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# Stochastic Methods in Analytical and Applied Problems (3526)

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# Publications

1. P.Kim, R.Song, Z.Vondraček: Minimal thinness with respect to symmetric Lévy processes, Trans. Amer. Math. Soc. 368:8787-8822, 2016.
2. N.Sandrić: Ergodic property of stable-like Markov chains, Journal of Theoretical Probability, 29(2):459–490, 2016.
3. I.Geček Tuđen, Z.Vondraček: A distributional equality for suprema of spectrally positive Lévy processes, Journal of Theoretical Probability, 29(3):826–842, 2016.
4. B.Basrak, D.Špoljarić: Extremes of random variables observed in renewal times, Statistics and Probability Letters, 97:216-221, 2014.
5. V.Kovač, K.A.Škreb: One modification of the martingale transform and its applications to paraproducts and stochastic integrals, J. Math. Anal. Appl. 426 (2):1143-1163, 2015.
6. Y.Shi, A.Demaria, S.Lubura, H.Šikić, S.Bassnett: The Penny Pusher: a cellular model of lens growth, Investigative Ophthalmology & Visual Science., 56:799–809, 2015. (cover article for February 2015)
7. H.Šikić, Y.Shi, S.Lubura, S.Bassnett: A stochastic model of eye lens growth, Journal of theoretical biology, 376:15-31, 2015. (highlighted article)
8.  M.Kassmann, A.Mimica: Intrinsic scaling properties for nonlocal operators, J. Eur. Math. Soc. 19: 983--1011, 2017.
9. R.L.Schilling, Z.Vondraček: Absolute continuity and singularity of probability measures induced by a purely discontinuous Girsanov transform of a stable process, Trans. Amer. Math. Soc., 369:1547-1577, 2017.
10. B.Basrak: Electron. Commun. Probab., 13pp, 2015.
11. P.Kim, R.Song, Z.Vondraček. Minimal thinness with respect to subordinate killed Brownian motions,  Stoch.Processes Appl., 126:1226-1263, 2016.
12. V.Kovač, C.Thiele, P.Zorin-Kranich: Dyadic triangular Hilbert transform of two general and one not too general function, Forum of Mathematics, Sigma 3, e25, 27pp, 2015.
13. P.Gressman, D.He, V.Kovač, B.Street, C.Thiele, P.-L.Yung: On a trilinear singular integral form with determinantal kernel, Proc. Amer. Math. Soc. 144(8):3465-3477, 2016.
14. D.Krizmanić, Functional weak convergence of partial maxima processes, Extremes, 19:7-23, 2016.
15. P.Kim, R.Song, Z.Vondraček: Martin boundary of unbounded sets for purely discontinuous Feller processes ,Forum Mathematicum 28:1067-1085, 2016.
16. A. Mimica: Exponential decay of measures and Tauberian theorems, J.Math.Anal.Appl., 440:266-285, 2016.
17. N. Sandrić: Long-time behavior for a class of Feller processes, Trans.Am. Math. Soc. 368(3):1871-1910, 2016.
18. G. Pang, N. Sandrić: Ergodicity and fluctuations of a fluid particle
driven by diffusions with jumps, Commun. Math. Sci. 14(2):327-362, 2016.
19. N. Sandrić: On recurrence and transience of two-dimensional Lévy and
Lévy-type processes, Stochastic Process. Appl. 126(2):414-438, 2016.
20. N. Sandrić: Homogenization of periodic diffusion with small jumps, J.
Math. Anal. Appl. 435(1):551-577, 2016.
21. N. Sandrić: Ergodicity of Lévy-type processes, ESAIM-Prob. Stat., 20:154-177, 2016.
22. N. Sandrić: On transience of Lévy-type processes, Stochastics, 88(7):1012-1040, 2016.
23. B. Basrak, D. Špoljarić: On randomly spaced observations and continuous time random walks, Journal of applied probability, 53(3), 2016.
24. K. Burdzy, T. Tadic: Random reflections in a high dimensional tube, Journal of Theoretical Probability, 31(1):466-493, 2018.
25. A.Mimica, On subordinate random walks, Forum Mathematicum 29:653-664, 2017.
26. A. Mimica: Heat kernel estimates for subordinate Brownian motions, Proc. London Math. Soc. 113:627-648, 2016.
27. V.Kovač: Quantitative norm convergence of double ergodic averages associated with two commuting group actions, Ergodic Theory Dynam. Systems., 36(3):860-874, 2016.
28. P. Durcik, V. Kovač, C. Thiele: Power-type cancellation for the simplex Hilbert transform, to appear in Journal d’Analyse Mathematique, 10pp, 2016.
29. Electron. Commun. Probab., 21(84):1-12, 2016.
30. D.Krizmanić, Weak convergence of multivariate partial maxima processes, Journal of Multivariate Analysis, 155:1-11, 2017.
31. P.Kim, R.Song, Z.Vondraček: Scale invariant boundary Harnack principle at infinity for Feller processes, Potential Analysis 47: 337-367, 2017.
