Ingemar Kaj, personal web page, preprints

Preprints and Publications

Preprints:

Channel capacity and performance analysis of a buffered cellular network

Journals:

I. Kaj, C.F. Mugal, R. Mueller, A Wright-Fisher graph model and the impact of directional selection on genetic variation. Theoretical Population Biology 159 (2024) 13-24.
I.Kaj, T. Morozova, Retransmission performance in a stochastic geometric cellular network model. Performance Analysis, June 2024.
R. Mueller, I. Kaj, C.F. Mugal. A nearly-neutral model of molecular signatures of natural selection after change in population size. Genome Biology and Evolution 14:5, May 2022.
I. Kaj, Synchronization in a self-exciting buffer model. Queueing Systems, doi.org/10.1007/s11134-022-09789-0, April 2022.
I. Kaj, D. Tahir, S. Glemin, M. Lascoux, Analysis of diversity-dependent species evolution using concepts in population genetics. Journal of Mathematical Biology 82:22, 2021.
D. Tahir, I. Kaj, K. Bartoszek, M. Majchrzak, P. Parniewski, S. Sakowski, Using multitype branching models to analyze bacterial pathogenicity. Mathematica Applicanda, 2020.
C.F. Mugal, V.E. Kutschera. F. Botero-Castro, J.B.W. Wolf, I. Kaj, Polymorphism data assist the estimation of the non-synonymous and synonymous fixation rate for closely related species. Molecular Biology and Evolution 37:1 (2020) 260-279.
I. Kaj, D. Tahir, Stochastic equations and limit results for some two-type branching models. Statistics and Probability Letters 150 (2019) 35-46.
D. Tahir, S. Glemin, M. Lascoux, I. Kaj, Modeling a trait-dependent diversification process coupled with molecular evolution on a random species tree. Journal of Theoretical Biology 461 (2019) 189-203
M. W. Hart, D. A. Stover, V. Guerra, S.V. Mozaffari, C. Ober, C.F. Mugal, I. Kaj, Positive selection on human gamete-recognition genes. PeerJ 6:e4259 https://doi.org/10.7717/peerj.4259, Jan 2018.
K. Bartoszek, M. Majchrzak, S. Sakowski, A.B. Kubiak-Szeligowska, I. Kaj, P. Parnewski, Predicting pathogenicity behavior in E. coli population through a state dependent model and TRS profiling. PLOS Computational Biology, 14(1), Jan 2018.
K. Bartoszek, S. Glemin, I. Kaj, M. Lascoux, Using the Ornstein-Uhlenbeck process to model the evolution of interacting populations. Journal of Theoretical Biology 429 (2017) 35-45.
I. Kaj, C.F. Mugal, The non-equilibrium allele frequency spectrum in a Poisson random field framework. Theoretical Population Biology, Vol 111, 51--64, 2016.
I. Kaj, V. Konane, Modeling battery cells under discharge using kinetic and stochastic battery models. Applied Mathematical Modelling, Vol. 40, no 17-18, 7901--7915, 2016.
Carina F. Mugal; Jochen B. W. Wolf; Ingemar Kaj, Why time matters: Codon evolution and the temporal dynamics of dN/dS. Molecular Biology and Evolution 2014 31: 212-231.
