In this paper, we prove that the laws of interacting brownian particles are characterized as Gibbs fields on pathspace associated to an explicit class of hamiltonian functionals. More generally, we show that a large class of Gibbs fields on pathspace corresponds to brownian diffusions. Some applications to time reversal in the stationary and non stationary case are presented.
In this paper, we prove that the laws of interacting Brownian particles are characterized as Gibbs fields on pathspace associated to an explicit class of Hamiltonian functionals. More generally, we show that a large class of Gibbs fields on pathspace corresponds to Brownian diffusions. Some applications to time reversal in the stationary and non stationary case are presented.
We develop the theory of invariant random fields in vector bundles. The spectral decomposition of an invariant random field in a homogeneous vector bundle generated by an induced representation of a compact connected Lie group G is obtained. We discuss an application to the theory of relic radiation, where G = SO(3). A theorem about equivalence of two different groups of assumptions in cosmological theories is proved.
Let, for each t∈T, ψ(t, ۔) be a random measure on the Borel σ-algebra in ℝd such that Eψ(t, ℝd)k < ∞ for all k and let (t, ۔) be its characteristic function. We call the function (t1,…, tl ; z1,…, zl) = of arguments l∈ ℕ, t1, t2… ∈T, z1, z2∈ ℝd the covaristic of the measure-valued random function (MVRF) ψ(۔, ۔). A general limit theorem for MVRF's in terms of covaristics is proved and applied to functions of the kind ψn(t, B) = µ{x : ξn(t, x) ∈B}, where μ is a nonrandom finite measure...
Let, for each t ∈ T, ψ(t, ۔) be a random measure on the Borel σ-algebra in ℝd such that Eψ(t, ℝd)k < ∞ for all kand let (t, ۔) be its characteristic function. We call the function (t1,…, tl ; z1,…, zl) = of argumentsl ∈ ℕ, t1, t2… ∈ T, z1, z2 ∈ ℝd the covaristic of the measure-valued random function (MVRF) ψ(۔, ۔). A general limit theorem for MVRF's in terms of covaristics is proved and applied to functions of the kind ψn(t, B) = µ{x : ξn(t, x) ∈ B}, where μ is a nonrandom finite measure...
(Local) self-similarity is a seminal concept, especially for Euclidean random fields. We study in this paper the extension of these notions to manifold indexed fields. We give conditions on the (local) self-similarity index that ensure the existence of fractional fields. Moreover, we explain how to identify the self-similar index. We describe a way of simulating Gaussian fractional fields.
(Local) self-similarity is a seminal concept, especially for Euclidean random fields. We study in this paper the extension of these notions to manifold indexed fields. We give conditions on the (local) self-similarity index that ensure the existence of fractional fields. Moreover, we explain how to identify the self-similar index. We describe a way of simulating Gaussian fractional fields.
A solution to the marginal problem is obtained in a form of parametric exponential (Gibbs–Markov) distribution, where the unknown parameters are obtained by an optimization procedure that agrees with the maximum likelihood (ML) estimate. With respect to a difficult performance of the method we propose also an alternative approach, providing the original basis of marginals can be appropriately extended. Then the (numerically feasible) solution can be obtained either by the maximum pseudo-likelihood...
We define multifractional Brownian fields indexed by a metric space, such as a manifold with its geodesic distance, when the distance is of negative type. This construction applies when the Brownian field indexed by the metric space exists, in particular for spheres, hyperbolic spaces and real trees.
Let P1, ..., Pd be commuting Markov operators on L∞(X,F,μ), where (X,F,μ) is a probability measure space. Assuming that each Pi is either conservative or invertible, we prove that for every f in Lp(X,F,μ) with 1 ≤ p < ∞ the averagesAnf = (n + 1)-d Σ0≤ni≤n P1n1 P2n2 ... Pdnd f (n ≥ 0)converge almost everywhere if and only if there exists an invariant and equivalent finite measure λ for which the Radon-Nikodym derivative v = dλ/dμ is in the dual space Lp'(X,F,μ). Next we study the case in...