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Maslowski B.: Lower estimates of transition densities and bounds on exponential ergodicity for stochastic PDE’s
"... A formula for the transition density of a Markov process defined by an infinitedimensional stochastic equation is given in terms of the Ornstein–Uhlenbeck bridge and a useful lower estimate on the density is provided. As a consequence, uniform exponential ergodicity and Vergodicity are proved for ..."
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Cited by 5 (2 self)
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A formula for the transition density of a Markov process defined by an infinitedimensional stochastic equation is given in terms of the Ornstein–Uhlenbeck bridge and a useful lower estimate on the density is provided. As a consequence, uniform exponential ergodicity and Vergodicity are proved for a large class of equations. We also provide computable bounds on the convergence rates and the spectral gap for the Markov semigroups defined by the equations. The bounds turn out to be uniform with respect to a large family of nonlinear drift coefficients. Examples of finitedimensional stochastic equations and semilinear parabolic equations are given. 1. Introduction. The
Euclidean Gibbs measures of interacting quantum anharmonic oscillators
 985– 1047. MR 2317266 (2008d:82009
, 2007
"... Abstract. A rigorous description of the equilibrium thermodynamic properties of an infinite system of interacting νdimensional quantum anharmonic oscillators is given. The oscillators are indexed by the elements of a countable set L ⊂ Rd, possibly irregular; the anharmonic potentials vary from site ..."
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Abstract. A rigorous description of the equilibrium thermodynamic properties of an infinite system of interacting νdimensional quantum anharmonic oscillators is given. The oscillators are indexed by the elements of a countable set L ⊂ Rd, possibly irregular; the anharmonic potentials vary from site to site and the interaction has infinite range. The description is based on the representation of the Gibbs states in terms of path measures – the so called Euclidean Gibbs measures. It is proven that: (a) the set of such measures Gt is nonvoid and compact; (b) every µ ∈ Gt obeys an exponential integrability estimate, the same for the whole set Gt; (c) every µ ∈ Gt has a LebowitzPresutti type support; (d) Gt is a singleton at high temperatures. The case of attractive interaction and ν = 1 is studied in more detail. We prove that: (a) Gt > 1 at low temperatures; (b) Gt  = 1 due to quantum effects and at a nonzero external field. Thereby, a qualitative theory of phase transitions and quantum effects, which interprets most important experimental data known
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"... Stock market trading rule discovery using technical charting heuristics ..."
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Stock market trading rule discovery using technical charting heuristics
Poisson cluster measures: quasiinvariance,
, 803
"... integration by parts and equilibrium stochastic dynamics ..."
© Hindawi Publishing Corp. ON GROMOV’S THEOREM AND L 2HODGE DECOMPOSITION
, 2002
"... Using a functional inequality, the essential spectrum and eigenvalues are estimated for Laplacetype operators on Riemannian vector bundles. Consequently, explicit upper bounds are obtained for the dimension of the corresponding L 2harmonic sections. In particular, some known results concerning Gro ..."
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Using a functional inequality, the essential spectrum and eigenvalues are estimated for Laplacetype operators on Riemannian vector bundles. Consequently, explicit upper bounds are obtained for the dimension of the corresponding L 2harmonic sections. In particular, some known results concerning Gromov’s theorem and the L 2Hodge decomposition are considerably improved. 2000 Mathematics Subject Classification: 58J50, 58J65. 1. Introduction. Recall