Additive-multiplicative stochastic models of financial mean-reverting processes

We investigate a generalized stochastic model with the property known as mean reversion, that is, the tendency to relax towards a historical reference level. Besides this property, the dynamics is driven by multiplicative and additive Wiener processes. While the former is modulated by the internal behavior of the system, the latter is purely exogenous. We focus on the stochastic dynamics of volatilities, but our model may also be suitable for other financial random variables exhibiting the mean reversion property. The generalized model contains, as particular cases, many early approaches in the literature of volatilities or, more generally, of mean-reverting financial processes. We analyze the long-time probability density function associated to the model defined through a It\^o-Langevin equation. We obtain a rich spectrum of shapes for the probability function according to the model parameters. We show that additive-multiplicative processes provide realistic models to describe empirical distributions, for the whole range of data.Comment: 8 pages, 3 figure

Gas Rich Dwarf Spheroidals

We present evidence that nearly half of the dwarf spheroidal galaxies (dSph and dSph/dIrr) in the Local Group are associated with large reservoirs of atomic gas, in some cases larger than the stellar mass. The gas is sometimes found at large distance (~10 kpc) from the center of a galaxy and is not necessarily centered on it. Similarly large quantities of ionized gas could be hidden in these systems as well. The properties of some of the gas reservoirs are similar to the median properties of the High-Velocity Clouds (HVCs); two of the HI reservoirs are catalogued HVCs. The association of the HI with the dwarf spheroidals might thus provide a link between the HVCs and stars. We show that the HI content of the Local Group dSphs and dIrrs exhibits a sharp decline if the galaxy is within 250 kpc of either the Milky Way or M31. This can be explained if both galaxies have a sufficiently massive x-ray emitting halo that produces ram-pressure stripping if a dwarf ventures too close to either giant spiral. We also investigate tidal stripping of the dwarf galaxies and find that although it may play a role, it cannot explain the apparent total absence of neutral gas in most dSph galaxies at distances less than 250 kpc. For the derived mean density of the hot gas, n_0 = 2.5e-5 cm^-2, ram-pressure stripping is found to be more than an order of magnitude more effective in removing the gas from the dSph galaxies. The hot halo, with an inferred mass of 1e10 solar masses, may represent a reservoir of ~1000 destroyed dwarf systems, either HVCs or true dwarf galaxies similar to those we observe now.Comment: AASTex preprint style, 27 pages including 12 figures. Submitted to ApJ. See also http://astro.berkeley.edu/~robisha

The escape problem under stochastic volatility: the Heston model

We solve the escape problem for the Heston random diffusion model. We obtain exact expressions for the survival probability (which ammounts to solving the complete escape problem) as well as for the mean exit time. We also average the volatility in order to work out the problem for the return alone regardless volatility. We look over these results in terms of the dimensionless normal level of volatility --a ratio of the three parameters that appear in the Heston model-- and analyze their form in several assymptotic limits. Thus, for instance, we show that the mean exit time grows quadratically with large spans while for small spans the growth is systematically slower depending on the value of the normal level. We compare our results with those of the Wiener process and show that the assumption of stochastic volatility, in an apparent paradoxical way, increases survival and prolongs the escape time.Comment: 29 pages, 12 figure

Cepheid Period-Radius and Period-Luminosity Relations and the Distance to the LMC

We have used the infrared Barnes-Evans surface brightness technique to derive the radii and distances of 34 Galactic Cepheid variables. Radius and distance results obtained from both versions of the technique are in excellent agreement. The radii of 28 variables are used to determine the period-radius relation. This relation is found to have a smaller dispersion than in previous studies, and is identical to the period-radius relation found by Laney & Stobie from a completely independent method, a fact which provides persuasive evidence that the Cepheid period-radius relation is now determined at a very high confidence level. We use the accurate infrared distances to determine period-luminosity relations in the V, I, J, H and K passbands from the Galactic sample of Cepheids. We derive improved slopes of these relations from updated LMC Cepheid samples and adopt these slopes to obtain accurate absolute calibrations of the PL relation. By comparing these relations to the ones defined by the LMC Cepheids, we derive strikingly consistent and precise values for the LMC distance modulus in each of the passbands which yield a mean value of DM (LMC) = 18.46 +- 0.02. Our results show that the infrared Barnes-Evans technique is very insensitive to both Cepheid metallicity and adopted reddening, and therefore a very powerful tool to derive accurate distances to nearby galaxies by a direct application of the technique to their Cepheid variables, rather than by comparing PL relations of different galaxies, which introduces much more sensitivity to metallicity and absorption corrections which are usually difficult to determine.Comment: LaTeX, AASTeX style, 9 Figures, 10 Tables, The Astrophysical Journal in press (accepted Oct. 14, 1997). Fig. 3 replace

