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Institute of Stochastics

Secretariat
Kollegiengebäude Mathematik (20.30)
Room 2.056 und 2.002

Address
Karlsruher Institut für Technologie
Institut für Stochastik

Englerstr. 2
D-76131 Karlsruhe

Postadresse:
D-76128 Karlsruhe

Office hours:
Mo-Fr 10:00 - 12:00

Tel.: +49 721 608 43270/43265

Fax.: +49 721 608 46066

Publications

Preprints

  • C. Hirsch, G. Last (2017): On maximal hard-core thinnings of stationary particle processes. arXiv:1707.00494
  • F. Gieringer, G. Last (2017): Concentration inequalities for measures of a Boolean model. arXiv:1703.04971
  • G. Last, W. Tang and H. Thorisson (2016): Transporting random measures on the line and embedding excursions into Brownian motion. arXiv:1608.02016

Publications

71. G. Last and S. Ziesche (2017): On the Ornstein-Zernike equation for stationary cluster processes and the random connection model.
To appear in Advances in Applied Probability. An earlier version is available via arXiv:1607.02962

70. M. Klatt, G. Last, K. Mecke, C. Redenbach, F.M. Schaller, G.E. Schröder-Turk (2017): Cell shape analysis of random tessellations based on Minkowski tensors.
In. Tensor Valuations and their Applications in Stochastic Geometry and Imaging (M. Kiderlen, Eva B. Vedel Jensen, eds.), Springer, 2017. An earlier version is available via arXiv:1606.07653

69. D. Hug, M. Klatt, G. Last and M. Schulte (2017): Second order analysis of geometric functionals of Boolean models.
In: Tensor Valuations and their Applications in Stochastic Geometry and Imaging (M. Kiderlen, Eva B. Vedel Jensen, eds.), Springer, 2017. An earlier version is available via arXiv:1601.06718

68. Z . Kabluchko, G. Last and D. Zaporozhets (2017): Inclusion-exclusion principles for convex hulls and the Euler relation.
To appear in Discrete and Computational Geometry.
arXiv:1603.01357

67. G. Last (2016): Stochastic analysis for Poisson processes.
In: Stochastic Analysis for Poisson Point Processes(G. Peccati and M. Reitzner, eds.), Springer, 2016.
An earlier version is available via arXiv:1405.4416

66. G. Last, M.D. Penrose and S. Zuyev (2016): On the capacity functional of the infinite cluster of a Boolean model.
To appear in Annals of Applied Probability. An earlier version is available via arXiv:1601.04945

65. G. Last, G. Peccati and M. Schulte (2016): "Normal approximation on Poisson spaces: Mehler's formula, second order Poincaré inequalities and stabilization".
Probability Theory and Related Fields 165, 667-723. An earlier version is available via arXiv:1401.7568

64. D. Hug, G. Last and M. Schulte (2016): "Second order properties and central limit theorems for geometric functionals of Boolean models".
Annals of Applied Probability 26, 73-135, 2016. arXiv:1308.6519
arXiv:1308.6519v2 is an extended version of the paper containing two additional appendices.

63. G. Last and H. Thorisson (2015): "Construction and characterisation of stationary and mass-stationary random measures on R^d".
Stochastic Processes and their Applications, 125, 4473-4488, 2015. arXiv:1405.7566

62. D.J. Daley, S. Ebert, G. Last (2016): "Two lilypond systems of finite line-segments".
Probability and Mathematical Statistics 36, 221-246.
An earlier version is available via arXiv:1406.0096

61. S. Ebert and G. Last (2015): On a class of growth-maximal hard-core processes.
Stochastic Models 31, 153-184. arXiv:1303.2092

60. G. Last, M.D. Penrose, M. Schulte and C. Thaele (2014): "Moments and central limit theorems for some multivariate Poisson functionals".
Adv. in Appl. Probab. 46, 348-364. arXiv: 1205.3033v1

59. D. Hug, G. Last, Z. Pawlas and W. Weil (2014): "Statistics for Poisson models of overlapping spheres".
Advances in Applied Probability, 46, 937-962. arXiv:1301.1499

