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 in  the Fractional Black–Scholes pricing model. University of Helsinki, Department of Mathematics, Preprint 335, 13 p. (submitted to Statistics and Decisions, under revision)