FB Informatik und Mathematik Institut für Mathematik
Schwerpunkt Stochastik
 
 
 

Prof. Dr. Wakolbinger

 Preprints

  • F. Hermann, A. González Casanova, R. dos Santos, A. Tóbiás and A. Wakolbinger, From clonal interference to Poissonian interacting trajectories, arXiv:2407.00793 [math.PR], submitted.

 Publikationen

  • J. L. Igelbrink, A. González Casanova, Ch. Smadi and A. Wakolbinger, Muller's ratchet in a near-critical regime: tournament versus fitness proportional selection, Theor. Popul. Biol. 158, 121-138 (2024), part of special issue celebrating Alison Etheridge's contribution to mathematical population genetics, edited by A. Véber, S. Pennington, A. Sturm. arXiv:2306.00471 [q-bio.PE])

  • A. González Casanova, Ch. Smadi and A. Wakolbinger, Quasi-equilibria and click times for a variant of Muller's ratchet, Electron. J. Probab. 28, 1-37 (2023), Oberwolfach preprint OWP-2022-18 (v2), arXiv:2211.13109 [math.PR] (v5)

  • A. Blancas, S. Gufler, S.Kliem, V. C.Tran and A. Wakolbinger, Evolving genealogies for branching populations under selection and competition, Ann. Appl. Probab. 33 (2023), 4528-4569, arXiv:2106.16201 [math.PR]

  • P. Pfaffelhuber and A. Wakolbinger, A diploid population model for copy number variation of genetic elements, Electron. J. Probab. 28 (2023), paper no. 47, 1-15; arXiv:2204.11140 [math.PR]

  • J. L. Igelbrink and A. Wakolbinger, Asymptotic Gaussianity via coalescence probabilities in the Hammond-Sheffield urn, ALEA Lat. Am. J. Probab. Math. Stat. 20 (2023), 53-74 , arxiv:2201.06576 [math.PR]

  • Z. Li, E. Pardoux and A. Wakolbinger, The height process of a continuous state branching process with interaction, J. Theor. Probab. 35 (2022) 142-185, arXiv:1904.04151 [math.PR]

  • F. Boenkost, A. González Casanova, C. Pokalyuk and A. Wakolbinger, Haldane's formula in Cannings models: The case of moderately strong selection, J. Math. Biol. 83, 70 (2021), arXiv:2008.02225 [math.PR]

  • E. Baake and A. Wakolbinger (eds.), Probabilistic Structures in Evolution , EMS Press, Berlin, 2021.

  • E. Baake and A. Wakolbinger, Microbial populations under selection, in Probabilistic Structures in Evolution, in E. Baake, A. Wakolbinger, eds., EMS Press, Berlin, 2021, pp. 43-68. arXiv:2004.01011 [q-bio.PE]

  • G. Kersting and A. Wakolbinger, Probabilistic aspects of Λ-coalescents in equilibrium and in evolution, in Probabilistic Structures in Evolution, E. Baake, A. Wakolbinger, eds., EMS Press, Berlin, 2021, pp. 223-246 . arXiv:2002.05250 [math.PR]

  • F. Boenkost, A. González Casanova, C. Pokalyuk and A. Wakolbinger, Haldane's formula in Cannings models: The case of moderately weak selection, Electron. J. Probab. 26 (2021), paper no. 4 (31 pages), arXiv:1907.10049 [math.PR]

  • C. Pokalyuk and A. Wakolbinger, Maintenance of diversity in a hierarchical host-parasite model with balancing selection and reinfection, Stoch. Proc. Appl. 30 (2020) 1119-1158. arXiv:1802.02429 [math.PR]

  • S.N. Evans and A. Wakolbinger, PATRICIA bridges. In: Genealogies of Interacting Particle Systems, eds. M. Birkner, R. Sun and J. Swart, Lecture Note Series, Institute for Mathematical Sciences, National University of Singapore, Vol. 38, pp. 233-267, World Scientific, 2020. arXiv:1806.06256 [math.PR]

  • E. Baake, A. González Casanova, S. Probst and A. Wakolbinger, Modelling and simulating Lenski's long-term evolution experiment, Theor. Popul. Biol. 127 (2019), 58-74. arXiv:1803.09995 [q-bio.PE].   Winner of the Feldman prize 2022

  • P. Pfaffelhuber and A. Wakolbinger, Fixation probabilities and hitting times under low levels of frequency-dependent selection, Theor. Popul. Biol. 124 (2018), 61-69. arXiv:1801.01584 [math.PR]

