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SDAEs with Small Noise

by Gernot Pulverer, Ewa B. Weinmüller, Roberta Bosi, Jean Dolbeault, Maria J. Esteban, Xavier Antoine, Anton Arnold, Christophe Besse, Matthias Ehrhardt, Tino Eibner, Jens Markus Melenk, Stephan Gadau, Anton Arnold, Winfried Auzinger, Herbert Lehner, Georg Kitzhofer, Othmar Koch, Gernot Pulverer, Ewa B. Weinmüller, Thorsten Sickenberger, Renate Winkler, Thorsten Sickenberger, Renate Winkler
"... transport Equations ..."
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transport Equations

of small noise constrained diffusions

by Amarjit Budhiraja, Zhen-qing Chen
"... On uniform positivity of transition densities ..."
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On uniform positivity of transition densities

The Small Noise Arbitrage Pricing Theory

by S. Satchell
"... This paper presents a small-noise version of the Arbitrage Pricing Theory (APT) which allows us to interpret the approximate linearity of the risk premia in terms of factor exposures for a fixed number of assets. The approximation becomes more accurate as the noise of the system decreases, even thou ..."
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This paper presents a small-noise version of the Arbitrage Pricing Theory (APT) which allows us to interpret the approximate linearity of the risk premia in terms of factor exposures for a fixed number of assets. The approximation becomes more accurate as the noise of the system decreases, even

Bursting oscillations induced by small noise

by Pawel Hitczenko, Georgi S. Medvedev , 2008
"... We consider a model of a square-wave bursting neuron residing in the regime of tonic spiking. Upon introduction of small stochastic forcing, the model generates irregular bursting. The statistical properties of the emergent bursting patterns are studied in the present work. In particular, we identif ..."
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We consider a model of a square-wave bursting neuron residing in the regime of tonic spiking. Upon introduction of small stochastic forcing, the model generates irregular bursting. The statistical properties of the emergent bursting patterns are studied in the present work. In particular, we

Exploration, normalization, and summaries of high density oligonucleotide array probe level data.

by Rafael A Irizarry , Bridget Hobbs , Francois Collin , Yasmin D Beazer-Barclay , Kristen J Antonellis , Uwe Scherf , Terence P Speed - Biostatistics, , 2003
"... SUMMARY In this paper we report exploratory analyses of high-density oligonucleotide array data from the Affymetrix GeneChip R system with the objective of improving upon currently used measures of gene expression. Our analyses make use of three data sets: a small experimental study consisting of f ..."
Abstract - Cited by 854 (33 self) - Add to MetaCart
SUMMARY In this paper we report exploratory analyses of high-density oligonucleotide array data from the Affymetrix GeneChip R system with the objective of improving upon currently used measures of gene expression. Our analyses make use of three data sets: a small experimental study consisting

On limits of wireless communications in a fading environment when using multiple antennas

by G. J. Foschini, M. J. Gans - Wireless Personal Communications , 1998
"... Abstract. This paper is motivated by the need for fundamental understanding of ultimate limits of bandwidth efficient delivery of higher bit-rates in digital wireless communications and to also begin to look into how these limits might be approached. We examine exploitation of multi-element array (M ..."
Abstract - Cited by 2426 (14 self) - Add to MetaCart
to the baseline n = 1 case, which by Shannon’s classical formula scales as one more bit/cycle for every 3 dB of signal-to-noise ratio (SNR) increase, remarkably with MEAs, the scaling is almost like n more bits/cycle for each 3 dB increase in SNR. To illustrate how great this capacity is, even for small n, take

Small Noise Asymptotics of Traveling Waves

by C. Mueller, L. Mytnik , J. Quastel , 2008
"... ..."
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Edgeworth expansions in small noise asymptotics ∗

by Lan Zhang, Per A. Mykl, Yacine Aït-sahalia , 2004
"... The paper considers Edgeworth expansions for estimators of volatility. Unlike the usual exapsions, we have found that in order to obtain meaningful terms, one needs to let the size of the noise to go zero asymptotically. This is reflected in our expansions. The results have application to Cornish-Fi ..."
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The paper considers Edgeworth expansions for estimators of volatility. Unlike the usual exapsions, we have found that in order to obtain meaningful terms, one needs to let the size of the noise to go zero asymptotically. This is reflected in our expansions. The results have application to Cornish

Large Deviations for Small Noise Diffusions with Discontinuous Statistics

by Michelle Boué, Paul Dupuis, Richard S. Ellis
"... This paper proves the large deviation principle for a class of non-degenerate small noise diffusions with discontinuous drift and with state-dependent diffusion matrix. The proof is based on a variational representation for functionals of strong solutions of stochastic differential equations and on ..."
Abstract - Cited by 7 (3 self) - Add to MetaCart
This paper proves the large deviation principle for a class of non-degenerate small noise diffusions with discontinuous drift and with state-dependent diffusion matrix. The proof is based on a variational representation for functionals of strong solutions of stochastic differential equations

THE SMALL NOISE LIMIT OF ORDER-BASED DIFFUSION PROCESSES

by Benjamin Jourdain, Julien Reygner , 2013
"... Abstract. We introduce order-based diffusion processes as the solutions to multidimensional stochastic differential equations, with drift coefficient depending only on the ordering of the coordinates of the process and diffusion matrix proportional to the identity. These processes describe the evolu ..."
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to the discontinuity of the drift coefficient, the corresponding ordinary differential equations are ill-posed. Therefore, the small noise limit of order-based diffusion processes is not covered by the classical Freidlin-Wentzell theory. The description of this limit is the purpose of this article. We first give a
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