金融与排队论中的分数布朗运动（国外研究生论文）-经管之家官网！

Title：Fractional Brownian motion in finance and queueing
Author：Tommi Sottinen
Department of Mathematics,Faculty of Science University of Helsinki, Helsinki 2003
Abstract:This thesis consists of two parts.
Part I is an introduction to the fractional Brownian motion and to the included articles. In Section 1 we consider briefly the (early) history of the fractional Brownian motion. In sections 2 and 3 we study some of its basic properties and provide some proofs. Regarding the proofs the author claims no originality. Indeed, they are mostly gathered from the existing literature. In sections 4 to 7 we recall some less elementary facts about the fractional Brownian motion that serve as background to the articles [a], [c] and [d]. The included articles are summarised in Section 8. Finally, Section 9 contains an errata of the articles.
Part II consists of the articles themselves:
[a] Sottinen, T. (2001) Fractional Brownian motion, random walks and binary market models. Finance Stoch. 5, no. 3, 343–355.
Kozachenko, Yu., Vasylyk, O. and Sottinen, T. (2002) Path Space Large Deviations of a Large Buffer with Gaussian Input Traffic.
Queueing Systems 42, no. 2, 113–129.
[c] Sottinen, T. (2002) On Gaussian processes equivalent in law to fractional Brownian motion. University of Helsinki, Department of Mathematics, Preprint 328, 17 p. (submitted to Journal of Theoretical Probability)
[d] Sottinen, T. and Valkeila, E. (2002) On arbitrage and replication inthe Fractional Black–Scholes pricing model. University of Helsinki, Department of Mathematics, Preprint 335, 13 p. (submitted to Statistics and Decisions, under revision)