Correction. Error estimates for binomial approximations of game options

Correction for Error estimates for binomial approximations of game options [math.PR/0607123]Comment: Published at http://dx.doi.org/10.1214/105051606000000808 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

An Extreme Family of Generalized Frobenius Numbers

We study a generalization of the \emph{Frobenius problem}: given $k$ positive relatively prime integers, what is the largest integer $g_0$ that cannot be represented as a nonnegative integral linear combination of these parameters? More generally, what is the largest integer $g_s$ that has exactly $s$ such representations? We illustrate a family of parameters, based on a recent paper by Tripathi, whose generalized Frobenius numbers $g_0, \ g_1, \ g_2, ...$ exhibit unnatural jumps; namely, $g_0, \ g_1, \ g_k, \ g_{\binom{k+1}{k-1}}, \ g_{\binom{k+2}{k-1}}, ...$form an arithmetic progression, and any integer larger than$g_{\binom{k+j}{k-1}}$has at least$\binom{k+j+1}{k-}$ representations. Along the way, we introduce a variation of a generalized Frobenius number and prove some basic results about it.Comment: 5 pages, to appear in Integers: the Electronic Journal of Combinatorial Number Theor

Nonconventional Large Deviations Theorems

We obtain large deviations theorems for nonconventional sums with underlying process being a Markov process satisfying the Doeblin condition or a dynamical system such as subshift of finite type or hyperbolic or expanding transformation