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.

Papers and Preprints

  1. Spectral heat content on a class of fractal sets for subordinate killed Brownian motions (with Yimin Xiao). To appear in Mathematische Nachrichten, (2022). PDF

  2. Large-time and small-time behaviors of the spectral heat content for time-changed stable processes (with Kei Kobayashi). To appear in Electronic Communications in Probability, (2022). PDF

  3. Spectral heat content for time-changed killed Brownian motions (with Kei Kobayashi). Journal of Theoretical Probability, (2022). PDF

  4. Spectral heat content for α-stable processes in C1,1 open sets (with Renming Song). Electronic Journal of Probability, Vol. 27, paper no. 22, 1–19, (2022). PDF

  5. 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

  6. 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

  7. 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

  8. T. Grzywny, H. Park and R. Song: Spectral heat content for Lévy processes, Mathematische Nachrichten, Volume 292, Issue 4, 805–825, (2019). PDF

  9. 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

  10. H. Park and R. Song: Trace estimates for relativistic stable processes. Potential Analysis, Vol. 41 1273–1291, (2014). PDF

  11. 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

  12. H. Park: Potential theory of subordinate Brownian motions and their perturbations. Ph. D. Thesis. UIUC (2013). PDF

Lecture Notes

  1. Lecture notes for Brownian Motions, Stochastic Calculus and SDE, May 2022 Yonsei University.

Upcoming Conferences

  1. Symposium for Undergraduate Mathematics Research, SUNY at New Paltz, September 10, 2022

Past Conferences

  1. Seminar on Stochastic Processes, Lehigh University, PA, 3/16-3/19, 2022.

  2. The 10th International Conference on Stochastic Analysis and its Applications. 9/6-9/10, 2021.

  3. Bernoulli-IMS 10th World Congress in Probability and Statistics. 7/19-7/23 2021. (Slide, Talk)

  4. Stochastics and Geometry (Online) (21w5184), Banff Canada, 3/8-3/12, 2021. Online Seminar

  5. 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)

  6. The Eighth Pacific Rim Conference in Mathematics, 8/3-8/3, 2020. Online seminar.

  7. One World Probability Seminar, March 2020. Online seminar using Zoom.

  8. 2020 Finger Lakes Probability Seminar, 4/24-4/25, 2020 Binghamton University - canceled due to COVID-19 outbreak

  9. 10th World Congress in Probability and Statistics, 8/17-8/21, 2020 Seoul National University, Seoul South Korea-postponed to 2021

  10. Stochastic Processes and their Applications 2019, 7/8-7/12, 2019 Northwestern University

  11. 2019 Spring Probability Workshop, 5/20-5/22, 2019 Academia Sinica, Taiwan

  12. AMS Fall Eastern Sectional Meeting-Special Session on Probability, Combinatorics, and Statistical Mechanics, 9/29-9/30, 2018, University of Delaware

  13. Seminar on stochastic processes 2018 May 9-11, 2018 Brown University

  14. Finger Lakes Probability Seminar, University of Rochester, 4/20-4/21, 2018

Useful sites

  1. Professor Carl Mueller’s advice for graduate students