  • G. Kersting and A. Wakolbinger, On the time to absorption in Λ-coalescents, Adv. Appl. Probab. 50(A) (2018), 177-190. arXiv:1712.07553 [math.PR]

  • G. Kersting, J. Schweinsberg and A. Wakolbinger, The size of the last merger and time reversal in Λ-coalescents, Ann. Inst. H. Poincaré Probab. Statist. 54 (2018),1527-1555. arXiv:1701.00549 [math.PR]

  • E. Baake and A. Wakolbinger, Lines of descent under selection, J. Stat. Phys. 172 (2018),156-174. arXiv:1710.08209 [math.PR].

  • S. N. Evans and A. Wakolbinger, Radix sort trees in the large, Electron. Commun. Probab. 22 (2017), paper no. 68.

  • S. N. Evans, R. Gruebel and A. Wakolbinger, Doob--Martin boundary of R\'emy's tree growth chain, Ann. Probab. 45 (2017), 225-277. arXiv:1411.2526 [math.PR].

  • A. Greven, P. Pfaffelhuber, C. Pokalyuk and A. Wakolbinger, The fixation time of a strongly beneficial allele in a structured population, Electron. J. Probab. 21 (2016), paper no. 61, 42 pp. arXiv:1402.1769 [math.PR]

  • E. Baake, U. Lenz and A. Wakolbinger, The common ancestor type distribution of a Λ-Wright-Fisher process with selection and mutation, Electron. Commun. Probab. 21 (2016), paper no. 59, 16 pp. arXiv:1603.03605 [math.PR]

  • A. González Casanova, N. Kurt, A. Wakolbinger and L. Yuan, An individual-based model for the Lenski experiment, and the deceleration of the relative fitness, Stoch. Processes Appl. 126 (2016), 2211-2252. arXiv:1505.01751 [math.PR].   Winner of the Itô prize 2017

  • E. Baake and A. Wakolbinger, Feller's Contributions to Mathematical Biology, in: Schilling, R.L., Vondracek, Z., Woyczynski, W.A.: The Selected Papers of William Feller, vol. 2, pp. 25-43, Springer Verlag, 2015. arXiv:1501.05278 [math.HO]

  • U. Lenz, S. Kluth, E. Baake and A. Wakolbinger, Looking down in the ancestral selection graph: A probabilistic approach to the common ancestor type distribution, Theor. Popul. Biol. 103 (2015), 27-37. arXiv:1409.0642 [q-bio.PE]

  • E. Pardoux and A. Wakolbinger, A path-valued Markov process indexed by the ancestral mass, ALEA Lat. Am. J. Probab. Math. Stat. 12 (2015), 193-212. arXiv:1409.1901 [math.PR]

  • A. Veber and A. Wakolbinger, The spatial Lambda-Fleming-Viot process: an event-based construction and a lookdown representation, Ann. Inst. H. Poincaré Probab. Statist. 51 (2015), 570-598, arXiv:1212.5909 [math.PR]

  • I. Dahmer, R. Knobloch and A. Wakolbinger, The Kingman tree length process has infinite quadratic variation, Electron. Comm. Probab. 19 (2014) paper no 87 , 12 pp.

  • G. Kersting und A.Wakolbinger, Stochastische Prozesse, Birkhäuser, Oktober 2014.

  • I. Dahmer, G. Kersting, and A.Wakolbinger, The total external branch length of Beta-coalescents, Combinatorics, Probability and Computing 23 (2014), 1010-1027, arXiv:1212.5909 [math.PR]

  • G. Kersting, J. Schweinsberg and A.Wakolbinger, The evolving beta coalescent, Electron. J. Probab. 19 (2014), paper no 64, 27 pp.

  • V. Le, E. Pardoux and A. Wakolbinger, "Trees under attack": a Ray-Knight representation of Feller's branching diffusion with logistic growth, Probab Theory Relat Fields 155 (2013) 583-619. arXiv:1603.03605 [math.PR]

  • P. Pfaffelhuber, P. Staab and A. Wakolbinger, Muller's ratchet with compensatory mutations, Ann. Appl. Probab. 22 (2012), 2108-2132, arXiv:1108.4059v2 [math.PR].

  • S. N. Evans, R. Gruebel and A. Wakolbinger, Trickle-down processes and their boundaries, Electron. J. Probab. 17 (2012) paper no 1, 58 pp.

