World's Best Scientists 2026 revealed!

D-Index & Metrics

Mathematics

D-Index
58
Citations
15671
World Ranking
624
National Ranking
314

Research.com Recognitions

  • 2007 - Fellow of the Royal Society of Edinburgh
  • 2004 - Steele Prize for Seminal Contribution to Research
  • 1993 - Fellow of the American Academy of Arts and Sciences

Overview

Nicolai V Krylov is affiliated with the University of Minnesota in the United States and has a research focus spanning mathematics and computer science. Their work prominently features applied mathematics, computational theory, and mathematical physics, reflecting an integration of mathematical approaches with theoretical and practical applications.

The scientist's research emphasizes advanced mathematical modeling, nonlinear partial differential equations, and stochastic processes with financial applications. They have contributed extensively to topics including advanced harmonic analysis, differential equations and boundary problems, and advanced mathematical physics problems.

They have authored numerous papers published in a variety of academic journals and venues. Key recent papers include:

  • On stochastic equations with drift in Ld, 2021, The Annals of Probability
  • Elliptic equations with VMO a, b∈ Ld, and c∈ Ld/2, 2020, Transactions of the American Mathematical Society
  • On Time Inhomogeneous Stochastic Itô Equations with Drift in LD+1, 2021, Ukrainian Mathematical Journal
  • On diffusion processes with drift in Ld, 2020, Probability Theory and Related Fields
  • On strong solutions of Itô's equations with σ∈ Wd1 and b∈ Ld, 2021, The Annals of Probability

They have published frequently in venues such as arXiv (Cornell University), Stochastic Processes and their Applications, Stochastic Partial Differential Equations Analysis and Computations, The Annals of Probability, and Journal of Mathematical Sciences.

Collaboration has featured prominently in their work, with frequent coauthors including:

  • István Gyöngy
  • R. Z. Khas'minskiĭ
  • Hongjie Dong
  • R R Abdulin
  • С. Л. Самсонович

Krylov's recognition includes awards such as the Fellow of the Royal Society of Edinburgh (2007), the Steele Prize for Seminal Contribution to Research (2004), and Fellowship of the American Academy of Arts and Sciences (1993).

Best Publications

  • Controlled Diffusion Processes

    Nicolai V. Krylov

  • Stochastic evolution equations

    N. V. Krylov;B. L. Rozovskii

  • A CERTAIN PROPERTY OF SOLUTIONS OF PARABOLIC EQUATIONS WITH MEASURABLE COEFFICIENTS

    N V Krylov;M V Safonov

  • BOUNDEDLY NONHOMOGENEOUS ELLIPTIC AND PARABOLIC EQUATIONS IN A DOMAIN

    N V Krylov

  • Strong solutions of stochastic equations with singular time dependent drift

    Nicolai V Krylov;M. Röckner

  • Nonlinear elliptic and parabolic equations of the second order

    Nikolai Vladimirovich Krylov

  • Existence of strong solutions for Itô's stochastic equations via approximations

    István Gyöngy;Nicolai Krylov

  • Fokker-planck-kolmogorov Equations

    Vladimir Bogachev;Nicolai Krylov;Michael Röckner;Stanislav Shaposhnikov

  • Nonlinear Elliptic and Parabolic Equations of the Second Order Equations

    Unknown

  • Parabolic and elliptic equations with VMO coefficients

    Nicolai V Krylov

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

    V. I. Bogachev;Nicolai V Krylov;M. Röckner

  • Introduction to the theory of diffusion processes

    Nicolai V. Krylov

  • On the rate of convergence of finite-difference approximations for Bellmans equations with variable coefficients

    N.V. Krylov

  • On stochastic equations with respect to semimartingales I.

    I. Gyöngy;N. V. Krylov

  • ON THE CAUCHY PROBLEM FOR LINEAR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS

    N V Krylov;B L Rozovskiĭ

  • Sequences of convex functions and estimates of the maximum of the solution of a parabolic equation

    N. V. Krylov

  • BOUNDEDLY NONHOMOGENEOUS ELLIPTIC AND PARABOLIC EQUATIONS

    N V Krylov

  • On the general notion of fully nonlinear second-order elliptic equations

    N. V. Krylov

  • On stochastics equations with respect to semimartingales ii. itô formula in banach spaces

    I. Gyöngy;N. V. Krylov

  • Parabolic equations with VMO coefficients in Sobolev spaces with mixed norms

    Nicolai V Krylov

  • Introduction to the theory of random processes

    N. V. Krylov

  • Nonlinear analysis on Manifolds: Monge-Ampère equations

    A. T. Fomenko;N. V. Krylov

Frequent Co-Authors

Michael Röckner
Michael Röckner Bielefeld University
Vladimir I. Bogachev
Vladimir I. Bogachev National Research University Higher School of Economics
Hongjie Dong
Hongjie Dong Brown University

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