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A class of integration by parts formulae in stochastic analysis I
"... Introduction Consider a Stratonovich stochastic differential equation dx t = X(x t ) ffi dB t +A(x t )dt (1) with C 1 coefficients on a compact Riemannian manifold M , with associated differential generator A = 1 2 \Delta M +Z and solution flow f¸ t : t 0g of random smooth diffeomorphisms of ..."
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Cited by 19 (10 self)
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Introduction Consider a Stratonovich stochastic differential equation dx t = X(x t ) ffi dB t +A(x t )dt (1) with C 1 coefficients on a compact Riemannian manifold M , with associated differential generator A = 1 2 \Delta M +Z and solution flow f¸ t : t 0g of random smooth diffeomorphisms
Differentiation of Heat Semigroups and Applications
, 1994
"... Introduction Consider the Stratonovich stochastic differential equation dx t = X(x t ) ffi dB t +A(x t )dt: (1) on R n with coefficients A : R n ! R n a smooth vector field and X : R n ! L (R m ; R n ) a smooth map into the space of linear maps of R m into R n , driven by the white ..."
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Introduction Consider the Stratonovich stochastic differential equation dx t = X(x t ) ffi dB t +A(x t )dt: (1) on R n with coefficients A : R n ! R n a smooth vector field and X : R n ! L (R m ; R n ) a smooth map into the space of linear maps of R m into R n , driven
Concerning the Geometry of Stochastic Differential Equations and Stochastic Flows
 Kusuoka and I. Shigekawa (Eds.) New Trends in Stochastic Analysis. Proc. Taniguchi Symposium
, 1995
"... Le Jan and Watanabe showed that a nondegenerate stochastic flow f¸ t : t 0g on a manifold M determines a connection on M . This connection is characterized here and shown to be the LeviCivita connection for gradient systems. This both explains why such systems have useful properties and allows u ..."
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Cited by 16 (10 self)
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Bochner vanishing theorem. 1 Introduction and Notations A. Consider a Stratonovich stochastic differential equation dx t = X(x t ) ffi dB t +A(x t )dt (1) on an ndimensional C 1 manifold M , e.g. M = R n . Here A is a C 1 vector field on M , so A(x) lies in the tangent space T x M to M at x
Measurements of a ScaleModel OrthoMode Transducer
"... This memo describes measurements made of a scalemodel orthomode transducer to evaluate its suitability for use at millimeter wavelengths. The device consists of four probes placed in a single crosssectional plane of a cylindrical waveguide. Each pair of probes is driven in antiphase with a 18 ..."
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Cited by 2 (0 self)
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180 ffi hybrid. A good 50\Omega match with a return loss of 20 dB and polarization isolation of 40 dB was achieved with a fixed backshort in a 40% bandwidth. An implementation in the 3mm band is suggested. 1. Introduction The simultaneous detection of two orthogonal polarizations allows
Optimum and Practical Noncausal Smoothing Filters for Estimating Carrier Phase With Phase Process Noise
, 1997
"... Noncausal smoothing fllters have signiflcant performance advantages over causal fllters for estimation of the phase of radio frequency signals. This article presents the optimum smoothing fllters for the cases where the spectral density of the carrier phase is of the form f¡fi, where fi = 3 is typic ..."
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Cited by 1 (1 self)
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Noncausal smoothing fllters have signiflcant performance advantages over causal fllters for estimation of the phase of radio frequency signals. This article presents the optimum smoothing fllters for the cases where the spectral density of the carrier phase is of the form f¡fi, where fi = 3
Ionization of Rydberg Atoms by a Stark Kick
, 1994
"... We provide a rigorous lower bound for the ionization probability of a Rydberg atom under the perturbation by a timedependent electric field in the form of an ultrashort pulse idealized as a Dirac ffi function. This estimate is of the form 1 \Gamma O(F \Gamma4 0 ) for large values of the electri ..."
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We provide a rigorous lower bound for the ionization probability of a Rydberg atom under the perturbation by a timedependent electric field in the form of an ultrashort pulse idealized as a Dirac ffi function. This estimate is of the form 1 \Gamma O(F \Gamma4 0 ) for large values
The New APOE?
