World's Best Scientists 2026 revealed!

D-Index & Metrics

Mathematics

D-Index
47
Citations
7326
World Ranking
1291
National Ranking
574

Overview

Renming Song is affiliated with the University of Illinois at Urbana-Champaign in the United States. Their research is primarily situated within the field of Mathematics, with significant focus on Mathematical Physics, Applied Mathematics, Finance, Computational Theory and Mathematics, and Statistics and Probability.

The scientist's work encompasses several main topics, including:

  • Stochastic processes and statistical mechanics
  • Stochastic processes and financial applications
  • Advanced Mathematical Modeling in Engineering
  • Nonlinear Partial Differential Equations
  • Markov Chains and Monte Carlo Methods
  • Advanced Harmonic Analysis Research
  • Mathematical Dynamics and Fractals

Renming Song has contributed numerous papers, including recent publications such as:

  • "Factorization and estimates of Dirichlet heat kernels for non-local operators with critical killings" (2020), Journal de Mathématiques Pures et Appliquées
  • "The extremal process of super-Brownian motion" (2021), Stochastic Processes and their Applications
  • "Sharp space-time regularity of the solution to stochastic heat equation driven by fractional-colored noise" (2020), Stochastic Analysis and Applications
  • "Homogenization of nonlocal partial differential equations related to stochastic differential equations with Lévy noise" (2022), Bernoulli
  • "Gradient estimates for the fundamental solution of Lévy type operator" (2020), Advances in Nonlinear Analysis

The scientist has published extensively in a range of venues, with frequent contributions to:

  • arXiv (Cornell University)
  • Stochastic Processes and their Applications
  • Electronic Journal of Probability
  • Journal of Differential Equations
  • Advances in Applied Probability

Collaboration is a notable aspect of their scholarly activity, with frequent co-authors including:

  • Yan-Xia Ren
  • Haojie Hou
  • Panki Kim
  • Zoran Vondraček
  • Soobin Cho

Best Publications

  • Bernstein Functions: Theory and Applications

    René L. Schilling;Renming Song;Zoran Vondracek

  • Integral Inequalities for Convex Functions of Operators on Martingales

    Burgess Davis;Renming Song

  • Potential Analysis of Stable Processes and its Extensions

    Krzysztof Bogdan;Tomasz Byczkowski;Tadeusz Kulczycki;Michal Ryznar

  • Estimates on Green functions and Poisson kernels for symmetric stable processes

    Zhen Qing Chen;Renming Song

  • Heat kernel estimates for the Dirichlet fractional Laplacian

    Zhen Qing Chen;Panki Kim;Renming Song

  • Heat Kernel Estimates for Dirichlet Fractional Laplacian

    Panki Kim;Zhen-Qing;Renming Song

  • Two-sided eigenvalue estimates for subordinate processes in domains

    Zhen Qing Chen;Renming Song

  • Potential theory of subordinate killed Brownian motion in a domain

    Renming Song;Zoran Vondraček

  • A Geometric Condition that Implies the Existence of Certain Singular Integrals of Banach-Space-Valued Functions

    Burgess Davis;Renming Song

  • Harnack inequality for some classes of Markov processes

    Renming Song;Zoran Vondraček

  • Dirichlet heat kernel estimates for fractional Laplacian with gradient perturbation

    Zhen Qing Chen;Panki Kim;Renming Song

  • Intrinsic ultracontractivity and conditional gauge for symmetric stable processes

    Zhen Qing Chen;Renming Song

  • Mean exit time and escape probability for dynamical systems driven by Lévy Noises

    Ting Gao;Jinqiao Duan;Jinqiao Duan;Xiaofan Li;Renming Song

  • Boundary Harnack principle for $\Delta + \Delta^{; ; ; ; ; lpha/2}; ; ; ; ; $

    Zhen Qing Chen;Panki Kim;Renming Song;Zoran Vondraček

  • Boundary Harnack Principle for Symmetric Stable Processes

    Renming Song;Jang Mei Wu

  • Potential theory of subordinate Brownian motions revisited

    Panki Kim;Renming Song;Zoran Vondracek

  • Drift transforms and Green function estimates for discontinuous processes

    Zhen Qing Chen;Renming Song

  • Two-sided heat kernel estimates for censored stable-like processes

    Zhen Qing Chen;Panki Kim;Renming Song

  • Conditional gauge theorem for non-local Feynman-Kac transforms

    Zhen Qing Chen;Renming Song

  • Sharp heat kernel estimates for relativistic stable processes in open sets

    Zhen Qing Chen;Panki Kim;Renming Song

  • A Geometrical Characterization of Banach Spaces in Which Martingale Difference Sequences are Unconditional

    Burgess Davis;Renming Song

Frequent Co-Authors

Panki Kim
Panki Kim Seoul National University
Zhen-Qing Chen
Zhen-Qing Chen University of Washington
Jinqiao Duan
Jinqiao Duan Great Bay University
Yimin Xiao
Yimin Xiao Michigan State University
Xicheng Zhang
Xicheng Zhang Wuhan University
Andreas E. Kyprianou
Andreas E. Kyprianou University of Warwick

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