My research fields are probability theory and stochastic processes. I am especially interested in random processes that move by jumps (jump processes). Jump processes are natural mathematical objects and they are widely used in many fields such as PDE and finance. I am working on potential and spectral properties of those processes.
J. Lee and H. Park: Dichotomy in the small-time asymptotics of spectral heat content for Lévy Processes. arXiv.
K. Kobayashi and H. Park: Heat content for Gaussian processes: small-time asymptotic analysis. Bernoulli, 31(2), (2025), 1606--1632. PDF.
K. Kobayashi and H. Park: A unified approach to the small-time behavior of the spectral heat content for isotropic Lévy processes. Stochastic Processes and their Applications, 171 (2024), Paper No. 104331, 11 pp. PDF arXiv.
H. Park and Y. Xiao: Spectral heat content on a class of fractal sets for subordinate killed Brownian motions. Mathematische Nachrichten. Volume 296, Issue 9, 4192--4205 (2023) PDF
K. Kobayashi and H. Park: Spectral heat content for time-changed killed Brownian motions. Journal of Theoretical Probability, Volume 36, 1148--1180 (2023). PDF
K. Kobayashi and H. Park: Large-time and small-time behaviors of the spectral heat content for time-changed stable processes. Electronic Communications in Probability, Vol 27, article no. 39, 1--11, (2022). PDF
H. Park and R. Song: Spectral heat content for α-stable processes in C1,1 open sets. Electronic Journal of Probability, Vol. 27, paper no. 22, 1--19, (2022). PDF
Higher order terms of the spectral heat content for killed subordinate and subordinate killed Brownian motions related to symmetric α-stable processes in ℝ. Potential Analysis, Vol 57 283--303, (2022). PDF
H. Park, Y. Xiao, and X. Yang: Uniform dimension results for the inverse images of symmetric Lévy processes, Journal of Theoretical Probability, Volume 33, 2213--2232, (2020). PDF
H. Park and R. Song: Small time asymptotics of spectral heat contents for subordinate killed Brownian motions related to isotropic 𝛼-stable processes, Bulletin of London Mathematical Society, Volume 51, Issue 2 371--384, (2019). PDF
T. Grzywny, H. Park and R. Song: Spectral heat content for Lévy processes, Mathematische Nachrichten, Volume 292, Issue 4, 805--825, (2019). PDF
H. Park: Fatou’s theorem for subordinate Brownian motions with Gaussian components on C1,1 open sets , Illinois Journal of Mathematics, Volume 60, Number 3-4, 761--790, (2016). PDF
H. Park and R. Song: Trace estimates for relativistic stable processes. Potential Analysis, Vol. 41 1273--1291, (2014). PDF
P. Kim, H. Park and R. Song: Sharp estimates on the Green functions of perturbations of subordinate Brownian motions in bounded κ-fat open sets. Potential Analysis, Vol. 38 319--344, (2013). PDF
H. Park: Potential theory of subordinate Brownian motions and their perturbations. Ph. D. Thesis. UIUC (2013). PDF
Lecture notes for Brownian Motions, Stochastic Calculus and SDE, May 2022 Yonsei University
Recent Trends in Discrete and Continuous Probability, AMS Sectional Meeting at Saint Louis University, St. Louis, Missouri, October 18--19,
2025 Progress in Discrete and Continuous Probability, July 22--July 25, 2025, Union College NY
Probability Summer School in Korea 2025, 6/22--26, Sokcho-si, Gangwon-do, South Korea Photo1, Photo2
Finger Lakes Probability Seminar, April 25--26, 2025, University of Rochester, Rochester NY
Seminar on Stochastic Processes 2025, Indiana University, Bloomington, March 19--22, 2025
Recent Progress in Stochastic Analysis and its Applications, Loyola University, Chicago, USA, July 15-19, 2024 Photo
Summer school on Optimal Transport, Stochastic Analysis and Applications to Machine Learning, KAIST, South Korea, June 3-7, 2024
11th Bielefeld-SNU Joint Workshop in Mathematics, Seoul National University, April 8-10, 2024 Photo
Analysis on fractals and networks, and applications, March 18-22, 2024, CIRM, Luminy, France Photo
Probability Workshop in Korea 2024, January 21 (Sun)-24 (Wed), 2024, South Korea
Probability Winter School in Korea 2023, December 26-29, 2023, South Korea
The 22nd Northeast Probability Seminar (NEPS), New York, November 16-17, 2023.
Workshop on Stochastic Analysis, Random Fields, and Applications, Aug 14-16, 2023, Michigan State University
Frontiers in Stochastic Analysis, Aug 9--11, 2023, UIC
The 21st International Conference on Random Structures and Algorithms, June 12-16, 2023, Carnegie Mellon University. Photo
Seminar on Stochastic Processes, University of Arizona, Tucson, AZ March 8-11, 2023. Photo1, Photo2
Finger Lakes Probability Seminar, Binghamton, New York, February 24-25, 2023.
Joint Mathematics Meetings 2023, Boston, January 4-7, 2023
The Twenty-first Northeast Probability Seminar (NEPS), Davis auditorium, Columbia University, New York, N.Y., November 17-18 2022.
Focus Sessions-Analysis and probability (invited), Global KMS International Conference, October 18-20, 2022.
Symposium for Undergraduate Mathematics Research, SUNY at New Paltz, September 10, 2022, Photo
Seminar on Stochastic Processes, Lehigh University, PA, 3/16-3/19, 2022. Photo
The 10th International Conference on Stochastic Analysis and its Applications. 9/6-9/10, 2021.
Bernoulli-IMS 10th World Congress in Probability and Statistics. 7/19-7/23 2021. (Slide, Talk)
Stochastics and Geometry (Online) (21w5184), Banff Canada, 3/8-3/12, 2021. Online Seminar
Bernoulli-IMS One World Symposium 2020, 8/24-8/28, 2020. Online seminar.
Slide, Presentation (Spectral heat content for α-stable processes in C1,1 open sets)
The Eighth Pacific Rim Conference in Mathematics, 8/3-8/3, 2020. Online seminar.
One World Probability Seminar, March 2020. Online seminar using Zoom.
2020 Finger Lakes Probability Seminar, 4/24-4/25, 2020 Binghamton University - canceled due to COVID-19 outbreak
10th World Congress in Probability and Statistics, 8/17-8/21, 2020 Seoul National University, Seoul South Korea-postponed to 2021
Stochastic Processes and their Applications 2019, 7/8-7/12, 2019 Northwestern University
2019 Spring Probability Workshop, 5/20-5/22, 2019 Academia Sinica, Taiwan
AMS Fall Eastern Sectional Meeting-Special Session on Probability, Combinatorics, and Statistical Mechanics, 9/29-9/30, 2018, University of Delaware
Seminar on stochastic processes 2018 May 9-11, 2018 Brown University
Finger Lakes Probability Seminar, University of Rochester, 4/20-4/21, 2018
How to Maintain A Successful Research Program While Teaching 12 Credit-Hours Per Semester, Jeremy F. Alm
Navigating the Tenure Process in a Mathematics Department, Jeremy F. Alm and Kevin P. Knudson
Applying for Grants and Jobs, Matthew Badger