Preprint Search

Distribution-Dependent SDEs for Landau Type Equations

Project: A5

Published: Stochastic Processes and their Applications 128 (2018), 595–621

Absolutely continuous solutions for continuity equations in Hilbert spaces

Project: A5

Published: Journal de Mathématiques Pures et Appliquées 128 (2019), 42–86

On SPDE and backward filtering equations for SDE systems (direct approach) - 2

Project: A5, B1

Existence and uniqueness theorems for solutions of McKean-Vlasov stochastic equations

Project: A5, B1

Published: Theory Probab. Math. Statist. No. 103 (2020), 59–101

Yet again on iteration improvement for averaged expected cost control for 1D ergodic diffusions

Project: A5, B1

Published: SIAM J. Control Optim. 58, no. 4 (2020), 2312–2331

Nonlinear Fokker-Planck equations for Probability Measures on Path Space and Path-Distribution Dependent SDEs

Project: A5

Published: Discrete and Continuous Dynamical Systems 39, no. 6 (2019), 3017–3035

Quasi-Linear (Stochastic) Partial Differential Equations with Time-Fractional Derivatives

Project: A5, B1

Published: SIAM Journal on Mathematical Analysis 50, no. 3 (2018), 2588–2607

Convergence in variation of solutions of nonlinear Fokker–Planck–Kolmogorov equations to stationary measures

Project: A5

Published: Journal of Functional Analysis 12 (2019), 3681–3713

Probabilistic representation for solutions to nonlinear Fokker-Planck equations

Project: A5, B1

Published: SIAM Journal on Mathematical Analysis 50, no. 4 (2018), 4246–4260

Continuity equation in LlogL for the 2D Euler equations under the enstrophy measure

Project: A5

Published: Stochastics and Partial Differential Equations: Analysis and Computations 9, no. 2 (2021), 491-509

The Poisson equation and estimates for distances between stationary distributions of diffusions

Project: A5

Published: Journal of Mathematical Sciences 232 (2018), 254–282

Estimates for Invariant Probability Measures of Degenerate SPDEs with Singular and Path-Dependent Drifts

Project: A5

Published: Probab. Theory Relat. Fields 172 (2018), 1181–1214

Space-Distribution PDEs for Path Independent Additive Functionals of McKean-Vlasov SDEs

Project: A5

To appear: Infinite Dimensional Anaysis, Quantum Probability and Related Topics (2020)

Distribution Dependent SDEs with Singular Coefficients

Project: A5

Published: Stochastic Processes and their Applications 129 (2019), 4747—4770

Well-posedness of distribution dependent SDEs with singular drifts

Project: A5, B1

Published: Bernoulli Journal 27, no. 2 (2021), 1131–1158

Bismut Formula for Lions Derivative of Distribution Dependent SDEs and Applications

Project: A5

Published: Journal of Differential Equations 267 (2019), 4745—4777

From nonlinear Fokker-Planck equations to solutions of distribution dependent SDE

Project: A5

Published: Ann. Probab. 48, no. 4 (2020), 1902–1920

Asymptotic Log-Harnack Inequality and Applications for Stochastic Systems of Infinite Memory

Project: A5

Published: Stochastic Processes and their Applications 129 (2019), 4576—4596

Total variation distance estimates via $L^2$-norm for polynomials in log-concave random vectors

Project: A5

Published: International Mathematics Research Notices (2019), DOI: 10.1093/imrn/rnz278

On the Ambrosio–Figalli–Trevisan superposition principle for probability solutions to Fokker–Planck–Kolmogorov equations

Project: A5

Published: Journal of Dynamics and Differential Equations 33, no. 2 (2021), 715-739

Notes: DOI: 10.1007/s10884-020-09828-5

The evolution to equilibrium of solutions to nonlinear Fokker-Planck equation

Project: A5

To appear: Indiana University Mathematical Journal (2021)

Diffusions and PDEs on Wasserstein Space

Project: A5

Linearization of Nonlinear Fokker-Planck Equations and Applications

Project: A5

Published: Journal of Differential Equations, no. 322 (2022), 1-37

On convergence to stationary distributions for solutions of nonlinear Fokker–Planck–Kolmogorov equations

Project: A5

Published: Journal of Mathematical Sciences 1 (2019), 69–84

Upper envelopes of families of Feller semigroups and viscosity solutions to a class of nonlinear Cauchy problems

Project: A5, C5

Published: SIAM Journal of Control and Optimization 59, no. 6 (2021), 4400-4428

Notes: https://doi.org/10.1137/20M1314823

Strong dissipativity of generalized time-fractional derivatives and quasi-linear (stochastic) partial differential equations

Project: B1, A5

Published: Journal of Functional Analysis 281, no. 8 (2021), 34 pp.

