This paper addresses the problem of accurate voxel-level estimation of tissue proportions in the human brain magnetic resonance imaging (MRI). Due to the finite resolution of acquisition systems, MRI voxels can contain contributions from more than a single tissue type. The voxel-level estimation of this fractional content is known as partial volume coefficient estimation. In the present work, t...

We study a linear recursion with random Markov-dependent coefficients. In a “regular variation in, regular variation out” setup we show that its stationary solution has a multivariate regularly varying distribution. This extends results previously established for i.i.d. coefficients.

We prove a few interesting inequalities for Lorentz polynomials. A highlight of this paper states that the Markov-type inequality max x∈[−1,1] |f (x)| ≤ n max x∈[−1,1] |f(x)| holds for all polynomials f of degree at most n with real coefficients for which f ′ has all its zeros outside the open unit disk. Equality holds only for f(x) := c((1± x) − 2n−1) with a constant 0 6= c ∈ R. This should be...

We compute some dependence coefficients for the stationary Markov chain whose transition kernel is the Perron-Frobenius operator of an expanding map T of [0, 1] with a neutral fixed point. We use these coefficients to prove a central limit theorem for the partial sums of f ◦ T , when f belongs to a large class of unbounded functions from [0, 1] to R. We also prove other limit theorems and momen...

Dielectric constants have been determined for dimethylsiloxane chains (CH3)3Si[OSi(CHJ210Si(CH3)3 in the thermodynamically good solvent cyclohexane and in the undiluted state, for degrees of polymerization x + 1 ranging from lQ2 to 1/nm 2 (where <,...2> is the mean-...

The joint distribution of sequences (f`(P`(n)))n∈N, ` = 1, 2, . . . , d and (f`(P`(p)))p∈P respectively, where f` are q`-additive functions and P` polynomials with integer coefficients, is considered. A central limit theorem is proved for a larger class of q` and P` than by Drmota [3]. In particular, the joint limit distribution of the sum-of-digits functions sq1 (n), sq2 (n) is obtained for ar...

The Donsker-Varadhan rate functional I(μ) for Markov processes has a simple form in the case that the generator of the process is self-adjoint, or equivalently, that the Markov process is reversible. In particular, in the case of a reversible diffusion generated by a secondorder elliptic operator L on a compact manifold, this allows one to give a simple necessary and sufficient criterion on the...

Using the coupling method and Girsanov’s theorem, we study the strong Feller property and irreducibility for the transition probabilities of stochastic differential equations with non-Lipschitz and monotone coefficients. Then, the exponential ergodicity and the spectral gap for the corresponding transition semigroups are obtained under fewer assumptions.

The existing q-Markov COVER realization theory does not take into account the problems of arithmetic errors due to both the quantization of states and coefficients of the reduced order model. All q-Markov COVERs allow some freedom in the choice of parameters. In this paper we exploit this freedom in the existing theory to optimize the models with respect to thes,_ finite wordlength effects. *De...

Let X be the minimal diffusion associated with a uniformly elliptic differential operator L on a bounded subdomain of Rd, with C2 boundary. Under the only assumption that the coefficients of L be Hölder continuous, we prove all the standard quasistationary limit theorems (cf. Markov chain theory). Moreover, we show that the laws of X, conditioned on explosion occuring after time s, converge in ...