32. P.Kim, R.Song, Z.Vondraček: Accessibility, Martin boundary and minimal thinness for Feller processes in metric measure spaces, Revista Matematica Iberoamericana,  34:541-592, 2018.
33. H. Šikić, Y. Shi, S. Lubura, S. Bassnett: A full lifespan model of vertebrate lens growth, Royal Society Open Science, 4:1-26, 2017.
34. P. Durcik, V. Kovač, K. A. Škreb, C. Thiele: Norm-variation of ergodic averages with respect to two commuting transformations, to appear in Ergodic Theory Dynam. Systems, 33pp, 2017.
35. P. Durcik, V. Kovač, L. Rimanić: On side lengths of corners in positive density subsets of the Euclidean space, to appear in Int. Math. Res. Not., 16pp, 2017.
36. Z.Vondraček, V.Wagner: On purely discontinuous additive functionals of subordinate Brownian motions, Stochastic Process. Appl., 128(2):707-725, 2018.
37. V. Kovač, K. A. Škreb: Bellman functions and $L^p$ estimates for paraproducts, Probab. Math. Statist., 21pp, 2017.
38. N. Sandrić: A note on the Birkhoff ergodic theorem, Results in Mathematics 72(1-2):715-730, 2017.
39. P. Kim, R. Song, Z. Vondraček: Heat kernels of non-symmetric jump processes: beyond the stable case, Potential Analysis, 49:37-90, 2018.
40. P. Kim, R. Song, Z. Vondraček: Potential theory of subordinate killed Brownian motion, Trans. Amer. Math. Soc. 371:3917-3969, 2019.
41. K. Burdzy, T. Tadic: Can one make a laser out of cardboard?, Annals of Applied Probability, 27(4):1951-1991, 2017.
42. M. Huzak: Estimating a class of diffusions from discrete observations via approximate maximum likelihood method, to appear in Statistics, 31pp, 2017.
43. P. Kim, A. Mimica: Asymptotical properties of distributions of isotropic Lévy processes, Stochastic Process. Appl., 128:2688-2709, 2018.
44. B.Basrak, H.Planinić, P.Soulier: An invariance principle for sums and record times of regularly varying stationary sequences, to appear in Probab. Th. Rel. Fields, 46pp, 2017
45. A.Mimica, S.Šebek:Harnack inequality for subordinate random walks, to appear in J. Theor. Probab., 28pp, 2018.
46. D. Krizmanic: A note on joint functional convergence of partial sum and maxima for linear processes, Statist. Probab. Lett. 138, pp 42-26, 2018.
47. A. Mimica, N. Sandrić, R. L. Schilling: Markov chain approximation of pure jump processes, to appear in Acta Applicandae Mathematicae, 40 pp, 2018.
48. H. Planinić, P. Soulier: The tail process revisited, to appear in Extremes, 29 pp, 2018.
49. V. Kovač, D. Oliveira e Silva, J. Rupčić: A sharp nonlinear Hausdorff-Young inequality for small potentialsto appear in Proc. Amer. Math. Soc., 14pp, 2018.
50. D. Krizmanic: Joint functional convergence of partial sums and maxima for linear processes, Lith. Math. J., 58(4):457-479, 2018.
51. J.Cvitanić, D.Prelec, S.Radas, H.Šikić: Game of Duels: Information-Theoretic Axiomatization of Scoring Rules, to appear in IEEE Transactions on Information Theory, 12pp, 2018.
52. A. Arapostathis, G. Pang, N. Sandrić: Ergodicity of Levy-driven SDEs arising from multiclass many-server queues, Annals of Applied Probability 29(2): 1070-1126, 2019.
53. P.Kim, R.Song, Z.Vondraček: On the boundary theory of subordinate killed Levy processes, to appear in Potential Analysis, 54pp, 2019.
54. A. Martinčić Špoljarić, I. Rubelj, M. Huzak: Mathematical model and computer simulations of telomere loss, Journal of Theoretical Biology, 465:78-89, 2019.
55. V.Wagner: A note on the trace theorem for Besov-type spaces of generalized smoothness on d-sets,  to appear in Glasnik Matematički, 23 pp, 2019.
56. I. Geček Tuđen: Distribution of suprema for generalized risk processes, to appear in LSTM:  Stochastic Models, 14pp, 2019.
57. V. Kovač, H. Šikić: Characterizations of democratic systems of translates on locally compact abelian groups, to appear in Monatsh. Math., 27 pp, 2019.
58. D. Krizmanic: Functional convergence for moving averages with heavy tails and random coefficients, ALEA, Lat. Am. J. Probab. Math. Stat. 16, 729 757, 2019.
59. V.Wagner: Censored symmetric Lévy-type processes, to appear in Forum Mathematicum, 25 pp, 2019.
60. K.Burdzy, B.Kołodziejek, T.Tadić: Inverse Exponential Decay: Stochastic Fixed Point Equation and ARMA Models,Bernoulli, 25(4B):3939-3977, 2019.
61. T.Tadic: Time-like graphical models, Memoirs of the American Mathematical Society, 261 (2019), 1262; 1-174..
62. D. Krizmanic: On joint weak convergence of partial sum and maxima processes, Stochastics 92(6), 876-899, 2020.

