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)
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).
Exact asymptotics of component-wise extrema of two-dimensional Brownian motion. Extremes,
(2020), 23, 569--602. (with Debicki, K. and Langpeng Ji)
A note on the history of the Poisson process.
Antiquitates Mathematicae 13 (2019) , 3--17
pdf-file .
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
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.
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
In memoriam: Czeslaw Ryll-Nardzewski's contributions to probability theory. (2016)
(with W.A.Woyczynski)
pdf-file
Prediction in a mixed Poisson cluster model
Stochastic Models (2016) DOI 10.1080/15326349.2016.1170614
(with M. Matsui)
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.).
A continuous-time model for claims reserving. Appl. Math. (Warsaw)41 (2014), no. 4, 277–300 (with Tomanek, A.).
M. Mandjes, Z. Palmowski, T. Rolski (2012)
Quasi-stationary workload in a L\'evy-driven storage system. Stochastic Models, 28.3
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
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.
Rolski, T. (2011) Comments on: Light tail asymptotics in multidimensional reflecting processes
for queueing networks.
TOP,
Debicki, K., Kosinski, K. Mandjes, M. and Rolski, T. (2010)
Extremes of multidimensional Gaussian process.
Stochastic Processes and Their Applications,
120, 2289-2301.
Miyazawa, M. and Rolski, T. (2009)
Tail asymptotics for a L\'{e}vy-driven tandem queue with an intermediate input.
Queueing Systems . pdf-file
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.
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 ,
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.
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.
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.
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.
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.
Rolski, T. (2004) A note on the increasing
directionally concave monotonicity in queues.
ps-file
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
Debicki, K., Michna, Z. and Rolski, T. (2003)
Bounds and simulation of generalized
Pickands constants.
Stochastic Models .
ps-file
Palmowski, N. and Rolski, T. (2002) A technique
for exponential change of measure for Markov processes.
Bernoulli 8 , 767-785.
ps-file ,
pdf-file
Debicki, K. and Rolski, T. (2002)
A note on transient Gaussian fluid models.
Queueing Systems , 41 , 321-342
ps-file
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
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
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
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 Sciences13, 429-475.
ps-file
Levikson, B., Rolski, T. and Weiss, G. (1999)
On a Poisson hyperbolic staircase.
Probability in the Engineering and Informational Sciences13, 11-31.
ps-file
Rolski, T., Schmidt, V. and Schlegel, S. (1999)
Asymptotics of Palm-stationary buffer content distributions
in fluid flow queues.
Advances in Applied Probability31.1, 235-253
ps-file
Debicki, K., Michna, Z. and Rolski, T. (1998)
On the supremum from Gaussian processes over infinite horizon.
Probability and Mathematical Statistics18.
ps-file
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
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
Palmowski, Z. and Rolski, T. (1996)
A note on martingale inequalities
for fluid models.
Statistics & Probability Letters 31, 13-21
ps-file
Blaszczyszyn, B. and Rolski, T. (1996) Expansions for
Markov-modulated systems and approximations of ruin probability.
J. Appl. Probab.32, 57-70.
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 Statistics16, 19-28.
Asmussen, S, Frey, A., Rolski, T. and Schmidt, V. (1995)
Does Markov-modulation increase the risk ?
ASTIN Bulletin - A Journal of the International
Actuarial Association25,49-66.
Debicki, K., and Rolski, T. (1995)
A Gaussian fluid model.
Queueing Systems20, 433-452.
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.
Daley, D.J. and Rolski, T. (1994)
Light traffic approximations in general stationary single-server queues.
Stochastic Processes and Their Applications49, 41-58.
Asmussen, S. and Rolski, T. (1994)
Risk theory in a periodic environment: the Cramer-Lundberg
approximation and Lundberg's inequality.
Mathematics of Operations Research19,410-433.
Kulkarni, V. and Rolski, T. (1994)
Fluid model driven by an Orstein-Uhlenbeck process.
Probability in the Engineering and Informational Sciences8, 403-417.
Daley, D.J., R.D. Foley and Rolski, T. (1994)
Condition for finite moments of waiting times in G/G/1 queues.
Queueing Systems17, 89-106.
Blaszczyszyn, B. and Rolski, T. (1993)
Queues in series in light traffic.
Ann. Appl. Probab. 3, 881--896.
ps-file
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
Daley, D.J. and Rolski, T. (1992)
Light traffic approximations in many-server queues.
Advances in Applied Probability24, 285-298.
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.
Asmussen, S. and Rolski, T. (1991)
Computational methods in risk theory:
a matrix-algorithmic approach.
Insurance; Mathematics and Economics10, 259-274.
Rolski, T. and Szekli, R. (1991)
Stochastic ordering and thinning of point processes.
Stochastic Processes and Their Applications37, 299-312.
Daley, D.J. and Rolski, T.
(1991)
Light traffic approximations in queues.
Mathematics of Operations Research16
Rolski, T. (1990)
Ergodic properties of Poisson processes with almost
periodic intensity.
Probability Theory and Related Fields84, 27-37.
Books
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