Szymon Peszat (Professor)

• E-Mail Address: napeszat[AT]cyf-kr.edu.pl
• Address: Faculty of Mathematics and Computer Science, Jagiellonian University, Łojasiewicza 6, 30-348 Cracow, Poland.

Research Interests: Stochastic partial differential equations, stochastic fluid mechanics, statistical mechanics, Lévy processes, large deviations, stochastic control.

The most recent publications and pre-publications:

• S. Peszat, J. Zabczyk Heath-Jarrow-Morton model with linear volatility, submitted. arXiv:2304.08075.
  
  
• B. Goldys, S. Peszat, Stochastic flows for infinite dimensional stochastic linear sylstems, Trans. Amer. Math. Soc., to appear. arXiv:2105.04140.
  
  
• B. Goldys, S. Peszat, Linerar parabolic equations with Dirichlet white noise boundary conditions, J. Differential Equations 362 (2023), 382-437. arXiv:2109.05428.
  
  
• A. Kulik, S. Peszat, E. Priola, Gradient formula for transition semigroup corresponding to stochastic equation driven by a system of independent Lévy processes, NoDEA Nonlinear Differential Equations Appl. 30 (2003), Art. no. 7. arXiv:2006.09133.
  
  
• Z. Brzezniak, T. Komorowski, S. Peszat, Ergodicity for stochastic equation of Navier-Stokes type, Electron. Commun. Probab. 27 (2022), Art. no. 4, 10 pp. arXiv:2003.08764.
  
  
• S. Peszat, K. Twardowska, J. Zabczyk, Ergodicity of Burgers' system, J. Stoch. Anal. 2 (2021), no 3, Art. 10, 16 pp. arXiv:2006.10049.
  
  
• S. Peszat, D. Zawisza, The investor problem based on the HJM model, Ann. Polon. Math 127 (2021), 241-269. arXiv:2010.13915.
  
  
• Z. Dong, S. Peszat, and L. Xu, On some smoothening effects of the transition semigroup of a Lévy process, J. Math. Anal. Appl. 434 (2016), 1566-1580. (pdf-file)
  
  
• B. Goldys, S. Peszat, and J. Zabczyk, Time homogeneous Gauss-Markov processes on Hilbert spaces, Trans. Amer. Math. Soc. 368 (2016), 89-108. (pdf-file)
  
  
• S. Peszat and Ł. Stettner, Research problems of Jerzy Zabczyk, Stochastic Analysis, Special volume in honour of Jerzy Zabczyk, Banach Center Publications vol. 105, Warszawa, 2015, pp. 9-32. (pdf-file)
  
  
• S. Peszat, Stochastic partial differential equations with Lévy noise (a few aspects), in Stochastic Analysis: A Series of Lectures ( Robert C. Dalang, Marco Dozzi and Francesco Russo, eds.) Progress in Probability Vol. 68, Birkhauser Basel AG, Basel, 2015, pp. 333-357. (pdf-file)
  
  
• D. Crisan, Y. Otobe, and S. Peszat, Inverese problem for stochastic transport equation, Inverse Problems 31 (2015), no. 1, 015005, 20pp.
  
  
• Z. Brzezniak, B. Goldys, S. Peszat, and F. Russo, Second order PDEs with Dirichlet white noise boundary conditions, J. Evol. Equ. 15 (2015), 1-26. (pdf-file)
  
  
• S. Peszat and J. Zabczyk, Time regularity for stochastic Volterra equations by the dilation theorem, J. Math. Anal. Appl. 409 (2014), 676-683. (pdf-file)
  
  
• T. Komorowski, S. Peszat, and T. Szarek, Passive tracer in a flow corresponding to two dimensional stochastic Navier-Stokes equtions, Nonlinearity 26 (2013), 1999-2026. (pdf-file)
  
  
• S. Peszat and J. Zabczyk, Time regularity of solutions to linear equations with Lévy noise in infinite dimensions, Stochastic Processes Appl. 123 (2013), 719-751. (pdf-file)
  
  
• S. Peszat, Lévy-Ornstein-Uhlenbeck transition semigroup as second quantized operator, J. Funct. Anal. 260 (2011), 3457-3473.
  
  
• T. Komorowski, S. Peszat, and T. Szarek, On ergodicity of some Markov processes, Ann. Probab. 38 (2010), 1401-1443.
  
  
• S. Peszat and A. Talarczyk, Functional central limit theorem for additive functionals of α-stable processes, Potential Anal. 33 (2010), 199-209.
  
  
• S. Peszat and S. Tindel, Stochastic heat and wave equations on a Lie group, Stochastic Anal. Appl. 28 (2010), 662-695.
  
  
• Z. Brzezniak, B. Goldys, P. Imkeller, S. Peszat, E. Priola, and J. Zabczyk, Time irregularity of generalized Ornstein-Uhlenbeck processes C. R. Math. Acad. Sci. Paris 348 (2010), 273-276.
  
  
• Z. Brzezniak and S. Peszat, Hyperbolic equations with random boundary conditions, Recent Development in Stochastic Dynamics and Stochastic Analysis, (J. Duan, S. Luo and C. Wang, eds.) World Scientific, 2010, pp. 1-22. (pdf-file)
  
  
• T. Komorowski, S. Peszat, and L. Ryzhik, Limit of fluctuations of solutions of Wigner equations, Comm. Math. Phys. 292 (2009), 427-510.
  
  

Books:

• S. Peszat and J. Zabczyk, Stochastic Partial Differential Equations with Lévy Noise (an Evolution Equation Approach), Cambridge University Press, Cambridge, 2007.
  ERRATUM to Stochastic Partial Differential Equations with Lévy Noise