Uniqueness for nonlinear Fokker-Planck equations and weak uniqueness for McKean-Vlasov SDEs

Project: A5

Published: Stochastic Partial Differential Equations: Analysis and Computations 9, no. 3 (2021), 702-713

On Kantorovich multimarginal optimal transportation problems with density constraints

Project: A5

Superposition principle for non-local Fokker-Planck-Kolmogorov operators

Project: A5, B1

Published: Probab. Theory Relat. Fields 178, no. 3–4 (2020), 699–733

A Markov process for an infinite interacting particle system in the continuum

Project: A5, B1

Published: Electronic Journal of Probability 26 (2021), 1-53

Pathwise vs. path-by-path uniqueness

Project: A5, B1

Published: Ann. Inst. Henri Poincaré Probab. Stat. 58, no. 3 (2022), 1640–1649

Solutions for nonlinear Fokker-Planck equations with measures as initial data and McKean-Vlasov equations

Project: A5

Published: Journal of Functional Analysis 280, no. 7 (2021), 108926, 1--35

Precise Limit in Wasserstein Distance for Conditional Empirical Measures of Dirichlet Diffusion Processes

Project: A5

Published: J. Funct. Anal. 280, no. 11 (2021), 23 pp

Convergence in Wasserstein Distance for Empirical Measures of Dirichlet Diffusion Processes on Manifolds

Project: A5

Published: J. Eur. Math. Soc. (JEMS) 25, no. 9 (2023), 3695–3725

Donsker-Varadhan large deviations for path-distribution dependent SPDEs

Project: A5

Published: Journal of Mathematical Analysis and Applications 499, no. 1 (2021), Article No. 125000: 32 pp.

Derivative Estimates on Distributions of McKean-Vlasov SDEs

Project: A5

Published: Electron. J. Probab. 26, no. 15 (2021), 12 pp

Bismut Formula for Lions Derivative of Distribution-Path Dependent SDEs

Project: A5

Published: J. Differential Equations 282 (2021), J. Differential Equations

Euler Scheme for Density Dependent Stochastic Differential Equations

Project: A5, B1

Published: Journal of Differential Equations 274 (2021), 996–1014

A Restricted Superposition Principle for (non-)linear Fokker–Planck–Kolmogorov Equations on Hilbert Spaces

Project: A5, B1

To appear: Journal of Evolution Equations (2022)

Well-Posedness for Singular McKean-Vlasov Stochastic Differential Equations

Project: A5

Exponential Convergence in Entropy and Wasserstein for McKean-Vlasov SDEs

Project: A5

To appear: Nonlinear Analysis (2021)

Singular McKean-Vlasov (Reflecting) SDEs with Distribution Dependent Noise

Project: A5

Published: J. Math. Anal. Appl. 514, no. 1 (2022), 21 pp.

McKean-Vlasov SDEs with Drifts Discontinuous under Wasserstein Distance

Project: A5

Published: Discrete and Continuous Dynamical Systems 41, no. 4 (2021), 1667–1679

Mean-field analysis of industry dynamics under financial constraints

Project: A5, B1, C2

The invariance principle for nonlinear Fokker–Planck equations

Project: A5

Published: Journal of Differential Equations 315 (2022), 200–221

Stochastic generalized porous media equations over $\sigma$-finite measure spaces with non-continuous diffusivity function

Project: A5, B1

Published: Potential Anal. 61, no. 4 (2024), 731–773

Distribution Dependent Reflecting Stochastic Differential Equations

Project: A5

Published: Sci. China Math. 66, no. 11 (2023), 2411–2456

Exponential Ergodicity for Singular Reflecting McKean-Vlasov SDEs

Project: A5

Published: Stochastic Processes and their Applications 160 (2023), 265–293

Markov uniqueness and Fokker-Planck-Kolmogorov equations

Project: A5

Published: Festschrift Masatoshi Fukushima, Springer Proceedings in Mathematics and Statistics. In Honor of Masatoshi Fukushima's Beiju (2022)

