The problem of distinguishing a Brownian bridge from a Brownian motion, both with possible drift, on the closed unit interval, is investigated via a pair of hypothesis tests. The first, tests for observations obtained at n discrete time points to be arising from a Brownian bridge with drift by...

A histogram estimate of the Radon–Nikodym derivative of a probability measure with respect to a dominating measure is developed for binary sequences in {0,1}N. A necessary and sufficient condition for the consistency of the estimate in the mean-square sense is given. It is noted that the...

Consider a Brownian bridge from 0 to c0. It is known that the density of the expected occupation time by the Brownian bridge is constant in [0,c]. We give a simple elementary proof for this result based on a direct examination of the corresponding integral. The expected occupation time plays an...

Predicting the federal funds rate and beating the federal funds futures market: mission impossible? Not so. We employ a Markov transition process and show that this model outperforms the federal funds futures market in predicting the target federal funds rate. Thus, by using purely historical...

Let X,Xi i[greater-or-equal, slanted]1 be i.i.d. bounded from below continuous random variables, , and bn n[greater-or-equal, slanted]1 be a sequence of increasing positive numbers. When X belongs to the Feller class and bn is such that nP(Xbn)--[infinity] and , a functional central limit...

Let {X,Xi}i[greater-or-equal, slanted]1 be i.i.d. random variables with a symmetric continuous distribution and EX2=[infinity], and {bn}n[greater-or-equal, slanted]1 be a sequence of increasing positive numbers. When X belongs to the Feller class, and nP(Xbn)~[gamma]n[short up arrow][infinity],...

We provide a framework for the martingale representation for futures prices which has some concrete advantages over the classical treatments of Duffie (Dynamic Asset Pricing Theory, 3rd Edition, Princeton University Press, Princeton, NJ, 2001) or Karatzas and Shreve (Brownian Motion and...