Michael Scheutzow

Address:

Veranstaltungen im Sommersemester 2013

Stochastic Processes II/Wahrscheinlichkeitstheorie III

Seminar Wahrscheinlichkeitstheorie

Oberseminar Stochastische Analysis

Lecture Notes WT3

Publications

  1. Ph. D. Thesis

    Qualitatives Verhalten der Lösungen von eindimensionalen nichtlinearen stochastischen Differentialgleichungen mit Gedächtnis, Kaiserslautern, 1983.


  2. Habilitation

    Stationary and periodic stochastic differential systems: A study of qualitative changes with respect to the noise level and asymptotics, Kaiserslautern, 1988.


  3. Papers in refereed journals

    1. Scheutzow, M. (1984)
      Qualitative behaviour of stochastic delay equations with a bounded memory,
      Stochastics 12, 41-80.

    2. Krüger, W., Scheutzow, M., Beste A. and Petersen, J. (1985)
      Markov- und Rainflowrekonstruktionen stochastischer Beanspruchungszeitfunktionen, Forschungsberichte VDI Reihe 18, Nr. 22, VDI-Verlag.

    3. Scheutzow, M. (1985)
      Some examples of nonlinear diffusion processes having a time-periodic law,
      The Annals of Probability 13, 379-385.

    4. Scheutzow, M. (1985)
      Noise can create periodic behavior and stabilize nonlinear diffusions,
      Stoch. Proc. Appl. 20, 323-331.

    5. Mohammed, S. E. A., Scheutzow, M., Weizsäcker, H. v. (1986)
      Hyperbolic state space decomposition for a linear stochastic delay equation,
      SIAM J. Control and Opt. 24, 543-551.

    6. Scheutzow, M. (1986)
      Periodic behavior of the stochastic Brusselator in the mean-field limit,
      Prob. Theory and Rel. Fields 72, 425-462.

    7. Scheutzow, M. (1987)
      Uniqueness and nonuniqueness of solutions of Vlasov-McKean equations,
      Journal Austral. Math. Soc. (Series A) 43, 246-256.

    8. Scheutzow, M. (1988, 1991)
      Periods of nonexpansive operators on finite L1 - spaces,
      Europ. J. Combinatorics 9, 73-81 and 12, 183.

    9. Santoro,N., Scheutzow, M. and Sidney, J. (1988)
      On the expected complexity of distributed selection,
      J. Parallel and Distributed Computing 5, 194-203.

    10. Mohammed, S. E. A., Scheutzow, M. (1990)
      Lyaponov exponents and stationary solutions for affine stochastic delay equations,
      Stochastics and Stoch. Reports 29 , 259-283.

    11. Scheutzow, M. (1990)
      Stationary stochastic perturbation of a linear delay equation,
      Stochastic Processes and their Applications, ed.: S. Albeverio et al., 327-332. Kluwer.

    12. Pinsky, R., Scheutzow, M. (1992)
      Some remarks and examples concerning the transience and recurrence of random diffusions,
      Ann. Inst. Henri Poincaré 28, 519-536.

    13. Scheutzow, M. (1993)
      Stabilization and destabilization by noise in the plane,
      Stochastic Analysis and Applications 11, 97-113.

    14. Scheutzow, M. (1993)
      A martingale approach to the PASTA-property,
      Jour. Appl. Prob. 30, 252-257.

    15. Scheutzow, M. (1994)
      A law of large numbers for upcrossing measures,
      Stoch. Proc. Appl. 53, 285-305.

    16. Scheutzow, M. (1995)
      An integral inequality and its application to a problem of stabilization by noise,
      J. Math. Anal. and Appl. 193, 200-208.

    17. Arnold, L., Scheutzow, M. (1995)
      Perfect cocycles through stochastic differential equations,
      Prob. Theory Rel. Fields 101, 65-88.

    18. Scheutzow, M. (1996)
      Noise-induced transitions for one-dimensional diffusions,
      Stochastic Analysis and Applications 14, 535-563.

    19. Scheutzow, M. (1996)
      On the perfection of crude cocycles,
      Random and Comp. Dynamics 4, 235-255.

    20. Scheutzow, M. (1996)
      Stability and instability for stochastic systems with time delay,
      ZAMM 76, Suppl. 3, 363-365.

