Yıl: 2011 Cilt: 40 Sayı: 2 Sayfa Aralığı: 255 - 264 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022

Results on the supremum of fractional Brownian motion

Öz:
We show that the distribution of the square of the supremum of reflected fractional Brownian motion up to time a, with Hurst parameter H greater than 1/2, is related to the distribution of its hitting time to level 1, using the self similarity property of fractional Brownian motion. It is also proven that the second moment of supremum of reflected fractional Brownian motion up to time a is bounded above by $a^ {2H}$. Similar relations are obtained for the supremum of fractional Brownian motion with Hurst parameter greater than 1/2, and its hitting time to level 1. What is more, we obtain an upper bound on the complementary probability distribution of the supremum of fractional Brownian motion and re°ected fractional Brownian motion up to time a, using Jensen's and Markov's inequalities. A sharper bound is observed on the distribution of the supremum of fractional Brownian motion by the properties of Gamma distribution. Finally, applications of the given results to financial markets are investigated, and partial results are provided.
Anahtar Kelime:

Konular: Matematik İstatistik ve Olasılık
Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
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APA VARDAR ACAR C (2011). Results on the supremum of fractional Brownian motion. , 255 - 264.
Chicago VARDAR ACAR CEREN Results on the supremum of fractional Brownian motion. (2011): 255 - 264.
MLA VARDAR ACAR CEREN Results on the supremum of fractional Brownian motion. , 2011, ss.255 - 264.
AMA VARDAR ACAR C Results on the supremum of fractional Brownian motion. . 2011; 255 - 264.
Vancouver VARDAR ACAR C Results on the supremum of fractional Brownian motion. . 2011; 255 - 264.
IEEE VARDAR ACAR C "Results on the supremum of fractional Brownian motion." , ss.255 - 264, 2011.
ISNAD VARDAR ACAR, CEREN. "Results on the supremum of fractional Brownian motion". (2011), 255-264.
APA VARDAR ACAR C (2011). Results on the supremum of fractional Brownian motion. Hacettepe Journal of Mathematics and Statistics, 40(2), 255 - 264.
Chicago VARDAR ACAR CEREN Results on the supremum of fractional Brownian motion. Hacettepe Journal of Mathematics and Statistics 40, no.2 (2011): 255 - 264.
MLA VARDAR ACAR CEREN Results on the supremum of fractional Brownian motion. Hacettepe Journal of Mathematics and Statistics, vol.40, no.2, 2011, ss.255 - 264.
AMA VARDAR ACAR C Results on the supremum of fractional Brownian motion. Hacettepe Journal of Mathematics and Statistics. 2011; 40(2): 255 - 264.
Vancouver VARDAR ACAR C Results on the supremum of fractional Brownian motion. Hacettepe Journal of Mathematics and Statistics. 2011; 40(2): 255 - 264.
IEEE VARDAR ACAR C "Results on the supremum of fractional Brownian motion." Hacettepe Journal of Mathematics and Statistics, 40, ss.255 - 264, 2011.
ISNAD VARDAR ACAR, CEREN. "Results on the supremum of fractional Brownian motion". Hacettepe Journal of Mathematics and Statistics 40/2 (2011), 255-264.