SZYMON PESZAT
Curriculum vitae

General information: Last name: Peszat. First name: Szymon. Born: 26.11.1961 in Cracow, Poland. Polish citizen.

Address:

• Institute of Mathematics, Polish Academy of Sciences, Sw. Tomasza 30/7, 31-027 Cracow, Poland.
• Faculty of Applied Mathematics, University of Mining and Metallurgy, Al. Mickiewicza 30, 30-059 Cracow, Poland.

Telephone: (+4812) 4228706

FAX: (+4822) 6293997

E-mail address: napeszat[AT]cyf-kr.edu.pl

Education:

• 1980 - 1985 Institute of Mathematics, Jagiellonian University, Cracow, Poland.

Qualifications:

• 2000 Habilitation in mathematics, Institute of Mathematics, Polish Academy of Sciences.
• 1993 Ph.D. in mathematics, Institute of Mathematics, Polish Academy of Sciences. Thesis Advisor: Jerzy Zabczyk.
• 1985 M.Sc. in mathematics, Jagiellonian University, Cracow, Poland.

Topics of theses:

• Habilitation - Existence, uniqueness and regularity of solutions to stochastic evolution equations.
• Ph.D. - Large deviation principle for stochastic evolution equations (awarded the Waclawek Prize).

Employment:

• Since October 2007: Associate Professor, Faculty of Applied Mathematics, University of Mining and Metallurgy, Cracow.
• Since March 2001: Associate Professor, Institute of Mathematics, Polish Academy of Sciences, Cracow.
• December 2003 - September 2007: Associate Professor, Institute of Mathematics, University of Kielce.
• 1994 - 2001: Assistant Professor, Institute of Mathematics, Polish Academy of Sciences, Cracow.
• 1993 - 1994: Assistant Professor, Institute of Mathematics, University of Mining and Metallurgy, Cracow.
• 1985 - 1993 Assistant, Institute of Mathematics, University of Mining and Metallurgy, Cracow.

Visiting positions:

• September 2005 - December 2005: Chercheur Associé, November 2001 - March 2002, November 2000 - February 2001, March 2000 - June 2000: PAST (Professor Associé à Service Temporaire), Département de Mathématiques, Université Paris 13, Paris, France.
• April 1998 - March 1999: Research Associate, Department of Mathematics, Imperial College, London, United Kingdom. Taught: Stochastic Control.
• March 1996 - June 1996: Postdoctoral Researcher, March 1995 - February 1996: The Royal Society Postdoctoral Fellowship, School of Mathematics, University of Hull, Hull, United Kingdom.

Short term research visits:

• January - February 2010 (1 month), Isaac Newton Institute for Mathematical Sciences, Cambridge, United Kingdom.
• April 2008 (1 week), School of Mathematics and Computer Sciences, Nanjing Normal University, China.
• March 2008 (1 week), Department of Mathematics, Imperial College, London, United Kingdom.
• November - December 2007 (3 weeks), Institute Mittag-Leffler, Sweden.
• June - July 2007 (1 month), Department of Mathematics, University of York, United Kingdom.
• March - April 2007 (1 month), Département de Mathématiques, Université Paris 13, France.
• March 1995 (2 weeks), November 2004 (1 week) Mathematical Institute, Academy of Sciences, Prague, Czech Republic.
• February - April 2009 (3 months), March - April 2001 (2 months), June 1993 (2 weeks) Mathematical Research Institute, University of Warwick, Coventry, United Kingdom.
• September - October 2002 (1 month), April - August 1997 (3 months) Department of Mathematics, University of Hull, Hull, United Kingdom.
• November - December 2001 (1 month), July - August 1995 (6 weeks) School of Mathematics, University of New South Wales, Sydney, Australia.
• July 1997 (2 weeks), July 1996 (2 weeks), June 1995 (2 weeks) Scuola Normale Superiore de Pisa, Pisa, Italy.

Research interests: Stochastic PDEs, stochastic fluid mechanics, statistical mechanics, Lévy processes, large deviations, stochastic control.