C.F. Mugal, J.B.W. Wolf, I. Kaj, Supporting information: Basic properties of the Wright-Fisher diffusion process
C. Dombry, I. Kaj, Moment measures of heavy-tailed renewal point processes: asymptotics and applications. ESAIM: Probability and Statistics 17 (2013) 567-591.
C. Dombry, I. Kaj, The on-off network traffic model under intermediate scaling. Queueing Systems 69:1 (2011) 29-44.
H. Bierme, A. Estrade, I. Kaj, Self-similar random fields and rescaled random balls models. J. Theor. Probab. 23 (2010) 1110-1141.
I.Kaj, L. Leskelae, I. Norros, V. Schmidt, Scaling limits for random fields with long-range dependence. Ann. Probab. 35:2 (2007), 528-550.
P. Sjoedin, I. Kaj, S. Krone, M. Lascoux, M. Nordborg, On the meaning and existence of an effective population size. Genetics 169 (Jan 2005) 1061-1070.
R. Gaigalas, I. Kaj, Convergence of scaled renewal processes and a packet arrival model, Bernoulli 9:4 (2003) 671-703.
I. Kaj, S.M. Krone, The coalescent process in a population of stochastically varying size.J. Applied Probability 40:1 (2003) 33-48.
I. Kaj, S.M. Krone, and M. Lascoux, Coalescent theory for seed bank models, J. Applied Probability 38:2, (June 2001) 285-300.
A. Bose and I. Kaj, A scaling limit process for the age-reproduction structure in a Markov population, Markov Processes and Related Fields 6 (2000) 397-428.
I. Kaj and M. Lascoux, Probability of identity by descent in metapopulations, Genetics 152 (July 1999) 1217-1228.
B. Djehiche and I. Kaj, A sample path large deviation principle for L^2-martingale measure processes, Bulletin des Sciences Mathématiques 123 (1999) 467-499.
I. Kaj and S. Sagitov, Limit processes for age-dependent branching particle systems, J. Theor. Prob. 11 (1998) 225-257.
I. Kaj and S. Sagitov, Superprocess approximation for a spatially homogeneous branching walk. Electronic Communications in Probability 2 (1997) 59-70.
K. Fleischmann, J. Gärtner and I. Kaj, A Schilder type theorem for super-Brownian motion, Can. J. Math. 48 (1996) 542-568.
I. Kaj and P. Salminen, On the ultimate value of local time of one-dimensional super-Brownian motion, Stochastic Process. Appl. 59 (1995) 21-42.
B. Djehiche and I. Kaj, The rate function for some measure-valued jump processes, Ann. Probab. 23 (1995) 1414-1438.
A. Bose and I. Kaj, Diffusion approximation for an age-structured population, Ann. Appl. Probab. 5 (1995) 140-157.
K. Fleischmann and I. Kaj, Large deviation probabilities for some rescaled superprocesses, Annales de l'Institut Henri Poincaré 30 (1994) 607-645.
I. Kaj and P. Salminen, On a first passage problem for branching Brownian motions, Ann. Appl. Probab. 3 (1993) 173-185.
H. Egnell and I. Kaj, Positive global solutions of a nonhomogeneous semilinear elliptic equation, J. Math. Pure Appl. 70 (1991) 345-367.
I. Kaj, Time reversal and stationarity of infinite-dimensional Markov birth-and-death processes, Stochastic Process. Appl. 29 (1988) 1-50.

