Research Papers after 1990

  1. Derivatives of sup-functionals of fractional Brownian motion evaluated at H=1/2. Electronic J. of Probability 2022 27, 1-35 (2022). DOI: 10.1214/22-EJP848 (with K. Bisewski and K. Debicki)
  2. Derivative of the expected supremum of fractional Brownian motion at H=1. Queueing Systems . 2022 102 , issue 1, No 4, 53-68 (with K.Bisewski and K. Debicki).
  3. Exact asymptotics of component-wise extrema of two-dimensional Brownian motion. Extremes, (2020), 23, 569--602. (with Debicki, K. and Langpeng Ji)
  4. A note on the history of the Poisson process. Antiquitates Mathematicae 13 (2019) , 3--17 pdf-file .
  5. Logarithmic Asymptotics for Probability of Component-Wise Ruin in a Two-Dimensional Brownian Model. Risks 2019, 7(3), 83 (with Debicki, K. and Langpeng Ji), doi:10.3390/risks7030083
  6. Fluctuation theory for level-dependent Lévy risk processes. Stochastic Processes and Their Applications, 2019, 129, (12), 5406-5449 (with Czarna, I, Perez, J-L. and Yamazaki, K.), doi.org/10.1016/j.spa.2019.03.006.
  7. Extremal behavior of hitting a cone by correlated Brownian motion with d\ rift. Stochastic Processes and Their Applications, 2018, 128 (12) 4171--4206 (with K.~Debicki, E.~Hashorva i Langpeng Ji) doi: 10.1016/j.spa.2018.02.002
  8. In memoriam: Czeslaw Ryll-Nardzewski's contributions to probability theory. (2016) (with W.A.Woyczynski) pdf-file
  9. Prediction in a mixed Poisson cluster model Stochastic Models (2016) DOI 10.1080/15326349.2016.1170614 (with M. Matsui)
  10. Service-time ages, residuals, and lengths in an M/GI/∞ service system. Queueing Syst. (2015), 79 , 173--181, DOI 10.1007/s11134-014-9420-z (with Serfozo, R.; Stoyan, D.).
  11. A continuous-time model for claims reserving. Appl. Math. (Warsaw) 41 (2014), no. 4, 277–300 (with Tomanek, A.).
  12. M. Mandjes, Z. Palmowski, T. Rolski (2012) Quasi-stationary workload in a L\'evy-driven storage system. Stochastic Models, 28.3
  13. Polak, M. and Rolski, T. (2012) A note on the speed of convergence to the quasi-stationary distribution. Demonstratio Mathematica, tom dedykowany prof. A. Plucinskiej. pdf-file
  14. Rolski, T. and Tomanek, A. (2011) Asymptotics of conditional moments of the summand in Poisson compounds. J. Appl. Probab. {\it J. Appl. Prob.}, Spec. Vol. 48A, 65--76.
  15. Rolski, T. (2011) Comments on: Light tail asymptotics in multidimensional reflecting processes for queueing networks. TOP,
  16. Debicki, K., Kosinski, K. Mandjes, M. and Rolski, T. (2010) Extremes of multidimensional Gaussian process. Stochastic Processes and Their Applications, 120, 2289-2301.
  17. Miyazawa, M. and Rolski, T. (2009) Tail asymptotics for a L\'{e}vy-driven tandem queue with an intermediate input. Queueing Systems . pdf-file
  18. Asmussem, S., Fiorini, P.,Lipsky, L., Rolski, T. and Sheahan, P. (2008) Asymptotic Behavior of Total Times of Jobs That Must Start Over If a Failure Occurs. Mathematics of Operations Research , 33 , 932--944.
  19. Daley, D.J., Vesilo, R. and Rolski, T. (2007), Article ID 83852, 15 pages. Long range dependence in a Cox process directed by a Markov renewal process. Journal of Applied Mathematics and Decision Sciences ,
  20. Puchala, Z. and Rolski, T. (2008) The exact asymptotic of the collision time tail distribution for independent Brownian particles with different drifts. Probability Theory and Related Fields , 142, 595-617.
  21. Debicki, K., Dieker, A.B. and Rolski, T. (2007) Quasi-product forms for Levy-driven fluid networks. pdf-file Mathematics of Operations Research , 32 , 629-647.
  22. Palmowski, Z. and Rolski, T. (2006) On the exact asymptotics of the busy period in GI/G/1 queues. ps-file Advances in Applied Probability , 38 , 792- 803.
  23. Puchala, Z. and Rolski, T. (2005) The exact asymptotic of the time to collision. 1 ps-file, pdf-file Electronic Journal of Probability , 10 , 1359-1380.
  24. Palmowski, Z. and Rolski, T. (2004) Markov processes conditioned to never exit a subspace of the state space. ps-file Probability and Mathematical Statistics 24 339-353.
  25. Rolski, T. (2004) A note on the increasing directionally concave monotonicity in queues. ps-file
  26. Miyoshi, N. and Rolski, T. (2004) Ross type conjectures on monotonicity of queues. Festschrift for Daryl Daley, Phil Pollet and Peter Taylor Eds. Australian & New Zealand Journal of Statistics, 46 , 121-132. ps-file and pdf-file
  27. Debicki, K., Michna, Z. and Rolski, T. (2003) Bounds and simulation of generalized Pickands constants. Stochastic Models . ps-file
  28. Palmowski, N. and Rolski, T. (2002) A technique for exponential change of measure for Markov processes. Bernoulli 8 , 767-785. ps-file , pdf-file
