ON REGULARITY OF TRANSITION PROBABILITIES AND INVARIANT MEASURES OF SINGULAR DIFFUSIONS UNDER MINIMAL CONDITIONS

By Vladimir Bogachev, Nicolai V. Krylov, Michael Röckner. 2001

263 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/6699910d7488850325207b4fefb54b1296a0d767

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

On large deviations of coupled diffusions with time scale separation (2013, background): “16 in Bogachev, Krylov and Röckner [8],”
Steady States of Fokker–Planck Equations: I. Existence (2015, background): “The other one is a derivative formula which will be useful in conducting measure estimates of a stationary measure on sublevel sets of a Lyapunov-like function using differential inequalities.”
Uniqueness of solutions to weak parabolic equations for measures (2007, methodology): “We first recall the following two results from [6] and [1].”
Distances between transition probabilities of diffusions and applications to nonlinear Fokker–Planck–Kolmogorov equations (2016, background): “Therefore (see [7]), for every ball U and every compact interval [τ1, τ2] ⊂ (0, τ), there exists a number C̃(U,α, τ, τ1, τ2) bounding the Hölder norm (in both variables) of the density of the solution μ = F (σ) on U × [τ1, τ2].”
Ergodicity of stochastic differential equations with jumps and singular coefficients (2017, background): “11) are also studied in [5, 6, 10], see also [46].”
Elliptic equations for invariant measures on finite and infinite dimensional manifolds (2001, background): “1) have been obtained in [11,12] and [13].”
On Parabolic Equations for Measures (2008, methodology): “Moreover, according to [3], we can pick a further subsequence (denoted again by μ) for which the densities %n converge locally uniformly.”
Global properties of invariant measures (2005, background): “Local versions of the following proposition are contained in [4], where regularity results in fractional Sobolev spaces are also obtained for aij = ij .”
Elliptic and parabolic equations for measures (2009, background): “It follows from the proof in [33] that for every compact set E ⊂ Ω× (0,+∞), there exists a constant C(E) such that”