    21. Mohammed, S. E. A., Scheutzow, M. (1996)
      Lyapunovexponents of linear stochastic functional differential equations driven by semimartingales.
      Part I: The multiplicative ergodic theory,
      Ann. Inst. Henri Poincaré 32, 69-105.

    22. Mohammed, S. E. A., Scheutzow, M. (1997)
      Lyapunovexponents of linear stochastic functional differential equations.
      Part II: Examples and case studies,
      The Annals of Probability 25, 1210-1240.

    23. Kager, G., Scheutzow, M. (1997)
      Generation of one-sided random dynamical systems by stochastic differential equations,
      Electronic J. Prob. 2, Paper 8, 17 pages.

    24. Mohammed, S. E. A., Scheutzow, M. (1998)
      Spatial estimates for stochastic flows in Euclidean space,
      The Annals of Probability 26, 56-77.

    25. Nussbaum, R. D., Scheutzow, M. and Verduyn Lunel, S. (1998)
      Periodic points of nonexpansive maps and nonlinear generalizations of the Perron-Frobenius theory,
      Selecta Mathematica, New Ser. 4, 141-181.

    26. Scheutzow, M., Weizsäcker, H. v. (1998)
      Which moments of a logarithmic derivative imply quasiinvariance?
      Documenta Mathematica 3, 261-272.

    27. Nussbaum, R. D., Scheutzow, M. (1998)
      Admissible arrays and a nonlinear generalization of Perron-Frobenius theory,
      J. London Math. Soc. 58, 526-544.

    28. Imkeller, P., Scheutzow, M. (1999)
      On the spatial asymptotic behaviour of stochastic flows in Euclidean space,
      The Annals of Probability 27, 109-129.

    29. Mohammed, S. E. A., Scheutzow, M. (1999)
      The stable manifold theorem for stochastic ordinary differential equations,
      The Annals of Probability 27, 615-652.

    30. Cranston, M., Scheutzow, M., Steinsaltz, D. (1999)
      Linear expansion of isotropic Brownian flows,
      Elect. Comm. in Probab. 4, 91-101.

    31. Scheutzow, M. (2000)
      Stability and instability of routings through a queueing network,
      Queueing Systems 35, 117-128.

    32. Cranston, M., Scheutzow, M., Steinsaltz, D. (2000)
      Linear bounds for stochastic dispersion,
      The Annals of Probability 28, 1852-1869.

    33. Chueshov, I., Scheutzow, M. (2001)
      Inertial manifolds and forms for stochastically perturbed retarded semilinear parabolic equations,
      J. Dynamics and Diff. Equations 13, 355-380.

    34. Lisei, H., Scheutzow, M. (2001)
      Linear bounds and Gaussian tails in a stochastic dispersion model,
      Stochastics and Dynamics 1, 389-403.

    35. Scheutzow, M. (2002)
      Comparison of various concepts of a random attractor: A case study,
      Archiv d. Math. 78, 233-240.

    36. Matoussi, A., Scheutzow, M. (2002)
      Stochastic PDE's driven by nonlinear noise and Backward Doubly SDE's,
      Journal of Theoretical Probability 15, 1-39.

    37. Cranston, M., Scheutzow, M. (2002)
      Dispersion rates under finite mode Kolmogorov flows,
      The Annals of Applied Probability 12, 511-532.

    38. Scheutzow, M., Steinsaltz, D. (2002)
      Chasing balls through martingale fields,
      The Annals of Probability 30, 2046-2080.

    39. Scheutzow, M. (2002)
      Asymptotics for the maximum in the coupon collector's problem,
      Math. Scientist 27, 85-90.

    40. Dereich, S., Fehringer, F., Matoussi, A., Scheutzow, M. (2003)
      On the link between small ball probabilities and the quantization problem for Gaussian measures on Banach spaces,
      Journal of Theoretical Probability 16, 249-265.

    41. Scheutzow, M., Maier, M., Reisslein, M., Wolisz, A. (2003)
      Wavelength reuse for efficient packet-switched transport in an AWG-based metro WDM network,
      IEEE/OSA Journal of Lightwave Technology 21, 1435-1455.

    42. Maier, M., Scheutzow, M., Reisslein, M. (2003)
      The arrayed-waveguide grating based single-hop WDM network: An architecture for efficient multicasting,
      IEEE Journal on Selected Areas in Communications, Special Series "Optical Communications and Networking" 21, 1414-1432.

