transport Equations

On uniform positivity of transition densities

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

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

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

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

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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

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

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