On Sampling of stationary increment processes

Under a complex technical condition, similar to such used in extreme value theory, we find the rate q(\epsilon)^{-1} at which a stochastic process with stationary increments \xi should be sampled, for the sampled process \xi(\lfloor\cdot /q(\epsilon)\rfloor q(\epsilon)) to deviate from \xi by at most \epsilon, with a given probability, asymptotically as \epsilon \downarrow0. The canonical application is to discretization errors in computer simulation of stochastic processes.Comment: Published at http://dx.doi.org/10.1214/105051604000000468 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

On overload in a storage model, with a self-similar and infinitely divisible input

Let {X(t)}_{t\ge0} be a locally bounded and infinitely divisible stochastic process, with no Gaussian component, that is self-similar with index H>0. Pick constants \gamma >H and c>0. Let \nu be the L\'evy measure on R^{[0,\infty)} of X, and suppose that R(u)\equiv\nu({y\inR^{[0,\infty)}:supt\ge 0y(t)/(1+ct^{\gamma})>u}) is suitably ``heavy tailed'' as u\to\infty (e.g., subexponential with positive decrease). For the ``storage process'' Y(t)\equiv sup_{s\ge t}(X(s)-X(t)-c(s-t)^{\gamma}), we show that P{sup_{s\in[0,t(u)]}Y(s)>u}\sim P{Y(\hat t(u))>u} as u\to\infty, when 0\le \hat t(u)\le t(u) do not grow too fast with u [e.g., t(u)=o(u^{1/\gamma})]

Design, performance evaluation, and investigation of the theoretical capabilities of the NASA Millimeter-wave Imaging Radiometer (MIR)

The development of techniques for passive microwave retrieval of water vapor and precipitation parameters using millimeter- and sub-millimeter wavelength channels is reviewed. Channels of particular interest are in the tropospheric transmission windows at 90, 150, 220, and 340 GHz and centered around the water vapor lines at 183 and 325 GHz. Collectively, these channels have potential application in high-resolution mapping (e.g., from geosynchronous orbit), remote sensing of cloud and precipitation parameters, and retrieval of water vapor profiles. Both theoretical and experimental results to date are discussed

Investigation of passive atmospheric sounding using millimeter and submillimeter wavelength channels

Activities within the period from July 1, 1992 through December 31, 1992 by Georgia Tech researchers in millimeter and submillimeter wavelength tropospheric remote sensing have been centered around the calibration of the Millimeter-wave Imaging Radiometer (MIR), preliminary flight data analysis, and preparation for TOGA/COARE. The MIR instrument is a joint project between NASA/GSFC and Georgia Tech. In the current configuration, the MIR has channels at 90, 150, 183(+/-1,3,7), and 220 GHz. Provisions for three additional channels at 325(+/-1,3) and 8 GHz have been made, and a 325-GHz receiver is currently being built by the ZAX Millimeter Wave Corporation for use in the MIR. Past Georgia Tech contributions to the MIR and its related scientific uses have included basic system design studies, performance analyses, and circuit and radiometric load design, in-flight software, and post-flight data display software. The combination of the above millimeter wave and submillimeter wave channels aboard a single well-calibrated instrument will provide unique radiometric data for radiative transfer and cloud and water vapor retrieval studies. A paper by the PI discussing the potential benefits of passive millimeter and submillimeter wave observations for cloud, water vapor and precipitation measurements has recently been published, and is included as an appendix

Investigation of passive atmospheric sounding using millimeter and submillimeter wavelength channels

Activities within the period from January 1, 1992 through June 30, 1992 by Georgia Tech researchers in millimeter and submillimeter wavelength tropospheric remote sensing have been centered around the integration and initial data flights of the MIR on board the NASA ER-2. Georgia Tech contributions during this period include completion of the MIR flight software and implementation of a 'quick-view' graphics program for ground based calibration and analysis of the MIR imagery. In the current configuration, the MIR has channels at 90, 150, 183 +/- 1,3,7, and 220 GHz. Provisions for three additional channels at 325 +/-1,3 and 9 GHZ have been made, and a 325-GHz receiver is currently being built by the ZAX Millimeter Wave Corporation for use in the MIR. The combination of the millimeter wave and submillimeter wave channels aboard a single well-calibrated instrument will provide the necessary aircraft radiometric data for radiative transfer and cloud and water vapor retrieval studies. A paper by the PI discussing the potential benefits of passive millimeter and submillimeter wave observations for cloud, water vapor and precipitation measurements has recently been accepted for publication (Gasiewski, 1992), and is included as Appendix A. The MIR instrument is a joint project between NASA/GSFC and Georgia Tech. Other Georgia Tech contributions to the MIR and its related scientific uses have included basic system design studies, performance analyses, and circuit and radiometric load design