    43. Mohammed, S. E. A., Scheutzow, M. (2003)
      The stable manifold theorem for nonlinear stochastic systems with memory I: Existence of the semiflow,
      Journal of Functional Analysis 205, 271-305.

    44. Lemmens, B., Scheutzow, M. (2003)
      A characterization of the periods of periodic points of 1-norm nonexpansive maps,
      Selecta Mathematica, New Ser. 9, 557-578.

    45. Mohammed, S. E. A., Scheutzow, M. (2004)
      The stable manifold theorem for nonlinear stochastic systems with memory II: The local stable manifold theorem,
      Journal of Functional Analysis 206, 253-306.

    46. Herrmann, S., Scheutzow, M. (2004):
      Rate of convergence for some self-attracting diffusions,
      Stoch. Proc. Appl. 111, 41-55.

    47. Chueshov, I., Scheutzow, M. (2004):
      On the structure of attractors and invariant measures for a class of monotone random systems,
      Dynamical Systems: An International Journal 19(2), 127-144.

    48. Chueshov, I., Scheutzow, M., Schmalfuß, B. (2005):
      Continuity properties of inertial manifolds for stochastic retarded semilinear parabolic equations,
      in: Interacting Stochastic Systems, eds.: J-D. Deuschel and A. Greven, p. 355-375, Springer.

    49. Lemmens, B., Scheutzow, M. (2005):
      On the dynamics of sup-norm nonexpansive maps,
      Ergodic Theory and Dynamical Systems 25(3), 861-871.

    50. Scheutzow, M. (2005):
      Exponential growth rates for stochastic delay differential equations,
      Stochastics and Dynamics 5(2), 163-174.

    51. Maier, M., Herzog, M., Scheutzow, M., Reisslein, M. (2005):
      PROTECTORATION: A fast and efficient multiple-failure recovery technique for
      resilient packet ring (RPR) using dark fiber, IEEE/OSA Journal of Lightwave Technology, Special issue on optical networks 23(10), 2816-2838.

    52. Dereich, S., Scheutzow, M. (2006):
      High resolution quantization and entropy coding for fractional Brownian motion,
      Electronic J. Probab. 11, 700-722.

    53. Scheutzow, M., Seeling, P., Maier, M., Reisslein, M. (2006):
      Shortest path routing in optical WDM ring
      networks under multicast traffic,
      IEEE Communication Letters 10(7), 564-566.

    54. Maier, M., Scheutzow, M., Herzog, M., and Reisslein, M. (2006):
      Multicasting in IEEE 802.17 resilient packet ring (RPR),
      OSA J. Optical Networking, 5(11), 841-857.

    55. Lemmens, B., Scheutzow, M., Sparrow, C. (2007):
      Transitive actions of finite abelian groups of sup-norm isometries,
      Europ. J. Combinatorics , 28(4), 1163-1179 .

    56. Scheutzow, M., Seeling, P., Maier, M., and Reisslein, M. (2007):
      WDM star subnetwork upgrade of optical ring networks for maximum spatial reuse under multicast traffic,
      IEEE Journal on Selected Areas in Communications, Special Series "Optical Communications and Networking", 25(4), 55--67.

    57. Zähle, H., Scheutzow, M., Reisslein, M., and Maier, M. (2007):
      On the multicast capacity of unidirectional and bidirectional packet-switched WDM ring networks, IEEE Journal on Selected Areas in Communications, Special Series "Optical Communications and Networking", 25(4), 105--119.

    58. Scheutzow, M., Seeling, P., Maier, M., and Reisslein, M. (2007):
      Multicasting in WDM upgraded resilient packet ring (RPR),
      OSA J. Optical Networking, 6(5), 415--421.

    59. An der Heiden, M., Sortais, M., Scheutzow, M., Reisslein, M., Seeling, P., Herzog, M., and Maier, M. (2007):
      Multicast capacity of optical packet ring for hotspot traffic,
      IEEE/OSA Journal of Lightwave Technology, 25(9), 2638-2652.

    60. Aurzada, F., Scheutzow, M., Herzog, M., Maier, M., and Reisslein, M. (2008)
      Delay analysis of ethernet passive optical networks with gated service,
      OSA J. Optical Networking, 7(1), 25--41.