List of publications:

1. Z. Brzezniak, B. Goldys, P. Imkeller, S. Peszat, E. Priola, and J. Zabczyk, Time irregularity of generalized Ornstein-Uhlenbeck processes, C. R. Acad. Sci. Paris, Ser. I 348 (2010), 273-276.
2. S. Peszat and A. Talarczyk, Functional central limit theorem for additive functionals of α-stable processes, Potential Anal., to appear.
3. S. Peszat and S. Tindel, Stochastic heat and wave equations on a Lie group, Stochastic Anal. Appl, to appear.
4. T. Komorowski, S. Peszat, and L. Ryzhik, Limit of fluctuations of solutions of Wigner equation, Comm. Math. Phys. 292 (2009), 479-510.
5. 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.
6. T. Komorowski, S. Peszat, and T. Szarek, On ergodicity of some Markov processes, Ann. Probab., to appear.
7. S. Peszat and J. Zabczyk, Stochastic heat and wave equations driven by an impulsive noise, Stochastic Partial Differential Equations and Applications-VII, (G. Da Prato and L. Tubaro, eds.) Lect. Notes Pure Appl. Math., 245, Chapman & Hall/CRC, Boca Raton, 2006, pp. 229-242.
8. S. Peszat and F. Russo, Large noise asymptotics for one-dimensional diffusions, Bernoulli 11 (2005), 247-262.
9. T. Komorowski and S. Peszat, Transport of a passive tracer by an irregular velocity field, J. Statist. Phys. 115 (2004), 1383-1410.
10. S. Peszat, Stochastic Navier-Stokes equations, Proceedings of the conference on Probabilistic Problems in Atmospheric and Water Sciences, (Będlewo, 2002, K. Haman, B. Jakubiak, and J. Zabczyk, eds.), Wydawnictwo ICM, Warszawa, 2003, pp. 120-130.
11. S. Peszat, The Cauchy problem for a nonlinear stochastic wave equation in any dimension, J. Evol. Equ. 2 (2002), 383-394.
12. A. Fannjiang, T. Komorowski, and S. Peszat, Lagrangian dynamics for a passive tracer in a class of Gaussian Markovian flows, Stochastic Processes Appl. 97 (2002), 171-198.
13. S. Peszat, SPDEs driven by a homogeneous Wiener process, Stochastic Partial Differential Equations and Applications (Trento, 2000, G. Da Prato and L. Tubaro, eds.), Lectures Notes in Pure and Appl. Math., 227, Dekker, New York, 2001, pp. 417-427.
14. Z. Brzezniak, S. Peszat, and J. Zabczyk, Continuity of stochastic convolutions, Czechoslovak Math. J. 51 (2001), 679-684.
15. Z. Brzezniak and S. Peszat, Stochastic two dimensional Euler equations, Ann. Probab. 29 (2001), 1796-1832.
16. M. Capinski and S. Peszat, On the existence of a solution to stochastic Navier-Stokes equations, Nonlinear Anal. 44 (2001), 141-177.
17. G. Kondrat, S. Peszat, and B. Zegarlinski, Ergodicity for generalized Kawasaki dynamics, J. Phys. A 33 (2000), 5901-5912.
18. Z. Brzezniak and S. Peszat, Maximal inequalities and exponential estimates for stochastic convolutions in Banach spaces, Stochastic Processes, Physics and Geometry: New Interplays. I: A Volume in Honor of Sergio Albeverio (Leipzig 1999, F. Gesztesy, H. Holden, J. Jost, S. Paycha, M. Röckner, and S. Scarlatti, eds.), CMS Conf. Proc., 28, Amer. Math. Soc., Providence, RI, 2000, pp. 55-64.
