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Fractal Interpolation Densities
AbstractNecessary and sufficient conditions are found under which a continuous fractal interpolation function is the distribution density of a...
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Bayesian Filtering for Gaussian Densities
In the previous chapter, we considered dynamic inverse problems where the posterior density is updated sequentially as new observations become...
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Comparing weighted densities
In this paper we study inequalities between weighted densities of sets of natural numbers corresponding to different weight functions. Depending on...
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Conditional Gaussian Densities
Gaussian probability distributions are the workhorse in Bayesian scientific computing, providing a well understood subclass of distributions that...
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Posterior Densities, Ill-Conditioning,and Classical Regularization
Now that the basic principles guiding the design of likelihoods and priors have been introduced, we are ready to welcome on the stage the main...
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Leptin Densities in Amenable Groups
Consider a positive Borel measure on a locally compact group. We define a notion of uniform density for such a measure, which is based on a group...
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Typical large graphs with given edge and triangle densities
The analysis of large simple graphs with extreme values of the densities of edges and triangles has been extended to the statistical structure of...
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Malliavin calculus and densities for singular stochastic partial differential equations
We study Malliavin differentiability of solutions to sub-critical singular parabolic stochastic partial differential equations (SPDEs) and we prove...
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Cyclic reduction densities for elliptic curves
For an elliptic curve E defined over a number field K , the heuristic density of the set of primes of K for which E has cyclic reduction is given by...
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An adaptive FEM for the elastic transmission eigenvalue problem with different elastic tensors and different mass densities
The elastic transmission eigenvalue problem, arising from the inverse scattering theory, plays a critical role in the qualitative reconstruction...
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The Analysis of Particle Number Densities in Dilute Gas-Particle Flows: The Eulerian and Lagrangian Methods
AbstractThe predictions of the conditional quadrature methods of moments, conventional Lagrangian, and fully Lagrangian (FLA) approaches to the...
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Transition densities of spectrally positive Lévy processes
We deduce the asymptotic behavior of transition densities for a large class of spectrally one-sided Lévy processes of unbounded variation satisfying...
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Existence of weak solutions to a diffuse interface model involving magnetic fluids with unmatched densities
In this article we prove the global existence of weak solutions for a diffuse interface model in a bounded domain (both in 2D and 3D) involving...
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One-Dimensional Fokker–Planck Equations and Functional Inequalities for Heavy Tailed Densities
We present and discuss connections between the problem of trend to equilibrium for one-dimensional Fokker–Planck equations modeling socio-economic...
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Choice of Approximation Bases Used in Computational Functional Algorithms for Approximating Probability Densities on the Basis of Given Sample
AbstractIn this paper we formulate requirements for choosing approximation bases when constructing cost-effective optimized computational (numerical)...
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Manifolds, Tensors and Densities
The purpose of this chapter is to summarize the basic facts about manifolds and map**s between them which are most frequently used in the theory of...