    61. Scheutzow, M., Reisslein, M., Maier, M., and Seeling, P. (2008):
      Multicast capacity of packet-switched ring WDM networks,
      IEEE Transactions on Information Theory, 54(2), 623--644.

    62. McGarry, M.P., Reisslein, M., Colbourn, C.J., Maier, M., Aurzada, F. and Scheutzow, M. (2008):
      Just-in-time scheduling for multichannel EPONs,
      IEEE/OSA Journal of Lightwave Technology, 26(10), 1204-1216.

    63. Dimitroff, G., Scheutzow, M. (2009):
      Dispersion of volume under the action of isotropic Brownian flows,
      Stoch. Proc. Appl., 119(2), 588--601.

    64. Aurzada, F., Dereich, S., Scheutzow, M., and Vormoor, C. (2009):
      High resolution quantization and entropy coding of jump processes,
      J. Complexity, 25(2), 163--187.

    65. Crauel, H., Dimitroff, G., and Scheutzow, M. (2009):
      Criteria for strong and weak random attractors,
      J. Dynamics and Diff. Equations, 21(2), 233--247.

    66. Es-Sarhir, A., v. Renesse, M., and Scheutzow, M. (2009):
      Harnack inequality for functional SDEs with bounded memory, Electronic Comm. Probab., 14 560--565.

    67. Aurzada, F., Scheutzow, M., Reisslein, M., and Maier, M. (2010):
      Towards a Fundamental Understanding of the Stability and Delay of Offline WDM EPONs. IEEE/OSA Journal of Optical Communications and Networking, 2, 51--66.

    68. Es-Sarhir, A., v. Gaans, O., and Scheutzow, M. (2010):
      Invariant measures for stochastic functional differential equations with superlinear drift,
      Differential and Integral Equations, 23(1-2), 189--200.

    69. Dirr, N., Dondl, P., Grimmett, G., Holroyd, A., and Scheutzow, M. (2010):
      Lipschitz percolation, Electronic Comm. Probab., 15, 14--21.

    70. McGarry, M.P., Reisslein, M., Aurzada, F. and Scheutzow, M. (2010):
      Shortest Propagation Delay (SPD) First Scheduling for EPONs with Heterogeneous Propagation Delays, IEEE Journal on Selected Areas in Communications, special issue on "Next-Generation Broadband Optical Access Network Technologies", 28, 849--862.

    71. Ghazisaidi, N., Scheutzow, M., and Maier, M. (2010):
      Frame aggregation in fiber-wireless (FiWi) broadband access networks, Electronics Letters, 46(5), 377--379.

    72. v. Renesse, M., Scheutzow, M. (2010):
      Existence and uniqueness of solutions of stochastic functional differential equations , Random Operators and Stochastic Equations, 18(3), 267--284.

    73. Ghazisaidi, N., Scheutzow, M., and Maier, M. (2011):
      Survivability analysis of next-generation PONs and fiber-wireless (FiWi) access networks , IEEE Transactions on Reliability, 60(2), 479--492.

    74. Aurzada, F., Scheutzow, M., Reisslein, M., Ghazisaidi, N. and Maier, M. (2011):
      Capacity and Delay Analysis of Next-Generation Passive Optical Networks (NG-PONs), IEEE Transactions on Communications, 59(5), 1378--1388.

    75. v. Bargen, H., Scheutzow, M., and Waßerroth, S. (2011):
      Exponential growth rates for derivatives of stochastic flows, Stochastics and Dynamics, 11(2-3), 227-242.

    76. Hairer, M., Mattingly, J., and Scheutzow, M. (2011):
      Asymptotic coupling and a general form of Harris' theorem with applications to stochastic delay equations,
      Prob. Theory Rel. Fields, 149(1-2), 223--259.

    77. Dimitroff, G., and Scheutzow, M. (2011):
      Attractors and expansion for Brownian flows, Electronic J. Probab., 16(42), 1193--1213.

    78. Aurzada, F., Döring, H., Ortgiese, M., and Scheutzow, M. (2011):
      Moments of recurrence times for Markov chains, Electronic Comm. Probab., 16(28), 296--303.

    79. Chen, X., Duan, J., Scheutzow, M. (2011):
      Evolution systems of measures for stochastic flows, Dynamical Systems: An International Journal, 26(3), 323-334.