58. G. Last, E. Ochsenreither (2014): "Percolation on stationary tessellations: models, mean values and second order structure".
Journal of Applied Probability, 51A, 311-332. arXiv:1312.6366

57. G. Last (2014): "Perturbation analysis of Poisson processes".
Bernoulli 20, 486-513. arXiv:1203.3181

56. G. Last, P. Mörters, H. Thorisson (2014): "Unbiased shifts of Brownian motion".
Annals of Probability 2014, Vol. 42, No. 2, 431-463. arXiv:1112.5373

55. G. Last and M. Penrose (2013): "Percolation and limit theory for the Poisson lilypond model".
Random Structures Algorithms 42 (2013) 226–249. arXiv:1008.0769v1

54. J. Kampf, G. Last and I. Molchanov (2012): "On the convex hull of symmetric stable processes".
Proc. Amer. Math. Soc. 140, 2527-2535. pdf

53. K.A. Borovkov and G. Last (2012): "On Rice's formula for stationary multivariate piecewise smooth processes".
Journal of Applied Probability, 49, 351-363. arXiv:1009.3885v1

52. G. Last and R. Szekli (2011): "Comparisons and asymptotics for empty space hazard functions of germ-grain models".
Adv. in Appl. Probab. 43, 943-962. arXiv:1012.3056v1

51. G. Last and M. Penrose (2011): "Martingale representation for Poisson processes with applications to minimal variance hedging".
Stochastic Processes and their Applications, 121, 1588-1606. arXiv:1001.3972v1

50. C. Bordenave, S. Foss and G. Last (2011): "On the greedy walk problem".
Queueing Systems: Theory and Applications 68, 333-338. pdf

49. G. Last and H. Thorisson (2011): "What is typical?"
Journal of Applied Probability 48A (Special Volume), 379-390. arXiv:1103.0092v1

48. G. Last and H. Thorisson (2011): "Characterization of mass-stationarity by Bernoulli and Cox transports".
Communications on Stochastic Analysis 5, 251-269. pdf

47. G. Last and M. Penrose (2011): "Poisson process Fock space representation, chaos expansion and covariance inequalities".
Probability Theory and Related Fields. 150, 663-690.
DOI: 10.1007/s00440-010-0288-5. An earlier version is available via arXiv:0909.3205v1.

46. D. Gentner and G. Last (2011): "Palm pairs and the general mass transport principle".
Mathematische Zeitschrift 267, 695-716. An earlier version is available via arXiv:0902.0068v2.

45. G. Last (2010): "Stationary random measures on homogeneous spaces".
Journal of Theoretical Probability 23, 478-497. DOI: 10.1007/s10959-009-0231-9. pdf

44. G. Last (2010): "Modern random measures: Palm theory and related models". New Perspectives in Stochastic Geometry (W. Kendall und I. Molchanov, eds.),
Oxford University Press, 2010. pdf

43. J. Hoferer, L.M. Hoffmann, J. Goebbels, G. Last, W. Weil and G. Kasper (2009): "Reconstruction algorithms for the internal packing density distribution of fibrous filter media based on tomographic data".
Filtration 9, 147-154.

42. V. Baumstark and G. Last (2009): "Gamma distributions for stationary Poisson flat processes".
Advances in Applied Probability 41, 911-939. pdf

41. G. Last and H. Thorisson (2009): "Invariant transports of stationary random measures and mass-stationarity",
Annals of Probability 37, 790-813. (electronic reprint in ArXiv)

40. K. Borovkov and G. Last (2008): "On level crossings for a general class of piecewise-deterministic Markov processes",
Advances in Applied Probability 40, 815-834.

39. M. Heveling and G. Last (2007): "Point shift characterization of Palm measures on Abelian groups",
Electronic Journal of Probability, 12, 122-137. pdf

38. V. Baumstark and G. Last (2007): "Some distributional results for Poisson Voronoi tessellations",
Advances in Applied Probability 39, 16-40.