  29. Debicki, K. and Rolski, T. (2002) A note on transient Gaussian fluid models. Queueing Systems , 41 , 321-342 ps-file
  30. Aldous, D., Miyazawa, M. and Rolski, T. (2000) On the stability of a batch clearing system with Poisson arrivals and subadditive service times. J. Appl. Probab. 38, 621-634. ps-file
  31. Levikson, B., Rolski, T. and Weiss, G. (2001) Layering of the Poisson process in the quadrant. Probability and Mathematical Statistics 21, 417-440. ps-file
  32. Debicki, K. and Rolski, T. (2000) Gaussian fluid models; a survey. Symposium on Performance Models for Information Communication Networks. Sendai, 23-25.01.2000. ps-file
  33. Gautam, N, Kulkarni, V.G., Palmowski, Z. and Rolski, T. (1999) Bounds for fluid models driven by semi-Markov inputs. Probability in the Engineering and Informational Sciences 13, 429-475. ps-file
  34. Levikson, B., Rolski, T. and Weiss, G. (1999) On a Poisson hyperbolic staircase. Probability in the Engineering and Informational Sciences 13, 11-31. ps-file
  35. Rolski, T., Schmidt, V. and Schlegel, S. (1999) Asymptotics of Palm-stationary buffer content distributions in fluid flow queues. Advances in Applied Probability 31.1, 235-253 ps-file
  36. Debicki, K., Michna, Z. and Rolski, T. (1998) On the supremum from Gaussian processes over infinite horizon. Probability and Mathematical Statistics 18. ps-file
  37. Bauerle, N. and Rolski, T. (1998) A monotonicity result for the work-load in Markov-modulated queues. Journal of Applied Probability 35, 741-747. ps-file
  38. Palmowski, Z. and Rolski, T. (1998) The superposition of alternating on-off flows and a fluid model. The Annals of Applied Probability , 8, 1998, 524-540. ps-file
  39. Palmowski, Z. and Rolski, T. (1996) A note on martingale inequalities for fluid models. Statistics & Probability Letters 31, 13-21 ps-file
  40. Blaszczyszyn, B. and Rolski, T. (1996) Expansions for Markov-modulated systems and approximations of ruin probability. J. Appl. Probab. 32, 57-70.
  41. Daley, D.J., Foley, , RD and Rolski, T. (1996) A note on convergence rates in the strong law for strong mixing sequences. Probability and Mathematical Statistics 16, 19-28.
  42. Asmussen, S, Frey, A., Rolski, T. and Schmidt, V. (1995) Does Markov-modulation increase the risk ? ASTIN Bulletin - A Journal of the International Actuarial Association 25,49-66.
  43. Debicki, K., and Rolski, T. (1995) A Gaussian fluid model. Queueing Systems 20, 433-452.
  44. Blaszczyszyn, B., Rolski, T. and Schmidt, V. (1995) Light-traffic approximations in queues and related stochastic models. In: Dshalalow, J.H. (ed.) Frontiers in Queueing: Models, Methods and Problems. CRC Press, Boca Raton, Florida.
  45. Daley, D.J. and Rolski, T. (1994) Light traffic approximations in general stationary single-server queues. Stochastic Processes and Their Applications 49, 41-58.
  46. Asmussen, S. and Rolski, T. (1994) Risk theory in a periodic environment: the Cramer-Lundberg approximation and Lundberg's inequality. Mathematics of Operations Research 19,410-433.
  47. Kulkarni, V. and Rolski, T. (1994) Fluid model driven by an Orstein-Uhlenbeck process. Probability in the Engineering and Informational Sciences 8, 403-417.
  48. Daley, D.J., R.D. Foley and Rolski, T. (1994) Condition for finite moments of waiting times in G/G/1 queues. Queueing Systems 17, 89-106.
  49. Blaszczyszyn, B. and Rolski, T. (1993) Queues in series in light traffic. Ann. Appl. Probab. 3, 881--896. ps-file
  50. Daley, D.J. and Rolski, T. (1992) Finiteness of waiting-time moments in general stationary single-server queues. The Annals of Applied Probability 2, 987-1008. ps-file
  51. Daley, D.J. and Rolski, T. (1992) Light traffic approximations in many-server queues. Advances in Applied Probability 24, 285-298.
  52. Rolski, T. (1992) Approximations of performance characteristics in periodic Poisson queues. in Queueing and Related Models, Ed. U.N. Bhat and I.V. Basava, Claredon Press, Exford, 285-298.
  53. Asmussen, S. and Rolski, T. (1991) Computational methods in risk theory: a matrix-algorithmic approach. Insurance; Mathematics and Economics 10, 259-274.
  54. Rolski, T. and Szekli, R. (1991) Stochastic ordering and thinning of point processes. Stochastic Processes and Their Applications 37, 299-312.
  55. Daley, D.J. and Rolski, T. (1991) Light traffic approximations in queues. Mathematics of Operations Research 16
  56. Rolski, T. (1990) Ergodic properties of Poisson processes with almost periodic intensity. Probability Theory and Related Fields 84, 27-37.