19. Z. Brzezniak and S. Peszat, Strong local and global solutions to stochastic Navier-Stokes equations, Infinite Dimensional Stochastic Analysis (Amsterdam 1999, Ph. Clément, F. den Hollander, J. van Neerven, and B. de Padter, eds.), Verh. Afd. Natuurkd. 1. Reeks. K. Ned. Akad. Wet., 52, R. Neth. Acad. Arts Sci., Amsterdam, 2000, pp. 85-98.
20. A. Constantin and S. Peszat, Global existence of solutions of semilinear parabolic evolution equations, Differential Integral Equations 13 (2000), 99-113.
21. S. Peszat and J. Zabczyk, Nonlinear stochastic wave and heat equations, Probab. Theory Related Fields 116 (2000), 421-443.
22. Z. Brzezniak and S. Peszat, Space-time continuous solutions to SPDEs driven by a homogeneous Wiener process, Studia Math. 137 (1999), 261-299.
23. B. Goldys and S. Peszat, Law equivalence of stochastic linear systems, Statist. Probab. Lett. 43 (1999), 265-274.
24. S. Peszat and J. Seidler, Maximal inequalities and space-time regularity of stochastic convolutions, Math. Bohem. 123 (1998), 7-32.
25. M. Capinski and S. Peszat, Local existence and uniqueness of strong solutions to 3-D stochastic Navier-Stokes equations, NoDEA Nonlinear Differential Equations Appl. 4 (1997), 185-200.
26. S. Peszat and J. Zabczyk, Stochastic evolution equations with a spatially homogeneous Wiener process, Stochastic Processes Appl. 72 (1997), 187-204.
27. S. Peszat, Sobolev spaces of functions on an infinite-dimensional domain, Stochastic Processes and Related Topics (Siegmundsberg, 1994, H. J. Engelbert, H. Föllmer, and J. Zabczyk, eds.), Stochastics Monogr., 10, Gordon and Breach, Yverdon, 1996, pp. 103-116.
28. S. Peszat, Existence and uniqueness of the solution for stochastic equations on Banach spaces, Stochastics Stochastics Rep. 55 (1995), 167-193.
29. S. Peszat and J. Zabczyk, Strong Feller property and irreducibility for diffusions on Hilbert spaces, Ann. Probab. 23 (1995), 157-172.
30. S. Peszat, Large deviation principle for stochastic evolution equations, Probab. Theory Related Fields 98 (1994), 113-136.
31. S. Peszat, On a Sobolev space of functions of infinite number of variables, Bull. Polish Acad. Sci. Math. 41 (1993), 55-60.
32. S. Peszat, Exponential tail estimates for infinite-dimensional stochastic convolutions, Bull. Polish Acad. Sci. Math. 40 (1992), 323-333.
33. S. Peszat, Equivalence of distribution of some Ornstein-Uhlenbeck processes taking values in Hilbert space, Probab. Math. Statist. 13 (1992), 7-17.
34. S. Peszat, Law equivalence of solutions of some linear stochastic equations in Hilbert spaces, Studia Math. 101 (1992), 269-284.