Preprints

1. J.Cvitanić, D.Prelec, S.Radas, H.Šikić: Mechanism design for an agnostic planner: universal mechanisms, logarithmic equilibrium payoffs and implementation (35 pp)
2. I. Geček Tuđen: Ruin probability for discrete risk processes, (12pp), 2017.
3. P.M.Luthy, H.Šikić, F.Soria, G.L.Weiss, E.N.Wilson: One-Dimensional Dyadic Wavelets (152pp), 2018.
4. B. Basrak, H. Planinić: A note on vague convergence of measures, 15 pp, 2018.
5. B. Basrak, H. Planinić: Compound Poisson approximation for random fields with application to sequence alignment, 34pp, 2018.
6. B. Basrak, O. Wintenberger, P. Žugec: On total claim amount for marked Poisson cluster models, 39 pp, 2018.
7. M. Nielsen, H, Šikić: Muckenhoupt class weight decomposition and BMO distance to bounded functions, 13pp, 2018.
8. W. Cygan, S. Šebek: Transition probability estimates for subordinate random walks, 34pp, 2018.

Ph.D. Theses

1. Snježana Lubura Strunjak: Local asymptotic properties of approximative maximum likelihood estimator of drift parameters in diffusion model, 27.10.2015.
2. Vanja Wagner: Censored Lévy and related processes, 25.5.2016.
3. Kristina Ana Škreb: The Bellman function technique for multilinear martingale estimates, 8.6.2017.
Last edited: August 25, 2020, 15:33