    80. Dirr, N., Dondl, P., Scheutzow, M. (2011):
      Pinning of interfaces in random media, Interfaces and Free Boundaries, 13(3), 411-421.

    81. Li, X.-M., Scheutzow, M. (2011):
      Lack of strong completeness for stochastic flows, Ann. Probab., 39(4), 1407-1421.

    82. An der Heiden, M., Sortais, M., Scheutzow, M., Reisslein, M., and Maier, M. (2012):
      Multicast capacity of optical ring network with hotspot traffic: The bi-directional WDM packet ring, Optical Switching and Networking, 9(1), 61-80.

    83. Dondl, P., Scheutzow, M. (2012):
      Positive speed of propagation in a semilinear parabolic interface model with unbounded random coefficients, Networks and Heterogeneous Media, 7(1), 137-150.

    84. Aurzada, F., Beck, S., Scheutzow, M. (2012):
      Wait-and-see strategies in polling models, Probab. Engrg. Inform. Sci., 26(1), 17-42.

    85. Chueshov, I., Scheutzow, M. (2013):
      Invariance and monotonicity for stochastic delay differential equations, Discrete Contin. Dyn. Syst. Ser. B, 18(6), 1533-1554.

    86. Scheutzow, M. (2013):
      Exponential growth rate for a singular linear stochastic delay differential equation, Discrete Contin. Dyn. Syst. Ser. B, 18(6), 1683-1696.

    87. Dereich, S., Scheutzow, M., Schottstedt, R. (2013):
      Constructive quantization: approximation by empirical measures, Ann. Inst. Henri Poincaré Probab. Stat., to appear.

    88. Kiaei, M., Fouli, K., Scheutzow, M., Maier, M., Reisslein, M., and Assi, C.:
      Low-latency polling schemes for long-reach passive optical networks, IEEE Transactions on Communications, to appear.

    89. Es-Sarhir, A., Scheutzow, M., Toelle, J. and v. Gaans, O.:
      Invariant measures for monotone SPDE's with multiplicative noise term, Appl. Math. Optim., to appear.

    90. Scheutzow, M. (2013):
      A stochastic Gronwall lemma, Infin. Dimens. Anal. Quantum Probab. Relat. Top., to appear.

  4. Papers in Proceedings

    1. Maier, M., Scheutzow, M., Reisslein, M., Wolisz, A. (2002):
      Wavelength reuse for efficient transport of variable-size packets in a metro WDM network,
      Proceedings of IEEE INFOCOM, 1432--1441, New York, June 2002.

    2. Lisei, H., Scheutzow, M. (2003):
      On the dispersion of sets under the action of an isotropic Brownian flow,
      in: Proceedings of the Swansea 2002 Workshop Probabilistic Methods in Fluids, 224--238, World Scientific.

    3. Scheutzow, M., Seeling, P., Maier, M., and Reisslein, M. (2005):
      Multicast capacity of packet-switched ring WDM networks,
      Proceedings of IEEE INFOCOM, 706--717, Miami, March 2005.

    4. Scheutzow, M. (2008):
      Attractors for ergodic and monotone random dynamical systems,
      in: Seminar on Stochastic Analysis, Random Fields and Applications V, 331--344,
      Birkhäuser.

    5. Scheutzow, M. (2009):
      Chaining techniques and their application to stochastic flows,
      in: Trends in Stochastic Analysis , eds: Blath, J., Mörters, P., Scheutzow, M., 35--63, Cambridge University Press.

    6. Kiaei, M., Fouli, K., Scheutzow, M., Maier, M., Reisslein, M., and Assi, C. (2012):
      Analysis for ethernet long-reach passive optical networks,
      Proceedings of the IEEE International Conference on Communications, Ottawa.

  5. Submitted papers

    1. Dondl, P., Scheutzow, M., Throm, S.:
      Pinning of interfaces in a random elastic medium and logarithmic lattice embeddings in percolation.

    2. Burdzy, K., Scheutzow, M.:
      Forward Brownian motion.

  6. Papers in preparation

    1. Schulze, S., Scheutzow, M.:
      Strong completeness and stochastic flows for stochastic differential equations with monotone drift.

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    Zuletzt aktualisiert am 15.4.2013