ON RELATIONS BETWEEN<i>A PRIORI</i>BOUNDS FOR MEASURES ON CONFIGURATION SPACES

Kondratiev, Yuri; Kuna, Tobias; Kutoviy, Oleksandr

doi:10.1142/s0219025704001578

Cited by 9 publications

(4 citation statements)

References 14 publications

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“…to Θ. However, by [KKK04], [Kun99], one has µ(Θ) = 1 for every probability measure µ on Γ whose correlation functions k (n) µ , n ∈ N, fulfill the so-called Ruelle bound, i.e., there is a C > 0 such that k (n) µ ≤ C n for every n ∈ N. This holds, for instance, for Gibbs measures w.r.t. superstable, lower and upper regular potentials, cf.…”

Section: A Probabilistic Approachmentioning

confidence: 95%

Equilibrium Kawasaki Dynamics of Continuous Particle Systems

Kondratiev

Lytvynov

Röckner

2007

Infin. Dimens. Anal. Quantum. Probab. Relat. Top.

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An infinite particle system of independent jumping particles is considered. Their constructions is recalled, further properties are derived, the relation with hierarchical equations, Poissonian analysis, and second quantization are discussed. The hydrodynamic limit for a general initial distribution satisfying a mixing condition is derived. The large time asymptotic is computed under an extra assumption.

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Section: A Probabilistic Approachmentioning

confidence: 95%

Equilibrium Kawasaki Dynamics of Continuous Particle Systems

Kondratiev

Lytvynov

Röckner

2007

Infin. Dimens. Anal. Quantum. Probab. Relat. Top.

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“…We emphasize that for essentially all classes of Gibbs measures in equilibrium statistical mechanics of interacting infinite particle systems in R d the set ad has measure one (cf. [15]). In particular, this is true for Ruelle measures (see [20]).…”

Section: Diffusions In Random Mediamentioning

confidence: 99%

Strong solutions of stochastic equations with singular time dependent drift

Крылов

Röckner

2004

Probab. Theory Relat. Fields

398

468

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We prove existence and uniqueness of strong solutions to stochastic equations in domains G ⊂ R d with unit diffusion and singular time dependent drift b up to an explosion time. We only assume local L q L p -integrability of b in R × G with d/p + 2/q < 1. We also prove strong Feller properties in this case. If b is the gradient in x of a nonnegative function ψ blowing up as G x → ∂G, we prove that the conditions 2D t ψ ≤ Kψ, 2D t ψ + ψ ≤ Ke εψ , ε ∈ [0, 2), imply that the explosion time is infinite and the distributions of the solution have sub Gaussian tails.

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“…The aim of this paper is to study the moment equations for the BDLP model by methods of functional analysis and analysis on the configuration spaces developed in [13], [14], [15] and already applied to the non-equilibrium birth-and-death type continuous space stochastic dynamics in [16], [18]. We obtain some rigorous results concerning the existence and properties of the solution for different classes of initial conditions.…”

Section: Introductionmentioning

confidence: 99%