Summary The Radon-Nikodym derivative between a centered fractional Brownian motion Z and the same process with constant drift is derived by nding an integral transformation which changes Z to a process with independent increments. A representation of Z through a standard Brownian motion on a nite interval is given. The maximum likelihood estimator of the drift and some other applications are presented.

Efficacy of drugs for the acute treatment of migraine in children has not so far been studied in well controlled trials. We conducted a study to evaluate the efficacy of acetaminophen and ibuprofen. Eighty-eight children, aged 4.0 to 15.8 years, with migraine participated in a double-blind crossover study. Three attacks per child were treated in random order with single oral doses of 15 mg/kg acetaminophen, 10 mg/kg ibuprofen, and placebo at home. The primary end point, reduction in severe or moderate headache (grade > or = 3 on a scale of 1 to 5) by at least two grades after 2 hours, was reached twice as often with acetaminophen and three times as often with ibuprofen as with placebo. Ibuprofen was twice as likely as acetaminophen to abort migraine within 2 hours. In the intent-to-treat analysis, children improved twice as often with ibuprofen and acetaminophen as with placebo. Both ibuprofen and acetaminophen are effective and economical treatments for severe or moderate migraine attacks in children. Ibuprofen gave the best relief.

Arbitrage, Pricing, Quadratic variation, Robust hedging, G10, G13,

Abstract. We survey some new progress on the pricing models driven by fractional Brownian motion or mixed fractional Brownian motion. In particular, we give results on arbitrage opportunities, hedging, and option pricing in these models. We summarize some recent results on fractional Black & Scholes pricing model with transaction costs. We end the paper by giving some approximation results and indicating some open problems related to the paper. JEL Classification: G10, G13Mathematics Subject Classification (2000): 91B28, 91B70, 60G15, 60H05

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The association between serum selenium concentration and five-year risk of cardiovascular disease was studied in 1,110 men aged 55 to 74 years in two rural areas of Finland. In the total cohort, all-cause and cardiovascular deaths were associated significantly with serum selenium of less than 45 micrograms/liter, an adjusted relative risk of 1.4 (95% confidence interval (Cl), 1.0-2.0, p less than 0.05) and 1.6 (95% Cl, 1.1-2.3, p less than 0.05), respectively. Among men free of coronary heart disease at the outset, these associations were of similar magnitude but did not attain statistical significance. Among men free of stroke at the outset, low serum selenium was associated significantly with stroke mortality, an adjusted relative risk of 3.7 (95% Cl, 1.0-13.1). The associations of coronary deaths and myocardial infarctions with low serum selenium were nonsignificant.

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We show that a pathwise stochastic integral with respect to fractional Brownian motion with an adapted integrand g can have any prescribed distribution, moreover, we give both necessary and sufficient conditions when random variables can be represented in this form. We also prove that any random variable is a value of such integral in some improper sense. We discuss some applications of these results, in particular, to fractional Black-Scholes model of financial market.