- Language
- eng
- Keyword
- path-regularity; Brownian motion; fractional Brownian motion; H？lder continuity; the law of the iterated logarithm
- Alternative Abstract
- 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.
- Fulltext
- Appears in Collections:
- Graduate School of Ajou University > Department of Mathematics > 3. Theses(Master)
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