Stochastic Models with Power-Law Tails. The Equation X = AX + B.
with E. Damek and T. Mikosch.
Springer Series in Operations Research and Financial Engineering, 2016
Preprints
(with A. Iksanov, V. Kotelnikova) Limit theorems for sums of independent indicators, with applications to the Ginibre point process and Karlin's occupancy scheme, pdf.
(with A. Iksanov, A. Marynych) Critical branching processes in a sparse random environment, pdf.
List of publications
(with P. Dyszewski, A. Kołodziejska) Weak quenched limit theorems for a random walk in a sparse random environment, Electronic Journal of Probability, 29,1-30, 2024.
(with C. Dong, A. Iksanov, A. Marynych) Limit theorems for random Dirichlet series, Stochastic Processes and their Applications, 165, 246-274, 2023.
(with C. Dong, A. Iksanov, A. Marynych) Critical branching processes in a sparse random environment, Modern Stochastics: Theory and Applications, 10(4), 397-411, 2023.
(with G. Alsmeyer and S. Brofferio) Asymptotically linear iterated function systems on the real line, Annals of Applied Probability, Vol. 33, No. 1, 161–199, 2023.
(with P. Dyszewski and A. Marynych) Solutions of kinetic-type equations with perturbed collisions, Stochastic Processes and their Applications, 159, 199–224, 2023.
(with P. Dyszewski) Precise large deviation estimates for branching process in random environment, Annales de l’Institut Henri Poincaré, Vol. 58, No. 3, 1669-1700, 2022.
(with S. Brofferio and T. Szarek) On uniqueness of invariant measures for random walks on HOMEO(R), Ergodic Theory and Dynamical Systems, 42, 2207–2238, 2022.
(with E. Damek) Limit theorems for supercritical branching processes in random environment, Bernoulli, 28(3), 1602–1624, 2022.
(with A. Iksanov and A. Marynych) Central limit theorem for the least common multiple of a uniformly sampled m-tuple of integers, Journal of Number Theory, Vol. 233, 301-336, 2022.
(with A. Iksanov and B. Mallein) On the derivative martingale in a branching random walk, Annals of Probability, Vol. 49, No. 3, 1164–1204, 2021.
(with K. Kolesko and M. Meiners) Solutions to kinetic-type evolution equations: beyond the boundary case, Electronic Journal of Probability, Vol. 26, no. 2, 18 pp, 2021.
(with B. Dovgay and A. Marynych) Moderate parts in regenerative compositions: the case of regular variation, Journal of Mathematical Analysis and Applications, Vol. 497, 124894, 2021.
(with B. Dovgay and A. Iksanov) On intermediate levels of nested occupancy scheme in random environment generated by stick-breaking, Electronic Journal of Probability, Vol. 25, no. 123, 1-24, 2020.
(with P. Dyszewski, A. Iksanov and A. Marynych) Random walks in a strongly sparse random environment, Stochastic Processes and their Applications, 130, 3990-4027, 2020.
(with K. Bogus and A. Marynych) Self-similar solutions of kinetic-type equations: the critical case, Stochastic Processes and their Applications, 130(2), 677-693, 2020.
(with M. Maślanka) Large deviation estimates for branching random walks, ESAIM: Probability and Statistics, 23, 823–840, 2019.
(with P. Dyszewski, A. Iksanov, A. Marynych and A. Roitershtein) Random walks in a moderately sparse random environment, Electronic Journal of Probability, 24(69), 1-44, 2019.
(with M. Maślanka) Precise large deviations for the first passage time of a random walk with negative drift, Proceedings of AMS, 147(9), 4045-4054, 2019.
(with P. Dyszewski and K. Kolesko) Local fluctuations of critical Mandelbrot cascades, Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, 55(2), 1179–1202, 2019.
(with P. Dyszewski) Precise large deviations for random walk in random environment, Electronic Journal of Probability, 23 (114), 2018.
(with E. Damek and J. Zienkiewicz) Pointwise estimates for exceedance times of perpetuity sequences, Stochastic Processes and their Applications, 128(9), 2923-2951, 2018.
(with P. Dyszewski, A. Iksanov and A. Marynych) On perpetuities with gamma-like tails, Journal of Applied Probability, 55(2), 368-389, 2018.
(with G. Alsmeyer and A. Iksanov) Null-recurrence and transience of random difference equations in the contractive case, Journal of Applied Probability, 54(4), 1089-1110, 2017.
(with S. Mentemeier) Precise Tail Asymptotics for Attracting Fixed Points of Multivariate Smoothing Transformations, Markov Processes and Related Fields, 23, 147-170, 2017.
(with E. Damek) A simple proof of heavy tails estimates for affine type Lipschitz recursions, Stochastic Processes and their Applications, 127, 657–668, 2017.
(with E. Damek and J. Zienkiewicz) On the Kesten-Goldie constant, Journal of Difference Equations and Applications, 22(11), 1646-1662, 2016.
(with J. F. Collamore, E. Damek and J. Zienkiewicz) Large deviation estimates for exceedance times of perpetuity sequences and their dual processes, Annals of Probability, Vol. 44, No. 6, 3688-3739, 2016.
(with S. Mentemeier) Precise Large Deviation Results for Products of Random Matrices, Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Vol. 52, No. 3, 1474–1513, 2016.
(with S.Brofferio) On unbounded invariant measures of stochastic dynamical systems, Annals of Probability 43(3), 1456-1492, 2015.
