Through a Metropolis-like algorithm with single step computational cost of order one, we build a Markov chain that relaxes to the canonical Fermi statistics for k non-interacting particles among m energy levels. Uniformly over the temperature as well as the energy values and degeneracies of the energy levels we give an explicit upper bound with leading term km ln k for the mixing time of the dynamics. We obtain such construction and upper bound as a special case of a general result on (non-homogeneous)...

In this paper, we consider the problem of estimating the covariation of two diffusion processes when observations are subject to non-synchronicity. Building on recent papers [Bernoulli11 (2005) 359–379, Ann. Inst. Statist. Math.60 (2008) 367–406], we derive second-order asymptotic expansions for the distribution of the Hayashi–Yoshida estimator in a fairly general setup including random sampling schemes and non-anticipative random drifts. The key steps leading to our results are a second-order decomposition...

In the context of self-stabilizing processes, that is processes attracted by their own law, living in a potential landscape, we investigate different properties of the invariant measures. The interaction between the process and its law leads to nonlinear stochastic differential equations. In [S. Herrmann and J. Tugaut. Electron. J. Probab. 15 (2010) 2087–2116], the authors proved that, for linear interaction and under suitable conditions, there exists a unique symmetric limit measure associated...

In the context of self-stabilizing processes, that is processes attracted by their own law, living in a potential landscape, we investigate different properties of the invariant measures. The interaction between the process and its law leads to nonlinear stochastic differential equations. In [S. Herrmann and J. Tugaut. Electron. J. Probab. 15 (2010) 2087–2116], the authors proved that, for linear interaction and under suitable conditions, there...

Kernel functions of stable, self-similar mixed moving averages are known to be related to nonsingular flows. We identify and examine here a new functional occuring in this relation and study its properties. To prove its existence, we develop a general result about semi-additive functionals related to cocycles. The functional we identify, is helpful when solving for the kernel function generated by a flow. Its presence also sheds light on the previous results on the subject.

The aim of the paper is two-fold. First, we investigate the ψ-Bessel potential spaces on ${ℝ}_{0+}^{n+1}$ and study some of their properties. Secondly, we consider the fractional powers of an operator of the form $-A_{\pm }=-\psi \left(D_{x^{\text{'}}}\right)\pm \partial /\left(\partial x_{n+1}\right)$, $(x^{\text{'}},x_{n+1})\in {ℝ}_{0+}^{n+1}$, where $\psi \left(D_{x^{\text{'}}}\right)$ is an operator with real continuous negative definite symbol ψ: ℝⁿ → ℝ. We define the domain of the operator $-{(-A_{\pm })}^{\alpha }$ and prove that with this domain it generates an $L_p$-sub-Markovian semigroup.

Let be a locally compact Hausdorff space. Let $A_i$, i = 0,1,...,N, be generators of Feller semigroups in C₀() with related Feller processes $X_i=X_i\left(t\right),t\ge 0$ and let ${\alpha }_i$, i = 0,...,N, be non-negative continuous functions on with ${\sum }_{i=0}^N{\alpha }_i=1$. Assume that the closure A of ${\sum }_{k=0}^N{\alpha }_k{A}_k$ defined on ${\bigcap }_{i=0}^N\left(A_i\right)$ generates a Feller semigroup T(t), t ≥ 0 in C₀(). A natural interpretation of a related Feller process X = X(t), t ≥ 0 is that it evolves according to the following heuristic rules: conditional on being at a point p ∈ , with probability ${\alpha }_i\left(p\right)$, the process...

In this note we prove that the local martingale part of a convex function f of a d-dimensional semimartingale X = M + A can be written in terms of an Itô stochastic integral ∫H(X)dM, where H(x) is some particular measurable choice of subgradient $$ ∇ f ( x ) off at x, and M is the martingale part of X. This result was first proved by Bouleau in [N. Bouleau, C. R. Acad. Sci. Paris Sér. I Math. 292 (1981) 87–90]. Here we present a new treatment of the problem. We first prove the result for $\tilde{X}=X+ϵB$ x10ff65;...