Nonlinear Fokker–Planck equations with time-dependent coefficients

Project: A5

Published: SIAM Journal on Mathematical Analysis 55, no. 1 (2023), 1–18

Singular Density Dependent Stochastic Differential Equations

Project: A5

Published: Journal of Differential Equations 361 (2023), 562–589

Bismut formula for intrinsic/Lions derivatives of distribution dependent SDEs with singular coefficients

Project: A5

Published: Discrete Contin. Dyn. Syst. 42, no. 9 (2022), 4597–4614

Derivative formula for singular McKean-Vlasov SDEs

Project: A5

Published: Commun. Pure Appl. Anal. 22, no. 6 (2023), 1866–1898

Convergence in Wasserstein distance for empirical measures of semilinear SPDEs

Project: A5

Published: Ann. Appl. Probab. 33, no. 1 (2023), 70–84

Exponential ergodicity for non-dissipative McKean-Vlasov SDEs

Project: A5

Published: Bernoulli  29, no. 2 (2023), 1035–1062

Second order McKean-Vlasov SDEs and kinetic Fokker-Planck-Kolmogorov equations

Project: A5

Published: Discrete Contin. Dyn. Syst. Ser. S 18, no. 10 (2025), 2973-3026

Existence, uniqueness and smoothness for incompressible Navier-Stokes equations

Project: A5

Uniqueness for nonlinear Fokker–Planck equations and for McKean–Vlasov SDEs: The degenerate case

Project: A5

Published: Journal of Functional Analysis 285, no. 4 (2023), Paper No. 109980, 37 pp.

Averaging principle for stochastic complex Ginzburg-Landau equations

Project: A5, B1

Published: Journal of Differential Equations 368 (2023), 58–104

Zvonkin's transform and the regularity of solutions to double divergence form elliptic equations

Project: A5

Published: Comm. Partial Differential Equations 48, no. 1 (2023), 119–149

Operator semigroups in the mixed topology and the infinitesimal description of Markov processes

Project: C5, C7, A5

Published: Journal of Differential Equations 412 (2024), 23–86

Strong convergence of propagation of chaos for McKean-Vlasov SDEs with singular interactions

Project: A5, B1

Published: SIAM Journal on Mathematical Analysis 56, no. 2 (2024), 2661–2713

Path continuity of Markov processes and locality of Kolmogorov operators

Project: A5, B1

Published: Stochastics and Partial Differential Equations: Analysis and Computations 12, no. 2 (2024), 1100–1140

A Markov process for a continuum infinite particle system with attraction

Project: A5

Published: Electronic Journal of Probability 28 (2023), Article number 67

On the ergodicity of nonlinear Fokker-Planck flows in $L^1(\mathbb{R}^d)$

Project: A5, B1

Published: Ukrainian Mathematical Journal 77, no. 4 (2025)

Nonlinear Fokker-Planck equations with fractional Laplacian and McKean-Vlasov SDEs with Lévy-Noise

Project: A5, B1

Published: Probab. Theory Relat. Fields 189, no. 3-4 (2024), 849−878

Strong Feller semigroups and Markov processes: A counter example

Project: A5, B1

Published: Stochastics and Partial Differential Equations: Analysis and Computations 12, no. 2 (2024), 968–983

Ornstein-Uhlenbeck type processes on Wasserstein space

Project: A5

Published: Stochastic Processes and their Applications 172 (2024), Article number 104339

On nonlinear Markov processes in the sense of McKean

Project: A5

Published: J. Theoret. Probab. 38, no. 3 (2025), 54 pp.

Kolmogorov problems on equations for stationary and transition probabilities of diffusion processes

Project: A5

Published: Theory Probab. Appl. 68, no. 3 (2023), 342–369

Entropy Estimate Between Diffusion Processes and Application to McKean-Vlasov SDEs

Project: A5

Convergence in Wasserstein distance for empirical measures of non-symmetric subordinated diffusion processes

Project: A5

Published: Stochastic Process. Appl 198, no. 104969 (2026)

Nonlinear Fokker--Planck--Kolmogorov equations as gradient flows on the space of probability measures

Project: A5

Published: J. Evol. Equ. 26, no. 2 (2026), 53

Nonlocal, nonlinear Fokker–Planck equations and nonlinear martingale problems

Project: A5

Uniqueness of distributional solutions to the 2D vorticity Navier–Stokes equation and its associated nonlinear Markov process

Project: A5

Published: Journal of the European Mathematical Society (2025)

Notes: DOI: 10.4171/JEMS/1664. Published online first.

