My research interests lie in understanding the qualitative and quantitative effects of introducing random forcing to ordinary or partial differential equations. A common feature of many of my early projects is the involvement of Lévy processes. Sample paths of a Lévy process exhibit (at most countably many) random jumps at random times within any finite time interval. The picture below illustrates examples of Lévy processes with different jump intensities.
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More recently, my work has focused on how even classical noises—such as white-type noise—interact with fluid dynamical systems. I apply tools from stochastic analysis and harmonic analysis to study the behavior of such systems.
I received the CAMS Graduate Student Prize for Excellence in Research in 2019.
📓Publications and Preprints
(With M. Aydin and I. Kukavica) The stochastic Navier-Stokes equations with general L3 data, arXiv: 2504.05648, 2025, submitted.
(With M. Aydin and I. Kukavica) Almost global existence for the stochastic Navier-Stokes equations with small H^{1/2} data, arXiv: 2501.10331, 2025, submitted.
(With I. Kukavica) Almost global existence of the stochastic Navier-Stokes equations in L3 with small data, arXiv: 2410. 02919, 2024, submitted.
(With M. Bagnara and M. Maurelli) No blow-up by nonlinear Ito noise for the Euler equations, Electronic Journal of Probability, vol(30), no.81, 1-29, 2025. arXiv:2305.09852.
(With I. Kukavica and F. Wang) Local existence of the stochastic Navier-Stokes equations in the whole space, Stoch PDE: Anal Comp, 2024. https://doi.org/10.1007/s40072-024-00341-0.
(With I. Kukavica) Local existence of strong solutions to the stochastic Navier-Stokes equations with Lp data, Journal of Differential Equations, vol(359), pp 183-210, 2023. arXiv: 2110.07091.
(With I. Kukavica and M. Ziane) Global existence for the stochastic Navier-Stokes equations with small Lp data, Stoch PDE: Anal Comp, 2021. https://doi.org/10.1007/s40072-021-00196-9
(With P. Przybyłowicz and M. Szölgyenyi ) Existence and uniqueness of solutions of SDEs with discontinuous drift and finite activity jumps, Statistics & Probability Letters, Vol 174, 2021. https://doi.org/10.1016/j.spl.2021.109072
(With I. Kukavica) Local existence for the stochastic Euler equation with Lévy noise, Asymptotic Analysis 113(1-2), 1-27, 2019.
(With R. Mikulevicius ) On some cadlaguity moment estimates of stochastic jump processes, Electronic Communications in Probability, vol(24), no. 77, pp 1-11, 2019.
On the Cauchy problem for integro-differential equations with space-dependent operators in generalized Hölder spaces, arXiv:1810.00677, 2018.
(With R. Mikulevicius ) On the Cauchy problem for nondegenerate parabolic integro-differential equations in the scale of generalized Hölder spaces, Potential Analysis, doi: 10.1007/s11118-019-09789-510.1007/s11118-019-09789-5, 2019. ( or an earlier version at arXiv:1806.07019.)
(With R. Mikulevicius ) On the rate of convergence of strong Euler approximation for SDEs driven by Lévy processes, Stochastics: An International Journal of Probability and Stochastic Processes, Vol 90 (4), 569-604, 2018. (or arXiv.)
(With Z. Tan and Y. Wang ) Large-time behavior of the full compressible Euler-Poisson system without the temperature damping, Discrete and Continuous Dynamical Systems-Series A, 36(3), 1583-1601, 2016.
🚵Collaborators in Alphabetical Order
Mustafa Aydin, Marco Bagnara, Igor Kukavica, Mario Maurelli, Remigijus Mikulevicius, Paweł Przybyłowicz, Michaela Szölgyenyi, Zhong Tan, Fei Wang, Yong Wang, Mohammed Ziane
📢Talks and Presentations
📢Talks and Presentations
Nov 2025 Joint Applied Math and Probability/Statistics Seminar, Lehigh University, PA
Aug 2025 Frontiers in Stochastic Analysis, West Lafayette, IN
Jun 2025 Nanjing University Overseas Alumni Academic Forum, Nanjing, China
Oct 2024 AMS Special Session on Recent Advances of PDEs in Modern Mathematical Physics, Theory and Applications, Savannah, GA (Conference Cancelled)
Apr 2024 AMS Special Session on Recent Advances in Harmonic Analysis and Their Applications to Partial Differential Equations, Washington D.C.
Feb 2024 Analysis Seminar, The University of Alabama at Birmingham, Birmingham, AL
Nov 2023 Analysis and Applied Mathematics Seminar, Wake Forest University, Winston-Salem, NC
Oct 2023 Special Session on Dynamics of Fluids, AMS Sectional Meeting, Mobile, AL
Mar 2023 Applied Mathematics Seminar, UC Berkeley / Lawrence Berkeley Laboratory, CA
Feb 2022 Mathematics Colloquium, Oregon State University, OR
Sep 2021 Probability/Math Finance Seminar, Carnegie Mellon University
Aug 2021 Symposium on Non-local methods for inverse problems, The IFIP TC7 conference, Ecuador
Mar 2021 Probability and Analysis Seminar, Chongqing University, China
Mar 2020 Probability/Math Finance Seminar, Carnegie Mellon University
Nov 2019 Trimester Seminar Series, Hausdorff Research Institute for Mathematics, Germany
Jan 2019 AMS Special Session on Stochastic Differential Equations and Applications, JMM
Jan 2019 AMS Contributed Paper Session on Integral Equations, Operational Calculus, and Harmonic Analysis , JMM
Nov 2018 Functional Inequalities in Probability, University of Connecticut
Oct 2018 USC WiSE STEM Bytes Seminar Series PDF.
Jun 2018 Recent Trends in Continuous and Discrete Probability Conference, Georgia Tech
May 2018 Poster Presentation, Seminar on Stochastic Processes 2018, Brown University
Mar 2018 WiMSoCal 2018, Pepperdine University
Apr 2017 Poster Presentation, Diversity in Mathematics Festival, University of California Irvine
Apr 2017 Probability Seminar, University of Southern California
Apr 2017 AWM Research Symposium 2017, University of California Los Angeles (The Best Poster Prize)
Feb 2017 The 10th Annual WiMSoCal, Los Angeles, CA
Jan 2017 Probability Seminar, University of Southern California
Nov 2016 Charlotte’s Web, University of Southern California
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