(with E.Damek and J. Zienkiewicz) Precise tail asymptotics of fixed points of the smoothing transform with general weights, Bernoulli 21(1), 489–504, 2015.
(with E. Damek and T. Przebinda) On the rate of convergence in the Kesten renewal theorem, Electronic Journal of Probability, 20 , no. 22, 1–35, 2015.
(with A. Iksanov) Functional limit theorems for divergent perpetuities in the contractive case, Electronic Communications in Probability, Vol. 20, no. 10, 1-14, 2015.
(with E. Damek, Y. Guivarc'h and S. Mentemeier) On multidimensional Mandelbrot cascades, Journal of Difference Equations and Applications, Volume 20, Issue 11, pages 1523-1567, 2014.
(with K.Kolesko) Linear stochastic equations in the critical case, Journal of Difference Equations and Applications, Volume 20, Issue 2, 188-209, 2014.
(with S. Brofferio and E.Damek) On solutions of the affine recursion and the smoothing transform in the critical case, Springer Proceedings in Mathematics & Statistics Volume 53, Random Matrices and Iterated Random Functions, 2013, pp 137-157.
(with E. Damek, T. Mikosch and J. Zienkiewicz) Large deviations for solutions to stochastic recurrence equations under Kesten's condition, Annals of Probability, Vol. 41, No. 4, 2755–2790, 2013.
(with E.Damek, S.Mentemeier and M.Mirek) Heavy tailed solutions of multivariate smoothing transforms, Stochastic Processes and their Applications, Vol. 123, 1947-1986, 2013.
(with M. Letachowicz) Limit theorems for stochastic recursions with Markov dependent coefficients, Colloquium Mathematicum, 128, 263-276, 2012.
(with S. Brofferio and E. Damek) On the invariant measure of the random difference equation $X_n=A_n X_{n-1}+ B_n$ in the critical case, Annales de l'Institut Henri Poincare (B) Probability and Statistics, Vol. 48, No. 2, 377–395, 2012.
(with E. Damek and M. Mirek) Asymptotics of stationary solutions of multivariate stochastic recursions with heavy tailed inputs and related limit theorems, Stochastic Processes and their Applications, Vol. 122(1), 42-67, 2012.
(with K. Kolesko) Random walks on the affine group of a homogeneous tree in the drift-free case , Journal of Theoretical Probability, Vol. 25(1), 189-204, 2012.
(with E. Damek and Y. Guivarch) Convergence to stable laws for a class of multidimensional stochastic recursions, Probability Theory and Related Fields, 148, 3-4, 333-402, 2010.
(with E. Damek) Regular behavior at infinity of stationary measures of stochastic recursion on NA groups, Colloquium Mathematicum, 118, 499-523, 2010.
On tails of fixed points of the smoothing transform in the boundary case, Stochastic Processes and their Applications, Vol. 119(11), 3955-3961, 2009.
(with E. Damek, Y. Guivarch, A. Hulanicki and R. Urban) Tail-homogeneity of stationary measures for some multidimensional stochastic recursions, Probability Theory and Related Fields, 145, 385-420, 2009.
On behavior at infinity of invariant measures of stochastic recursions in a critical case, Annals of Applied Probability, 17(4), 1245–1272, 2007.
On tails of stationary measures on a class of solvable groups, Annales de l'Institut Henri Poincare (B) Probability and Statistics, 43 (4), 417-440, 2007.
(with T. Martinez and J.L. Torrea) Calderon-Zygmund operators associated to ultraspherical expansions, Canadian Journal of Mathematics, Vol.59 , No.6, 1223-1244, 2007.
(with J.J. Betancor, J.C. Farina, T. Martinez and J.L. Torrea) On the Riesz transform associated to Hankel transformation, Proceedings of the Royal Society of Edinburgh. Sect A 137 (4) 701--725, 2007.
(with E. Damek and A. Hulanicki) Asymptotic behavior of Poisson kernels on NA groups, Communications in PDE, 31, 1547 - 1589, 2006.
(with T. Martinez, J.L. Torrea and R. Urban) On the Riesz transform and weighted inequalities associated with the ultraspherical polynomials, Journal d'Analyse Mathematique, Vol. 98, 113 -- 143, 2006.
(with Ch. Benson, E. Damek and G. Ratcliff) Differential systems of type (1,1) on Hermitian symmetric spaces and their solutions , Journal of Functional Analysis, 215 (2), 427-475, 2004.
(with A. Bonami, E. Damek, A.Hulanicki and Ph. Jaming) Maximum boundary regularity of bounded Hua-harmonic functions on tube domains, Journal of Geometric Analysis, 14(3), 457-486, 2004.
The Hua system on irreducible Hermitian symmetric spaces of nontube type, Annales De L'Institut Fourier, 54, 81-128, 2004.
(with A. Bonami, E. Damek, A. Hulanicki, R. Penney and B. Trojan) Hua system and pluriharmonicity for symmetric irreducible Siegel domains of type II, Journal of Functional Analysis, 188, no. 1, 38 - 74, 2002.
(with E. Damek and A. Hulanicki) Bounded pluriharmonic functions on symmetric irreducible Siegel domains, Mathematische Zeitschrift, 240, no. 1, 169 - 195, 2002..
(with E. Damek) Hua-harmonic functions on symmetric type two Siegel domains, Rend. Mat. Acc. Lincei, vol. 13, 2002.