Books:

1. S. Peszat and J. Zabczyk, Stochastic Partial Differential Equations with Lévy Noise (evolution equation approach), Cambridge University Press, Cambridge, 2007.
2. S. Peszat and J. Zabczyk, Stochastic Evolution Equations, ICM Publishers, Warsaw, 2004, (in Polish).

Most important international conferences (papers presented):

• Stochastic Partial Diffential Equations, Isaac Newton Institute for Mathematical Sciences, Cambrigde 4 - 8 January 2010, Regularity of solutions to linear SPDEs driven by Lévy process.
• International Workshop Choise and Calibration of Models of Natural Phenomena, Berlin 4 - 5 December 2009, Some aspects of the passive tracer dynamics.
• Workshop on Stochastic Partial Differential Equations: Modeling, Analysis, and Approximations, Darmstadt 24 - 28 August 2009, Regularity of solutions to linear SPDEs with Lévy noise.
• SPA 2009, 33rd Conference on Stochastic Processes and Their Applications, Berlin 27 - 31 July 2009, Stochastic PDEs with spatially homogeneous noise (special session invited speaker).
• Workshop on Stochastic Analysis and Related Fields, Cracow 20 - 22 July 2009, Regularity of Ornstein-Uhlenbeck processes.
• International Conference on Infinite Particle Systems and Complex Systems, Kazimierz Dolny (Poland) 22 - 26 September 2008, Regularity of stochastic convolutions.
• The Fifth World Congress of Nonlinear Analysts, Orlando (Florida, USA) 2 - 9 July 2008, Stochastic evolution equations of the bond market.
• International Conference on Stochastic Analysis and Related Fields, Huazhong University of Science and Technology, Wuhan (China) 7 - 11 April 2008, Heat equation with white noise Dirichlet boundary conditions.
• Conference on Stochastic Partial Differential Equations and Applications VIII, Levico, T. 6 - 12 January 2008, Law of large numbers for passive tracer.
• ESF PESC Exploratory Workshop on Computational Aspects of Stochastic Partial Differential Equations, Salzburg 17 - 21 September 2006, Solutions to the Heath-Jarrow-Morton equation.
• Workshop on Stochastic Fluid Mechanics and SPDEs, CRM Ennio De Giorgi, Pisa 24 - 28 July 2006, Passive tracer dynamics.
• Approximation and Probability, Conference on the occasion of the 70th anniversary of Professor Zbigniew Ciesielski, Będlewo 20 - 24 September 2004, Continuity of stochastic convolutions.
• Conference on Stochastic Partial Differential Equations and Applications - VII, Levico, T. 4 - 10 January 2004, Stochastic heat and wave equations driven by Poisson noise.
• Probabilistic Problems in Atmospheric and Water Sciences, Będlewo 16 - 18 December 2002, Stochastic Navier-Stokes equations.
• Probabilistic Methods in Fluids, Swansea 14 - 19 April 2002, Passive tracer in an irregular velocity field.
• Conference on Stochastic Partial Differential Equations and Applications - VI, Levico, T. 6 - 12 January 2002, Transport of a passive tracer by an irregular velocity field.
• Stochastic Evolution Equations and Applications, Oberwolfach 30 September - 6 October 2001, Dynamics of a passive tracer.
• Workshop on Infinite Dimensional Stochastic Systems, Prague 11 - 15 September 2000, Regularity of stochastic convolutions.
• Analyse Stochastique à l'ENST, Ecole Nationale Supérieure des Télécommunications, Paris 18 April 2000, Continuity of stochastic convolutions.
• Conference on Stochastic Partial Differential Equations and Applications - V, Levico, T. 10 - 16 January 2000, The Cauchy problem for a nonlinear wave equation in any dimension.
• Symposium on Stochastic Control and Infinite Dimensional Systems, Warsaw, Banach Center 8 - 12 June 1998, Stochastic heat and wave equations.
• Workshop on Infinite Dimensional Stochastic Systems, Prague 8 - 12 September 1997, Stochastic Navier-Stokes and Euler equations.
• Workshop on Deterministic and Stochastic Evolutionary Systems, Pisa, Scuola Normale Superiore de Pisa 16 - 18 July 1997, On stochastic Euler equation.
• Conference on Stochastic Partial Differential Equations and Applications - IV, Levico, T. 6 - 11 January 1997, Stochastic Navier-Stokes equations on the whole space.
• Workshop on Deterministic and Stochastic Evolutionary Systems, Pisa, Scuola Normale Superiore de Pisa 16 - 17 July 1996, Random evolutions on the whole space.
• 11th Winterschool on Stochastic Processes, Siegmundsburg (Germany) 17 - 23 March 1996, Law equivalence of stochastic linear systems.
• Conference on Dynamical Systems and Applications of Stochastic Differential Equations, Pisa, Scuola Normale Superiore de Pisa 29 - 30 June 1995, Stochastic partial differential equations with homogeneous random perturbations.
• Workshop on Parabolic Equations, Cortona (Italy) 19 - 24 September 1994, Stochastic reaction diffusion equations.
• Conference on Stochastic Partial Differential Equations and Random Media, Marseille-Luminy 30 May - 5 June 1994, Strong Feller property and irreducibility for diffusions on Hilbert spaces.
• 10th Winterschool on Stochastic Processes, Siegmundsburg (Germany) 13 - 20 March 1994, Stochastic evolution equations on Banach spaces.
• Workshop on Stochastic Evolution Equations, Warsaw, Banach Center 7 - 15 December 1993, Compactness of embeddings of some Sobolev spaces.
• Conference on Stochastic Partial Differential Equations, Marseille-Luminy 13 - 17 April 1992, Large deviation principle for stochastic evolution equations.

Selected talks:

Beside of talks on workshops and international conferences I have been given seminars in the following universities: University of Hull*, Imperial College* (London probability seminars and London analysis seminars), University of Warwick, University of York, University of Loughborough* (Stochastic analysis seminar and East Midlands stochastic analysis seminar), University of New South Wales* (Sydney), University of Swansea, Humboldt University (Berlin), University of Paris 1 (Sorbona), University of Paris 13*, University of Nancy*, University of Basel, Institute of Mathematics of the Czech Academy of Sciences* (Prague), Nanjing Normal University (China), Huazhong University of Science and Technology (Wuhan, China), Tsinghua University (Beijing, China), University of Warsaw*, University of Torun, University of Lublin, Jagiellonian University*.

   *several times  

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