Book:

I. Kaj, Stochastic Modeling in Broadband Communications Systems. SIAM Monographs on Mathematical Modeling and Computation 8, Society for Industrial and Applied Mathematics, Philadelphia PH, 2002.

Chapter in book:

I. Kaj, M.S. Taqqu, Convergence to fractional Brownian motion and to the Telecom process: the integral representation approach. In an Out of Equilibrium 2, Eds. M.E. Vares, V. Sidoravicius. Progress in Probability, Vol 60, 383-427. Birkhauser 2008.
I. Kaj, Limiting fractal random processes in heavy-tailed systems. In: Fractals in Engineering, New Trends in Theory and Applications, p 199-218. Eds. J. Levy-Lehel, E. Lutton, Springer-Verlag London 2005.

Refereed conference proceedings:

I. Kaj, T. Morozova, Performance evalutaion and capacity Analysis of a cellular network with retransmission policy. Extended Abstract, PhD Workshop. 35th International Teletraffic Congress, ITC35, 3-5 October 2023, Turin, Italy.
T. Morozova, I. Kaj, Analysis of a typical cell in the uplink cellular network model using stochastic simulation. In proceedings of IEEE 2nd Conference on Information Technology and Data Science, CITDS 2022, Debrecen, Hungary, July 2022.
I. Kaj, V. Konane, Analytical and stochastic modeling of battery cell dynamics. Proceed. 19th Intern. Conf. Analytic and Stochastic Modelling Techn. and Appl. K. Al-Begain, D. Fiems, and J.-M. Vincent (Eds.): ASMTA 2012, Lecture Notes in Computer Science, Vol 7314, 240--254, 2012.
I. Kaj, Probabilistic analysis of hierarchical cluster protocols for wireless sensor networks. Proceed. of NET-COOP 2009, Eds.: R.Nunez-Queija and J. Resing. Lecture Notes in Computer Science, Vol 5894, 137-151, 2009.
H. Bierme, A. Estrade, I. Kaj, Scaling properties of Poisson germ-grain models with power-law grain size (Extended Abstract) Russian-Scandinavian Symposium: Probability and Applied Probability, Petrozavodsk, August 2006.
H. Bierme, A. Estrade, I. Kaj, About scaling behavior of random balls models. 6th Int. Conf. on Stereology, Spatial Statistics and Stochastic Geometry, Prague, June 2006.
N. Gunnarsson, I. Kaj, P. Mannersalo, Propagation properties for a message in a Brownian sensor network. Second Workshop on Spatial Stochastic Models for Wireless Networks, Boston, MA, April 2006.
I. Kaj, I. Marsh, Modelling the arrival process for packet audio. Proceedings of 2nd international workshop on QoS in Multiservice IP Networks (QoS-IP 2003), Milano, Feb 2003. Springer Lecture Notes in Computer Science, Vol 2601, 35-49.
I. Kaj, On scaling limits of arrival processes with long-range dependence. Kalashnikov Memorial Seminar, Petrozavodsk, Sept 2002. Information Processes 2-2 (2002) 201-203.
I.Kaj, J. Olsén, Stochastic equilibrium modeling of the TCP dynamics in various AQM environments. Proceedings of SPECTS 2002, Editors: M.S. Obaidat et al., San Diego, July 2002, pp. 481-493, The Society for Modeling and Simulation International, San Diego, CA, 2002 .
I.Kaj, J. Olsén, Throughput modeling and simulation for single connection TCP-Tahoe, 17th International Teletraffic Congress ITC'01, Salvador da Bahia, Brazil, Dec. 2001, pp 705-718. Elsevier Science, Amsterdam, 2001.
I. Kaj, A weak interaction epidemic among diffusing particles, Stochastic Partial Differential Equations, A. Etheridge (Ed.), London Mathematical Society, Lecture Note Series 216 (1995) 162-180
I. Kaj and P. Salminen, A note on first passages in branching Brownian motions, Frontiers in Pure and Applied Probab. 1 95-102, H. Niemi et al. (Eds.) TVP/VSP Moscow 1993.

Popular Science:

I. Kaj, Paths of Motion. International Innovation, Eurofocus Issue 6 (2011) 93-95.

Lecture Notes:

I. Kaj, Stochastic Modeling for Engineering Studies, Lecture Notes, Department of Mathematics, Uppsala University, updated version 2010.
I. Kaj, Aspects of Wireless Network Modeling based on Poisson Point Processes, Fields Institute Workshop on Applied Probability, Carleton University, Ottawa, May 2006.

Other Publications

I. Kaj, M. Caglar, A buffer Hawkes process for limit order books arXiv:submit/2033002 [math.PR], October 2017
M. Goergens, I. Kaj, Gaussian processes, bridges and membranes extracted from selfsimilar random fields. arXiv:1410.0511 [math.PR], Oct 2014.
I. Kaj, A. Martin-Löf, Scaling limit results for the sum of many inverse Levy subordinators. arXiv:1203.6831v1 [math.PR].
N. Gunnarsson, I. Kaj, P. Mannersalo, A growth model for Brownian sensors. Department of Mathematics, Uppsala University, U.U.D.M. 2006:27.