37. G. Last (2006): "On mean curvature functions of Brownian paths",
Stochastic Processes and their Applications, 116, 1876-1891.

36. G. Last (2006): "Stationary partitions and Palm probabilities",
Advances in Applied Probability, 38, 602-620.

35. M. Heveling and G. Last (2006): "Existence, uniqueness and algorithmic computation of general lilypond systems",
Random Structures & Algorithms, 29, 338-350.

34. D. Hug, G. Last and W. Weil (2006): "Polynomial parallel volume, convexity and contact distributions of random sets",
Probability Theory and Related Fields, 135, 169-200. pdf

33. M. Heveling and G. Last (2005): "Characterization of Palm measures via bijective point-shifts",
Annals of Probability 33, 1698-1715. pdf

32. D. Daley and G. Last (2004): "Descending chains, the lilypond model, and mutual nearest neighbour matching",
Advances in Applied Probability, 37, 604-628.

31. T. Konstantopoulos, G. Last and S. Lin (2004): "On a class of Lévy stochastic networks",
Queueing Systems, 46, 409-437. pdf

30. G. Last (2004): "Ergodicity properties of stress release, repairable system and workload models",
Advances in Applied Probability, 36, 471-498.

29. D. Hug, G. Last and W. Weil (2004): "A local Steiner-type formula for general closed sets and applications",
Mathematische Zeitschrift, 246, 237-272. pdf

28. M. Heveling, D. Hug and G. Last (2004): "Does parallel volume imply convexity?",
Mathematische Annalen, 328, 469-479. pdf

27. Y.M. Kabanov and G. Last: "Hedging in a model with transaction costs",
Proceedings of Steklov Institute of Mathematics, 237, 208-214, 2003.

26. D. Hug, G. Last and W. Weil: "Distance measurements on processes of flats",
Advances in Applied Probability, 35, 70-95, 2003. pdf

25. D. Hug, G. Last and W. Weil: "A survey on contact distributions", Morphology of Condensed Matter. Physics and Geometry of Spatially Complex Systems. (K. Mecke, D. Stoyan, eds.), Lecture Notes in Physics, 317-357, Springer, Berlin, 2002. pdf

24. D. Hug, G. Last and W. Weil: "Generalized contact distributions of inhomogeneous Boolean models",
Advances in Applied Probability, 34, 21-47, 2002. pdf

23. Y.M. Kabanov and G. Last: "Hedging under transaction costs in currency markets: a continuous-time model",
Mathematical Finance, 12, 63-70, 2002.

22. G. Last and R. Szekli: "Moments and Blackwell's convergence for repairable systems with heavy tailed lifetimes",
Markov Processes and Related Fields, 7, 469-490, 2001.

21. G. Last and R. Schassberger: "On the second derivative of the spherical contact distribution function of smooth grain models",
Probability Theory and Related Fields, 121, 49-72, 2001.

20. T. Konstantopoulos and G. Last: "On the dynamics and performance of stochastic fluid systems",
Journal of Applied Probability, 37, 652-667, 2000.

19. D. Hug and G. Last: "On support measures in Minkowski spaces and contact distributions in stochastic geometry",
Annals of Probability, 28, 796-850, 2000. pdf

18. G. Last and R. Schassberger: "On stationary stochastic flows and Palm probabilities of surface processes",
Annals of Applied Probability, 10, 463-492, 2000.

17. G. Last and H. Stamer: "Recurrence and transience properties of some neural networks: an approach via fluid limit models",
Queueing Systems, 32, 99-130, 1999.

16. T. Konstantopoulos and G. Last: "On the use of Lyapunov function methods in renewal theory",
Stochastic Processes and their Applications 79, 165-178, 1999.

15. G. Last and M. Holtmann : "On the empty space function of some germ-grain models",
Pattern Recognition 32, 1587-1600, 1999.

14. G. Last and R. Szekli: "Time and Palm stationarity of repairable systems",
Stochastic Processes and their Applications 79, 17-43, 1999.