Hemodynamic effects of intravenous amiodarone

Amiodarone is a potent antiarrhythmic agent that is effective in controlling both atrial and ventricular arrhythmias. Recently, intravenous administration was demonstrated to be effective in the acute management of rhythm disorders and, in addition, appeared to shorten the loading period normally required for oral drug administration. This investigation examined the hemodynamic effects of amiodarone after both acute intravenous bolus and continuous intravenous administration. Patients with a left ventricular ejection fraction greater than 0.35 experienced improved cardiac performance due to both acute and chronic peripheral vasodilation. However, patients with a lower ejection fraction developed a 20% decrease in cardiac index and clinically significant elevation of right heart pressures after acute bolus administration; these changes were variably compensated for by peripheral vasodilation when the drug was administered intravenously over 3 to 5 days continuously. Therefore, intravenous amiodarone can result in significant impairment of left ventricular performance in patients with preexisting left ventricular dysfunction

Investigation of passive atmospheric sounding using millimeter and submillimeter wavelength channels

Progress by the Georgia Institute of Technology's Laboratory for Radio-science and Remote Sensing in developing techniques for passive microwave retrieval of water vapor profiles and cloud and precipitation parameters using millimeter and submillimeter wavelength channels is reviewed. Channels of particular interest are in the tropospheric transmission windows at 90, 166, 220, 340, and 410 GHz and centered around the water vapor lines at 183 and 325 GHz. Collectively, these channels have potential application in high-resolution precipitation mapping (e.g., from geosynchronous orbit), remote sensing of cloud and precipitation parameters, including cirrus ice mass, and improved retrieval of water vapor profiles. During the period from January 1, 1994 through June 30, 1994 research activities focussed on calibrating and interpreting data from the Millimeter-Wave Imaging Radiometer (MIR). The MIR was deployed on the NASA ER-2 during the Convective Atmospheric Moisture Experiment (CAMEX, September-October 1993) to obtain the first submillimeter-wave tropospheric imagery of convective precipitations. A 325-GHz radiometer consisted of a submillimeter-wave DSB receiver with three IF channels at +/- 1, 3, and 8.5 GHz, and approximately 14 dB DSB noise figure was successfully operated during these experiments. Activities supported under this grant include a study of the impact of local oscillator reflections from the MIR calibration loads, the development of optimal gain and offset filters for radiometric calibration, and the modeling and interpretation of the MIR 325-GHz data over both clear and cloudy atmospheres. In addition, polarimetric radiometer measurements and modeling for ocean surface and atmospheric cloud-ice studies_were supported

On the infimum attained by a reflected L\'evy process

This paper considers a L\'evy-driven queue (i.e., a L\'evy process reflected at 0), and focuses on the distribution of $M(t)$, that is, the minimal value attained in an interval of length $t$ (where it is assumed that the queue is in stationarity at the beginning of the interval). The first contribution is an explicit characterization of this distribution, in terms of Laplace transforms, for spectrally one-sided L\'evy processes (i.e., either only positive jumps or only negative jumps). The second contribution concerns the asymptotics of \prob{M(T_u)> u} (for different classes of functions $T_u$ and $u$ large); here we have to distinguish between heavy-tailed and light-tailed scenarios

Implied volatility of basket options at extreme strikes

In the paper, we characterize the asymptotic behavior of the implied volatility of a basket call option at large and small strikes in a variety of settings with increasing generality. First, we obtain an asymptotic formula with an error bound for the left wing of the implied volatility, under the assumption that the dynamics of asset prices are described by the multidimensional Black-Scholes model. Next, we find the leading term of asymptotics of the implied volatility in the case where the asset prices follow the multidimensional Black-Scholes model with time change by an independent increasing stochastic process. Finally, we deal with a general situation in which the dependence between the assets is described by a given copula function. In this setting, we obtain a model-free tail-wing formula that links the implied volatility to a special characteristic of the copula called the weak lower tail dependence function