Uniformly Integrable Operators and Large Deviations for Markov Processes

By Liming Wu. 2000

122 citations recorded by the source corpus.

Subfields: Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d0f30e3d169babf7d01d7a8bd11b5e139d702657

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Finance

In Mathematical Physics

Citations in the corpus

A simple proof of the Poincaré inequality for a large class of probability measures (2008, methodology): “assumptions it was proved by Wu ([8]) using spectral methods.”
Hypercontractivity and applications for stochastic Hamiltonian systems (2017, background): “SHS)” in probability theory (see [22]), and the distribution density of the solution solves the kinetic Fokker-Planck equation (see [14]).”
Geometric ergodicity of the Bouncy Particle Sampler (2018, background): “It is also possible to consider moderate deviation [22, 13] or large deviation principle [49, 29] 3.”
Rate of convergence for ergodic continuous Markov processes : Lyapunov versus Poincaré (2007, methodology): “The fact that a Lyapunov condition furnishes some Poincaré inequality in the symmetric case is already known see Wu [34, 36], but the techniques used by Wu are different and rely mainly on spectral ideas.”
Large and moderate deviations and exponential convergence for stochastic damping Hamiltonian systems (2001, methodology): “By an extension of the G artner–Ellis theorem (see Wu, 1991,1992,2000), if one can prove that ∀(fn)⊂ bB decreasing to zero pointwisely on E: K ′(fn)→ 0; (A.3) then the good upper bound [(a.1)+(a.3)] in Theorem 2.1 holds uniformly for z ∈ K ′ with J substituted by the Legendre transformation ( K…”
Bernstein type's concentration inequalities for symmetric Markov processes (2010, unknown): “(1.1)”
Functional Inequalities and Spectrum Estimates: The Infinite Measure Case (2002, background): “4), we introduce the notion of f-uniform integrability which generalizes Wu’s uniform integrability [15] Definition 3.”
Transportation-information inequalities for Markov processes (2007, background): “It is proved in [43, 44] that in the symmetric case, Iu(r) is exactly the rate function governing the large deviation principle of 1 t ∫ t 0 u(Xs) ds for bounded u.”
On hyperboundedness and spectrum of Markov operators (2014, background): “Several attempts have been made to find a counterexample or to prove Høegh-Krohn and Simon’s conjecture, but extra assumptions were always needed, see for instance the papers of Aida [6], Mathieu [7], Wu [8], Hino [9,10], Cattiaux [11], Wang [12], Gong and Wu [13] and the bibliographical comments gi”
FUNCTIONAL INEQUALITIES, SEMIGROUP PROPERTIES AND SPECTRUM ESTIMATES (2000, background): “symmetric Dirichlet form (see section 2). Following [ 64 ], we call a linear operator P on Lp(„)(p ‚ 1) Lp-uniformly integrable, if supkfkp=1 „(jPfj p 1fjPfj>rg) ! 0 as r ! 1.”
Essential spectral radius for Markov semigroups (I): discrete time case (2004, background): “5 in [46], for the good upper bound of large deviations in part (a) w.”
Harnack inequality and applications for stochastic evolution equations with monotone drifts (2008, background): “The compactness of Pt also follows from the [38].”
Spectral gap of positive operators and applications (2000, methodology): “positive. Applying Lemma 3.5 in [32] to the Markov operator Pf = 1 rsp(π)φ π(φf ) with invariant measure α = φψµ as in the proof of Corollary 3.3 in [ 32 ], we obtain Perron– Frobenius type theorem.”