Mykhaylo Shkolnikov
Professor
Address:
6128 Wean Hall
Department of Mathematical Sciences
Carnegie Mellon University
5000 Forbes Avenue
Pittsburgh, PA 15213
P: 412-268-2545
Education
Ph.D., Stanford University
Postdoctoral Appointments:
- Department of Statistics, UC Berkeley
- Mathematical Sciences Research Institute, Berkeley
Awards
- Early Career Prize by the Activity Group on Financial Mathematics & Engineering at the Society for Industrial and Applied Mathematics (SIAM)
- Erlang Prize by the Applied Probability Society of the Institute for Operations Research and the Management Sciences (INFORMS)
- E. Lawrence Keyes, Jr./Emerson Electric Co. Faculty Advancement Award by the School of Engineering and Applied Science, Princeton University
- Princeton Engineering Commendation List for Outstanding Teaching
Research
At the moment, I am studying interacting particle systems arising in mathematical finance, mathematical physics, and neuroscience using tools from stochastic analysis and PDE/SPDE. More broadly, my interests include a variety of topics in probability theory and PDEs: random operators, integrable probability, models of random growth, concentration of measure, large deviations, and probabilistic approaches to PDEs.
Select Publications
Almada Monter, S. A., Shkolnikov, M., Zhang, J. (2019). Dynamics of observables in rank-based models and performance of functionally generated portfolios. Ann. Appl. Probab. 29, 2849-2883.
Avanesyan, L., Shkolnikov, M., Sircar, R. (2020). Construction of forward performance processes in stochastic factor models and an extension of Widder’s theorem. Finance Stoch. 24, 981-1011.
Nadtochiy, S., Shkolnikov, M. (2020). Mean field systems on networks, with singular interaction through hitting times. Ann. Probab. 48, 1520-1556.
Delarue, F., Nadtochiy, S., Shkolnikov, M. (2022). Global solutions to the supercooled Stefan problem with blow-ups: regularity and uniqueness. Probab. Math. Phys. 3, 171-213.
Lacker, D., Shkolnikov, M., Zhang, J. (2020). Inverting the Markovian projection, with an application to local stochastic volatility models. Ann. Probab. 48, 2189-2211.
Baker, G., Shkolnikov, M. (2022). Zero kinetic undercooling limit in the supercooled Stefan problem. Ann. Inst. Henri Poincaré Probab. Stat. 58, 861-871.
Lacker, D., Shkolnikov, M., Zhang, J. (2023). Superposition and mimicking theorems for conditional McKean-Vlasov equations. J. Eur. Math. Soc. 25, 3229-3288.
Kaushansky, V., Reisinger, C., Shkolnikov, M., Song, Z. Q. (2023). Convergence of a time-stepping scheme to the free boundary in the supercooled Stefan problem. Ann. Appl. Probab. 33, 274-298.
Nadtochiy, S., Shkolnikov, M., Zhang, X. (2021). Scaling limits of external multi-particle DLA on the plane and the supercooled Stefan problem. To appear in Ann. Inst. Henri Poincaré Probab. Stat.
Baker, G., Shkolnikov, M. (2022). A singular two-phase Stefan problem and particles interacting through their hitting times. Submitted.
Nadtochiy, S., Shkolnikov, M. (2023). Stefan problem with surface tension: global existence of physical solutions under radial symmetry. Probab. Theory Related Fields 187, 385-422.
Mustapha, S., Shkolnikov, M. (2023). Well-posedness of the supercooled Stefan problem with oscillatory initial conditions. Submitted.
Guo, Y., Nadtochiy, S., Shkolnikov, M. (2023). Stefan problem with surface tension: uniqueness of physical solutions under radial symmetry. Submitted.
Shkolnikov, M., Soner, H. M., Tissot-Daguette, V. (2023). Deep level-set method for Stefan problems. Submitted.