Preprints and some papers (in pdf format):

•  T. Kulczycki, A. Kulik, M. Ryznar, “Drift reduction method for SDEs driven by inhomogeneous singular Lévy noise”, preprint (2022).

•  S. Jarohs, T. Kulczycki, P. Salani, “On the Bernoulli free boundary problems for the half Laplacian and for the spectral half Laplacian”, Nonlinear Anal. 222 (2022), Paper No. 112956, 39 pp.

•  T. Kulczycki, A. Kulik, M. Ryznar, “On weak solution of SDE driven by inhomogeneous singular Lévy noise”, Trans. Amer. Math. Soc. 375 (2022), 4567-4618. .

•  T. Kulczycki, M. Ryznar, P. Sztonyk, “Strong Feller property for SDEs driven by multiplicative cylindrical stable noise”, Potential Analysis 55 (2021), 75–126.

•  T. Kulczycki, M. Ryznar, “Semigroup properties of solutions of SDEs driven by L{\'e}vy processes with independent coordinates”, Stoch. Proc. Appl. 130 (2020) 7185-7217.

•  S. Jarohs, T. Kulczycki, P. Salani, “Starshape of the superlevel sets of solutions to equations involving the fractional Laplacian in starshaped rings”, Mathematische Nachrichten 292 (2019), 1008-1021.

•  T. Kulczycki, M. Ryznar, “Transition density estimates for diagonal systems of SDEs driven by cylindrical α-stable processes”, ALEA Lat. Am. J. Probab. Math. Stat. 15 (2018), 1335-1375.

•  T. Kulczycki, M. Ryznar, “Gradient estimates of Dirichlet heat kernels for unimodal Lévy processes” , Mathematische Nachrichten 291 (2018), 374-397.

•  T. Kulczycki, “On concavity of solutions of the Dirichlet problem for the equation $(-\Delta)^{1/2} \phi = 1$ in convex planar regions”, Journal of the European Mathematical Society 19 (2017), 1361-1420.

•  T. Kulczycki, “Mid-concavity of survival probability for isotropic Lévy processes”, Electron. Commun. Probab. 21 (2016), no. 29, 1-9.

•  T. Kulczycki, M. Kwaśnicki, B. Siudeja, “On the shape of the fundamental sloshing mode in axisymmetric containers”, Journal of Engineering Mathematics 99 (2016), 157-183.

•  T. Kulczycki, M. Ryznar, “Gradient estimates of harmonic functions and transition densities for Levy processes”, Trans. Amer. Math. Soc. 368 (2016), no. 1, 281-318.

•  T. Kulczycki, R. Stańczy, “Multiple solutions for Dirichlet nonlinear BVPs involving fractional Laplacian”, Discrete Contin. Dyn. Syst. Ser. B 19 (2014), 2581-2591.

•  T. Kulczycki “Gradient estimates of q-harmonic functions of fractional Schrödinger operator” , Potential Analysis 39 (2013), 69–98.

•  K. Burdzy, T. Kulczycki “Invisibility via reflecting coating” J. London Math. Soc. 88 (2013), 359-374.

•  K. Burdzy, T. Kulczycki, R. Schilling ”Stationary distributions for jump processes with inert drift” , in “Malliavin Calculus and Stochastic Analysis: A Festschrift in Honor of David Nualart”, Springer Proceedings in Mathematics & Statistics 34, Springer Science+Business Media New York (2013), 139-172.

•  T. Kulczycki, M. Kwaśnicki ”On high spots of the fundamental sloshing eigenfunctions in axially symmetric domains” Proc. London. Math. Soc. 105 (2012), 921-952.

•  K. Burdzy, T. Kulczycki, R. Schilling "Stationary distributions for jump processes with memory" Ann. Inst. Henri Poincaré Probab. Stat. 48 (2012), 609–630.

•  T. Kulczycki, N. Kuznetsov ”On the ‘high spots’ of fundamental sloshing modes in a trough” Proc. Roy. Soc. London Ser. A 467 (2011), 1491-1502.

•  R. Bañuelos, T. Kulczycki, I. Polterovich, B. Siudeja ”Eigenvalue inequalities for mixed Steklov problems” Operator Theory and Its Applications: In Memory of V. B. Lidskii (1924-2008), Advances in the Mathematical Sciences, AMS Translations 231, (2010), pp. 19-34.

•  T. Kulczycki, M. Kwaśnicki, J. Małecki, A. Stós ”Spectral properties of the Cauchy process on half-line and interval” Proc. London. Math. Soc. 101 (2010), 589-622.

•  K. Kaleta, T. Kulczycki ”Intrinsic ultracontractivity for Schrödinger operators based on fractional Laplacians” Potential Analysis 33 (2010), 313-339.

•  R. Bañuelos, T. Kulczycki, B. Siudeja ”On the traces of symmetric stable processes on Lipschitz domains” J. Funct. Anal. 257 (2009), 3329-3352.

•  T. Kulczycki, N. Kuznetsov „’High spots’ theorems for sloshing problems” Bull. Lond. Math. Soc. 41, (2009), 495-505.

•  R. Bañuelos, T. Kulczycki, B. Siudeja „Neumann Bessel heat kernel monotonicity" Potential Anal. 30 (2009), no. 1, 65-83.

•  R. Bañuelos, T. Kulczycki „Trace Estimates for Stable Processes" Probab. Theory Relat. Fields 142 (2008), 313-338.

•  K. Bogdan, T. Kulczycki, M. Kwaśnicki „Estimates and structure of  α-harmonic functions” Probab. Theory Relat. Fields 140 (2008), 345-381.