Interstellar extinction towards the inner Galactic Bulge

DENIS observations in the J (1.2 micron) and K_S (2.15 micron) bands together with isochrones calculated for the RGB and AGB phase are used to draw an extinction map of the inner Galactic Bulge. The uncertainty in this method is mainly limited by the optical depth of the Bulge itself. A comparison with fields of known extinction shows a very good agreement. We present an extinction map for the inner Galactic Bulge (approx. 20 sq. deg.)Comment: 4 pages, 4 figures, accepted for publication in A&A as a letter, see also http://www-denis.iap.fr/articles/extinction

Cepheid variables in the LMC cluster NGC 1866. I. New BVRI CCD photometry

We report BV(RI)c CCD photometric data for a group of seven Cepheid variables in the young, rich cluster NGC 1866 in the Large Magellanic Cloud. The photometry was obtained as part of a program to determine accurate distances to these Cepheids by means of the infrared surface brightness technique, and to improve the LMC Cepheid database for constructing Cepheid PL and PLC relations. Using the new data together with data from the literature, we have determined improved periods for all variables. For five fundamental mode pulsators, the light curves are now of excellent quality and will lead to accurate distance and radius determinations once complete infrared light curves and radial velocity curves for these variables become available.Comment: To appear in ApJ Supp., AASTeX, 24 pages, 8 tables, 8 figure

Stellar and Gas properties of High HI Mass-to-Light Ratio Galaxies in the Local Universe

We present a multi-wavelength study (BVRI band photometry and HI line interferometry) of nine late-type galaxies selected from the HIPASS Bright Galaxy Catalog on the basis of apparently high HI mass-to-light ratios (3 M_sun/L_sun < M_HI/L_B < 27 M_sun/L_sun). We found that most of the original estimates for M_HI/L_B based on available photographic magnitudes in the literature were too high, and conclude that genuine high HI mass-to-light ratio (>5 M_sun/L_sun) galaxies are rare in the Local Universe. Extreme high M_HI/L_B galaxies like ESO215-G?009 appear to have formed only the minimum number of stars necessary to maintain the stability of their HI disks, and could possibly be used to constrain galaxy formation models. They may to have been forming stars at a low, constant rate over their lifetimes. The best examples all have highly extended HI disks, are spatially isolated, and have normal baryonic content for their total masses but are deficent in stars. This suggests that high M_HI/L_B galaxies are not lacking the baryons to create stars, but are underluminous as they lack either the internal or external stimulation for more extensive star formation.Comment: 29 Pages, 59 Figures. Accepted for publication in AJ (to be published ~April 2006

Self-Averaging Scaling Limits of Two-Frequency Wigner Distribution for Random Paraxial Waves

Two-frequency Wigner distribution is introduced to capture the asymptotic behavior of the space-frequency correlation of paraxial waves in the radiative transfer limits. The scaling limits give rises to deterministic transport-like equations. Depending on the ratio of the wavelength to the correlation length the limiting equation is either a Boltzmann-like integral equation or a Fokker-Planck-like differential equation in the phase space. The solutions to these equations have a probabilistic representation which can be simulated by Monte Carlo method. When the medium fluctuates more rapidly in the longitudinal direction, the corresponding Fokker-Planck-like equation can be solved exactly.Comment: typos correcte

Mean Escape Time in a System with Stochastic Volatility

We study the mean escape time in a market model with stochastic volatility. The process followed by the volatility is the Cox Ingersoll and Ross process which is widely used to model stock price fluctuations. The market model can be considered as a generalization of the Heston model, where the geometric Brownian motion is replaced by a random walk in the presence of a cubic nonlinearity. We investigate the statistical properties of the escape time of the returns, from a given interval, as a function of the three parameters of the model. We find that the noise can have a stabilizing effect on the system, as long as the global noise is not too high with respect to the effective potential barrier experienced by a fictitious Brownian particle. We compare the probability density function of the return escape times of the model with those obtained from real market data. We find that they fit very well.Comment: 9 pages, 9 figures, to be published in Phys. Rev.