13. G. Last and R. Szekli: "Asymptotic and monotonicity properties of some repairable systems",
Advances in Applied Probability 30, 1089-1110, 1998.

12. S. Foss and G. Last: "On the stability of greedy polling systems with general service policies",
Probability in the Engineering and Informational Sciences 12, 49 - 68, 1998.

11. G. Last and R. Szekli: "Stochastic comparison of repairable systems by coupling",
Journal of Applied Probability 35, 348 - 370, 1998.

10. G. Last and R. Schassberger: "On the distribution of the spherical contact vector of stationary grain models", Advances in Applied Probability 30, 36 - 52, 1998.

9. S. Foss and G. Last: "Stability of polling systems with exhaustive service policies and state dependent routing",
Annals of Applied Probability 6, 116 - 137, 1996.

8. G. Last: "Coupling with compensators",
Stochastic Process. Appl. 65, 147 - 170, 1996.

7. G. Last and R. Schassberger: "A flow conservation law for surface processes",
Advances in Applied Probability 28, 13 - 28, 1996.

6. G. Last: "Predictable projections for point process filtrations",
Probability Theory and Related Fields 99, 361-388, 1994.

5 G. Last: "Filtering of derived point processes",
Stochastic Process. Appl. 49, 297-330, 1994.

4. A. Brandt and G. Last : "On the pathwise comparison of jump processes driven by stochastic intensities",
Mathematische Nachrichten 167, 21-42, 1994.

3. G. Last: "On dependent marking and thinning of point processes",
Stochastic Process. Appl. 45, 73-94, 1993.

2. G. Last: "On Bayes' formula for doubly stochastic point processes on the real half-line",
Statistics 22, 431-448, 1991.

1. G. Last: "Some remarks on conditional distributions for point processes",
Stochastic Process. Appl. 34, 121-135, 1990.




Books

  • N. Henze und G. Last: "Mathematik für Wirtschaftsingenieure und für naturwissenschaftlich-technische Studiengänge", Band 1, Vieweg Verlag, 2. Überarbeitete und erweiterte Auflage 2005.
  • N. Henze und G. Last: "Mathematik für Wirtschaftsingenieure und für naturwissenschaftlich-technische Studiengänge", Band 2, Vieweg Verlag, 1. Auflage 2004.
  • G. Last und A. Brandt: "Marked Point Processes on the Real Line: The Dynamic Approach", Springer-Verlag, New York, 1995.



Talks


  • "Unbiased shifts of Brownian motion and balancing random measures", 10th German Probability and Statistics Days 2012, Stochastik-Tage Mainz, 06.-09.03.2012: pdf
  • "Gamma distributions in Poisson Voronoi and hyperplane tessellations", Spatial Network Models for Wireless Communications, Newton Institute Cambridge, 06.04.2010-09.04.2010: pdf
  • "On the chaos expansion of Poisson functionals", 53rd Annual Meeting of the Australian Mathematical Society, Adelaide, 28.09-01.10.2009: pdf
  • "On level crossings of certain Markovian jump processes", Stochastic Networks and Related Topics, Bedlewo, 27.05-01.2007: pdf

  • "Distributional properties of Poisson Voronoi tessellations", Prague Stochastics 2006, 22 August, 2006: pdf

  • "Stationary partitions and shift-coupling": Frankfurter Stochastik-Tage 2006, Frankfurt am Main, 14-17 March 2006: pdf
  • "On Palm measures of stationary spatial point processes": Stochastic Geometry and its Applications, 3-7 October 2005, University of Bern: pdf
  • "Filtering of marked point processes", National ICT Australia, Canberra, 20.07.2005: pdf
  • "On Boolean models with general compact particles", Gaussian Measure and Geometric Convexity, Snowbird, 18-23 July, 2004: pdf
  • "Palm measures and point stationarity", Workshop on spatial stochastic modelling, Edinburgh, 9-12 June, 2004: pdf
  • "On the absence of percolation in the lilypond model", 6th German Open Conference on Probability and Stochastics, Karlsruhe, 23-26 April, 2004: pdf

Stand: 04.11.2016