Compound Poisson particle approximation for McKean-Vlasov SDEs

Project: A5

Published: IMA Journal of Numerical Analysis (2025)

Notes: https://doi.org/10.1093/imanum/drae095

Nonlinear Dirichlet forms associated with quasiregular mappings

Project: A5

Published: Potential Anal. 62, no. 3 (2025), 509–533

Weighted $L^1$-semigroup approach for nonlinear Fokker–Planck equations and generalized Ornstein–Uhlenbeck processes

Project: A5

Entropy estimate for degenerate SDEs with applications to nonlinear kinetic Fokker-Planck equations

Project: A5

Published: Journal of Mathematical Analysis and Applications 56, no. 4 (2024), 5330–5349

Probability distance estimates between diffusion processes and applications to singular McKean-Vlasov SDEs

Project: A5

Published: Journal of Differential Equations 420 (2025), 376–399

Functional inequalities for brownian motion on manifolds with sticky-reflecting boundary diffusion

Project: A5

Published: Probab. Theory Relat. Fields (2024)

Well-posedness of density dependent SDE driven by $\alpha$-stable process with Hölder drifts

Project: A5

Published: Stochastic Processes and their Applications 164 (2023), 416–442

Diffusion Processes on $p$-Wasserstein Space over Banach Space

Project: A5

Strong solutions to McKean–Vlasov SDEs associated to a class of degenerate Fokker–Planck equations with coefficients of Nemytskii-type

Project: A5, B1

Published: Probability Theory and Related Fields (2025)

$p$-Brownian motion and the $p$-Laplacian

Project: A5, B1

Published: Ann. Probab. 54, no. 4 (2026), 1877–1907

The stochastic evolution of an infinite population with logistic-type interaction

Project: A5

Published: Electronic Journal of Probability 2026, Vol. 31, paper no. 130, 1-57. (2017)

Heat kernel estimates for nonlocal kinetic operators

Project: A5

Heat kernel estimates for kinetic SDEs with drifts being unbounded and in Kato's class

Project: A5

Published: Bernoulli 31, no. 2 (2025), 1402–1427

Construction of Hunt processes by the Lyapunov method and applications to generalized Mehler semigroups

Project: A5

Published: J. Differential Equations 450 (2026)

Strong solutions to degenerate SDEs and uniqueness for degenerate Fokker-Planck equations

Project: A5

To appear: Stochastics and Partial Differential Equations. Analysis and Computations (2025)

Asymptotic behaviour of solutions to Fokker-Planck-Kolmogorov equations

Project: A5

Published: NoDEA Nonlinear Differential Equations Appl. 32, no. 93 (2025), 18 pp

The superposition principle for solutions to Fokker-Planck-Kolmogorov equations with potential terms

Project: A5

Published: Pure Appl. Funct. Anal. 11 (2026), no. 3, 511–527. (2017)

Nonlinear Fokker–Planck equations as smooth Hilbertian gradient flows

Project: A5

Published: Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 36, no. 1 (2025), 199-223

Row and column detection complexities of character tables

Project: C6, A5

The fluctuation behaviour of the stochastic point vortex model with common noise

Project: A5, B1

Published: Potential Anal. 64, no. 4 (2026), 62

Distribution dependent SDEs with singular interactions: Well-posedness and regularity

Project: A5

McKean-Vlasov equations and nonlinear Fokker-Planck equations with critical sigular Lorentz kernels

Project: A5

Stochastic intrinsic gradient flows on the Wasserstein space

Project: A5

The Leibenson process

Project: A5

Infinite-dimensional nonlinear stationary Fokker–Planck–Kolmogorov equations

Project: A5

To appear: Advanced Nonlinear Studies (2026)

Regularization of the superposition principle: Potential theory meets Fokker-Planck equations

Project: A5, B1

Non-Uniqueness for Nonlinear Fokker--Planck Equations and Their Associated Distribution-Dependent SDEs

Project: A5, B1

Uniqueness for nonlinear Fokker-Planck equations with general diffusion terms and their associated nonlinear Markov processes

Project: A5

On Solutions to Graphon McKean-Vlasov SDEs of Nemytskii-type

Project: A5