The goal of this paper is to prove a result conjectured in Follmer and Schachermayer [FS07], even in slightly more general form. Suppose that S is a continuous semimartingale and satisfies a large deviations estimate; this is a particular growth cond
ition on the mean-variance tradeoff process of S. We show that S then allows asymptotic exponential arbitrage with exponentially decaying failure probability, which is a strong and quantitative form of long-term arbitrage. In contrast to Follmer and Schachermayer [FS07], our result does not assume that S is a diffusion, nor does it need any ergodicity assumption.
Photometric maps, obtained with Spitzers Infrared Array Camera (IRAC), can provide a valuable probe of warm molecular hydrogen within the interstellar medium. IRAC maps of the supernova remnant IC443, extracted from the Spitzer archive, are strikingl
y similar to spectral line maps of the H2 pure rotational transitions that we obtained with the Infrared Spectrograph (IRS) instrument on Spitzer. IRS spectroscopy indicates that IRAC Bands 3 and 4 are indeed dominated by the H2 v=0-0 S(5) and S(7) transitions, respectively. Modeling of the H2 excitation suggests that Bands 1 and 2 are dominated by H2 v=1-0 O(5) and v=0-0 S(9). Large maps of the H2 emission in IC433, obtained with IRAC, show band ratios that are inconsistent with the presence of gas at a single temperature. The relative strengths of IRAC Bands 2, 3, and 4 are consistent with pure H2 emission from shocked material with a power-law distribution of gas temperatures. CO vibrational emissions do not contribute significantly to the observed Band 2 intensity. Assuming that the column density of H2 at temperatures T to T+dT is proportional to T raised to the power -b for temperatures up to 4000 K, we obtained a typical estimate of 4.5 for b. The power-law index, b, shows variations over the range 3 to 6 within the set of different sight-lines probed by the maps, with the majority of sight-lines showing b in the range 4 to 5. The observed power-law index is consistent with the predictions of simple models for paraboloidal bow shocks.
