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Bayesian Analysis of Simple Random Densities
Bayesian nonparametrics Bayesian density estimation.
2012/11/23
A tractable nonparametric prior over densities is introduced which is closed under sampling and exhibits proper posterior asymptotics.
Transition densities for stochastic Hodgkin-Huxley models
Hodgkin-Huxley model degenerate diffusion processes non time homogeneous diffusion processes Malliavin calculus Hormander condition
2012/7/11
We consider a stochastic Hodgkin-Huxley model driven by a periodic signal as model for the membrane potential of a pyramidal neuron. The associated five dimensional diffusion process is a time inhomog...
Local Holder continuity property of the Densities of Solutions of SDEs with Singular Coefficients
Malliavin Calculus non-smooth drift density function Probability
2012/6/21
We prove that the weak solution of a uniformly elliptic stochastic differential equation with locally smooth diffusion coefficient and H\"{o}lder continuous drift has a H\"{o}lder continuous density f...
Small Noise Asymptotics for Invariant Densities for a Class of Diffusions: A Control Theoretic View (with Erratum)
diffusions invariant density small noise limit Hamilton-Jacobi equation viscosity solution
2011/9/2
Abstract: The uniqueness argument in the proof of Theorem 5, p. 483, of "Small noise asymptotics for invariant densities for a class of diffusions: a control theoretic view, J. Math. Anal. and Appl. (...
Distances and Riemannian metrics for multivariate spectral densities
Riemannian metrics multivariate spectral densities Optimization and Control
2011/8/26
Abstract: We first introduce a class of divergence measures between power spectral density matrices. These are derived by comparing the suitability of different models in the context of optimal predic...
Invariant Measures with Bounded Variation Densities for Piecewise Area Preserving Maps
Bounded Variation Piecewise Area Preserving Maps Dynamical Systems
2011/8/30
Abstract: We investigate the properties of absolutely continuous invariant probability measures (ACIPs) for piecewise area preserving maps (PAPs) on $\mathbb{R}^d$. This class of maps unifies piecewis...
An inequality for the distance between densities of free convolutions
densities of free convolutions inequality Probability
2011/8/24
Abstract: It is shown that under some conditions the distance between densities of free convolutions of two pairs of probability measures is smaller than the maximum of the Levy distance between the c...
Homogenizations of integro-differential equations with L{é}vy operators with asymmetric and degenerate densities
Homogenizations of integro-differential equations L{é}vy operators asymmetric degenerate densities
2011/1/21
We consider periodic homogenization problems for the L´evy operators with asymmetric L´evy densities. The formal asymptotic expansion used for the -stable (symmetric) L´evy operator...
On local analytic expansions of densities in the context of (micro-)hypoelliptic and classes of semi-elliptic equations
On local analytic expansions of densities context of (micro-)hypoelliptic classes of semi-elliptic equations
2011/1/17
Explicit representations of densities for linear parabolic partial differential equations are useful in order to design computation schemes of high accuracy for a considerable class of diffusion model...
On the structure and probabilistic interpretation of Askey-Wilson densities and polynomials with complex parameters
Askey-Wilson densities polynomials complex parameters
2010/11/11
We give equivalent forms of Askey-Wilson (AW) polynomials expressing them with a help of Al-Salam-Chihara polynomials. After restricting parameters of AW polynomials to complex conjugate pairs we giv...
We de ne the limiting density of a minor-closed family of simple graphs F to be the smallest
number k such that every n-vertex graph in F has at most kn(1+o(1)) edges, and we investigate
the set of ...
Derivation of an integral of Boros and Moll via convolution of Student t-densities
Quartic integral Student t-density
2010/12/6
We show that the evaluation of an integral considered by Boros and Moll is a special case of a convolution result about Student t-densities obtained by the authors in 2008.
Inversion of analytic characteristic functions and infinite convolutions of exponential and Laplace densities
Infinite convolutions characteristic function entire functions
2010/12/1
We prove that certain quotients of entire functions are characteristic functions. Under some conditions,the probability measure corresponding to a characteristic function of that type has a density wh...
Bayesian Predictive Densities Based on Latent Information Priors
essentially complete class Jeffreys prior Kullback-Leibler divergence
2010/12/13
Construction methods for prior densities are investigated from a predictive viewpoint. redictive densities for future observables are constructed by using observed data. The simultaneous distribution ...
For a large class of self-similar sets F in Rd, analogues of the higher order mean curvatures
of differentiable submanifolds are introduced, in particular, the fractal Gauss-type curvature.
They are...