"... EE=ri " f=At4 t) lJLb66&L, APOEiETETOA=b\7>7Tf t> 28+ei i t i!nar\60t, buD\ [ , tc5 FOXObzo)&f li€=rdiElE=l.rd6Db [,n/dUr. Craic Willcoxit+l.l*, ftE*Edi'tlcaElrF.Aa.1ffi)tredJ Ltt'tc " '&lJJ\21aEA,\Efi*tLlcfflnTH&T66 " flEffE$lJa. I)\rE:olr* ..."
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EE=ri " f=At4 t) lJLb66&L, APOEiETETOA=b\7>7Tf t> 28+ei i t i!nar\60t, buD\ [ , tc5 FOXObzo)&f li€=rdiElE=l.rd6Db [,n/dUr. Craic Willcoxit+l.l*, ftE*Edi'tlcaElrF.Aa.1ffi)tredJ Ltt'tc " '&lJJ\21aEA,\Efi*tLlcfflnTH&T66 " flEffE$lJa. I
RICE UNIVERSITY Regime Change: Sampling Rate vs. BitDepth in Compressive Sensing
, 2011
"... The compressive sensing (CS) framework aims to ease the burden on analogtodigital converters (ADCs) by exploiting inherent structure in natural and manmade signals. It has been demonstrated that structured signals can be acquired with just a small number of linear measurements, on the order of t ..."
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The compressive sensing (CS) framework aims to ease the burden on analogtodigital converters (ADCs) by exploiting inherent structure in natural and manmade signals. It has been demonstrated that structured signals can be acquired with just a small number of linear measurements, on the order of the signal complexity. In practice, this enables lower sampling rates that can be more easily achieved by current hardware designs. The primary bottleneck that limits ADC sampling rates is quantization, i.e., higher bitdepths impose lower sampling rates. Thus, the decreased sampling rates of CS ADCs accommodate the otherwise limiting quantizer of conventional ADCs. In this thesis, we consider a different approach to CS ADC by shifting towards lower quantizer bitdepths rather than lower sampling rates. We explore the extreme case where each measurement is quantized to just one bit, representing its sign. We develop a new theoretical framework to analyze this extreme case and develop new algorithms for signal reconstruction from such coarsely quantized measurements. The 1bit CS framework leads us to scenarios where it may be more appropriate to reduce bitdepth instead of sampling rate. We find that there exist two distinct regimes of operation that correspond to high/low signaltonoise ratio (SNR). In the measurement
3 USING DOPERATORS TO CONSTRUCT ORTHOGONAL POLYNOMIALS SATISFYING HIGHER ORDER qDIFFERENCE EQUATIONS
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Eddy stirring in the Southern Ocean
"... [1] There is an ongoing debate concerning the distribution of eddy stirring across the Antarctic Circumpolar Current (ACC) and the nature of its controlling processes. The problem is addressed here by estimating the isentropic eddy diffusivity from a collection of hydrographic and altimetric observ ..."
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[1] There is an ongoing debate concerning the distribution of eddy stirring across the Antarctic Circumpolar Current (ACC) and the nature of its controlling processes. The problem is addressed here by estimating the isentropic eddy diffusivity from a collection of hydrographic and altimetric observations, analyzed in a mixing length theoretical framework. It is shown that, typically, is suppressed by an order of magnitude in the upper kilometer of the ACC frontal jets relative to their surroundings, primarily as a result of a local reduction of the mixing length. This observation is reproduced by a quasi‐geostrophic theory of eddy stirring across a broad barotropic jet based on the scaling law derived by Ferrari and Nikurashin (2010). The theory interprets the observed widespread suppression of the mixing length and in the upper layers of frontal jets as the kinematic consequence of eddy propagation relative to the mean flow within jet cores. Deviations from the prevalent regime of mixing suppression in the core of upper‐ocean jets are encountered in a few special sites. Such ‘leaky jet ’ segments appear to be associated with sharp stationary meanders of the mean flow that are generated by the interaction of the ACC with major topographic features. It is contended that the characteristic thermohaline structure of the Southern Ocean, consisting of multiple upper‐ocean thermohaline fronts separated and underlaid by regions of homogenized properties, is largely a result of the widespread suppression of eddy stirring by parallel jets.
Results 1  10
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