Kolmogorov Problems on Equations for Stationary and Transition Probabilities of Diffusion Processes

Smoothness and regularity of solutions to PDEs (35B65) Existence problems for PDEs: global existence, local existence, non-existence (35A01) PDEs with randomness, stochastic partial differential equations (35R60) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Fokker-Planck equations (35Q84) PDEs with measure (35R06)

Cites Work

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Well-posedness of multidimensional diffusion processes with weakly differentiable coefficients
Stochastic stability of differential equations. With contributions by G. N. Milstein and M. B. Nevelson
On \(C^1\), \(C^2\), and weak type-\((1,1)\) estimates for linear elliptic operators. II
Generalized second order differential operators and their lateral conditions
On nonuniqueness of solutions to elliptic equations for probability measures
Elliptic equations for measures: regularity and global bounds of densities
Lectures on diffusion problems and partial differential equations. Notes by Pl. Muthuramalingam, Tara R. Nanda
Harmonic spaces associated with adjoints of linear elliptic operators
The Poisson equation and estimates for distances between stationary distributions of diffusions
On non-uniqueness of probability solutions to the two-dimensional stationary Fokker-Planck-Kolmogorov equation
Stationary Fokker-Planck-Kolmogorov equations
Convergence in variation of solutions of nonlinear Fokker-Planck-Kolmogorov equations to stationary measures
Regularity of invariant measures on finite and infinite dimensional spaces and applications
Existence of flows for linear Fokker-Planck-Kolmogorov equations and its connection to well-posedness
Existence and regularity of infinitesimally invariant measures, transition functions and time-homogeneous Itô-SDEs
On the Ambrosio-Figalli-Trevisan superposition principle for probability solutions to Fokker-Planck-Kolmogorov equations
Uniqueness of a probability solution to the Kolmogorov equation with a diffusion matrix satisfying Dini's condition
Representations of solutions to Fokker-Planck-Kolmogorov equations with coefficients of low regularity
Existence and uniqueness of (infinitesimally) invariant measures for second order partial differential operators on Euclidean space
On convergence to stationary distributions for solutions of nonlinear Fokker-Planck-Kolmogorov equations
Degenerate elliptic equations and nonuniqueness of solutions to the Kolmogorov equation
Log-Sobolev-type inequalities for solutions to stationary Fokker-Planck-Kolmogorov equations
Integrability and continuity of solutions to double divergence form equations
On Sobolev regularity of solutions to Fokker-Planck-Kolmogorov equations with drifts in \(L^1\)
Existence and uniqueness of martingale solutions for SDEs with rough or degenerate coefficients
Global properties of invariant measures
Uniqueness of solutions of the Cauchy problem for parabolic equations
Distances between transition probabilities of diffusions and applications to nonlinear Fokker-Planck-Kolmogorov equations
Zur Theorie der stochastischen Prozesse. (Existenz- und Eindeutigkeitssätze.)
Integration of Fokker-Planck's equation in a compact Riemannian space
The parabolic differential equations and the associated semigroups of transformation
The abstract Cauchy problem and Cauchy's problem for parabolic differential equations
On diffusion processes with drift in \(L_d\)
Applications of Zvonkin's transform to stationary Kolmogorov equations
Regularity of solutions to Kolmogorov equations with perturbed drifts
ON REGULARITY OF TRANSITION PROBABILITIES AND INVARIANT MEASURES OF SINGULAR DIFFUSIONS UNDER MINIMAL CONDITIONS
On C¹, C², and weak type-(1,1) estimates for linear elliptic operators
On the Uniqueness of the Cauchy Problem for Parabolic Equations
On uniqueness of probability solutions of the Fokker-Planck-Kolmogorov equation
Fokker–Planck–Kolmogorov Equations
Elliptic and parabolic equations for measures
Global Properties of Transition Probabilities of Singular Diffusions
The generalized Vlasov kinetic equation
Equivalence of the Green's Functions for Diffusion Operators in R n : A Counterexample
On uniqueness of invariant measures for finite- and infinite-dimensional diffusions
A Generalization of Khasminskii's Theorem on the Existence of Invariant Measures for Locally Integrable Drifts
Uniqueness of solutions of elliptic equations and uniqueness of invariant measures of diffusions
Distances between Stationary Distributions of Diffusions and Solvability of Nonlinear Fokker--Planck--Kolmogorov Equations
Ornstein–Uhlenbeck operators and semigroups
Analytic Theory of Itô-Stochastic Differential Equations with Non-smooth Coefficients
Cauchy problems for parabolic equations degenerating at infinity
Zvonkin’s transform and the regularity of solutions to double divergence form elliptic equations
Elliptic equations for invariant measures on finite and infinite dimensional manifolds
On diffusion processes with drift in \(L_{d+1}\)
Kantorovich problem of optimal transportation of measures: new directions of research