Books

  • BBTR book Blaszczyszyn Bartlomiej, Rolski Tomasz,
    Introduction to Life Insurance Mathematics
    (in Polish: Podstawy matematyki ubezpieczen na zycie)
    WNT, Warszawa, 2004
  • Rolski, T., Schmidli, H., Schmidt, V. and Teugels, J.L. (1999) Stochastic Processes for Insurance and Finance. Wiley Series in Probability and Statistics; for the contents and chapter 1 download here ps-file
  • Rolski, T., Schmidli, H., Schmidt, V. and Teugels, J.L. (2000) Teacher's Manual. ; for the unfinished draft download here pdf-file , pdf-file

    Some less accesible papers; before 1990

  • Rolski, T. (1972) Some inequalities for GI/M/n queues. Applicationes Mathematicae XIII, 43--47. pdf-file
  • Rolski, T. (1976) Mean residual life. Proceddings of the 40th Sessions of the nternational Statistical Institute (Warsaw, 1975), vol. 4. Contributed papers. Bull. Inst. Internat. Statist. , 46, 266-270. pdf-file
  • Rolski, T. (1977) On some classes of distribution functions determined by an order relation. Proceddings of the Symposium to honour Jerzy Neyman (Warsaw, 1974), pp. 293-302. PWN, Warsaw pdf-file
  • Rolski, T. (1981) An approach to the formula $L=\lambda V$ via the theory of stationary point processes on a space of compact subsets of $R^k$. Lecture Notes in Statistics, vol. 8, Eds. Eds. P. Reve\'sz, L. Schmetterer and V.M.Zolotarev, 220--235. pdf-file

    Lecture notes

  • Lecture notes of the course given in the fall semester of 1999 at the Tokyo Institute of Technology in the series of Advanced Lectures on Mathematical Sciences and Information Science II. The course and lecture notes were prepared on the base of the book Stochastic Processes for Insurance and Finance, written by Tomasz Rolski, Hanspeter Schmidli, Volker Schmidt and Jozef Teugels, published by John Wiley, Chichester in 1999. ps-file
  • TWISTING IN APPLIED PROBABILITY - Lecture notes of the course given at the Department of Actuarial Sciences and Statistics, Heriot-Watt University, Edinburgh (May 2004). ps-file

    Other articles

  • Point processes an article written for EoAS ps-file
  • Change of measure an article written for EoAS ps-file