  • E. Pardoux and A. Wakolbinger, From Brownian motion with a local time drift to Feller's branching diffusion with logistic growth, Electron. Commun. Probab.16 (2011), paper 63, 720-731.

  • E. Pardoux and A Wakolbinger, From exploration paths to mass excursions - variations on a theme of Ray and Knight, in: Surveys in Stochastic Processes, Proceedings of the 33rd SPA Conference in Berlin, 2009, J. Blath, P. Imkeller, S. Roelly (eds.), EMS 2011. [pdf]

  • P. Pfaffelhuber, A. Wakolbinger and H. Weisshaupt, The tree length of an evolving coalescent, Probab Theory Relat Fields 151 (2011) 529-557, arXiv:0908.2444v1 [math.PR]

  • A. Etheridge, P. Pfaffelhuber and A. Wakolbinger, How often does the ratchet click? Facts, heuristics, asymptotics. in: "Trends in Stochastic Analysis" (Jochen Blath, Peter Mörters and Michael Scheutzow, eds), pp. 365-390, London Mathematical Society Lecture Note Series 353, Cambridge University Press 2009, arXiv:0709.2775v1 [math.PR].

  • G. Kersting und A. Wakolbinger, Elementare Stochastik, Birkhäuser 2008 (1st ed.), 2010 (2nd ed.)

  • M. Hutzenthaler and A. Wakolbinger: Ergodic behaviour of locally regulated branching populations, Ann. Appl. Probab. 17 (2007), no. 2, 474 - 501, arXiv:math/0509612v2 [math.PR].

  • P. Pfaffelhuber and A. Wakolbinger, The process of most recent common ancestors in an evolving coalescent, [ArXiv math.PR/0511743], Stoch. Processes Appl. 116 (2006), 1836-1859.

  • P. Pfaffelhuber, B. Haubold and A. Wakolbinger, Approximate genealogies under genetic hitchhiking, Genetics 174 (2006), 1995-2008.[pdf]

  • A. Etheridge, P. Pfaffelhuber and A. Wakolbinger, An approximate sampling formula under genetic hitchhikng, [ArXiv math.PR/0503485], [ESI preprint 1636], Ann. Appl. Probab. 16 (2006), 685-729.

  • D.A. Dawson, L.G. Gorostiza and A. Wakolbinger, Degrees of transience and recurrence and hierarchical random walks, [ArXiv math.PR/0401422], Potential Analysis (2005) 22: 305-350.

  • M. Birkner, J. Blath, M. Capaldo, A. Etheridge, M. Möhle, J. Schweinsberg and A. Wakolbinger, Alpha-stable branching and Beta coalescents, Electron. J. Probab. 10 (2005), 303-325 [paper]

  • M. Birkner, J.A. López Mimbela, A. Wakolbinger, Comparison results and steady states for the Fujita equation with fractional Laplacian, [ESI preprint 1265], [ArXiv math.AP/0302353], Annales Insitut Henri Poincaré (Analyse non lineaire) 22 (2005) 83-97.

  • D. Metzler, R. Fleißner, A. Wakolbinger, A. von Haeseler, Stochastic Insertion-Deletion Processes and Statistical Sequence Alignment [MFWvH04.pdf], in: "Interacting Stochastic Systems" (J. D. Deuschel, A. Greven, eds), pp. 247-267, Springer-Verlag Berlin Heidelberg 2005.

  • D.A. Dawson, L.G. Gorostiza and A. Wakolbinger, Hierarchical random walks, in: Asymptotic Methods in Stochastics: Festschrift for Miklós Csörgö. (L. Horváth, B. Szyszkowicz, eds) AMS, 2004 [ps 584k]

  • D.A. Dawson, L.G. Gorostiza and A. Wakolbinger, Hierarchical Equilibria of Branching populations, Electron. J. Probab 9 (2004) 316-381 (Paper 12)

  • K. Fleischmann, V. Vatutin, A. Wakolbinger, Branching systems with long living particles at the critical dimension. Theory Probab. Appl. 47 (3) (2002) 417-451 [ps 428k]
  • M. Birkner, J.A. López Mimbela, A. Wakolbinger, Blow-up of semilinear PDE's at the critical dimension. A probabilistic approach. Proc. Amer. Math. Soc. 130 (2002), no. 8, 2431-2442, [pdf 232k]

  • D. Metzler, S. Grossmann, A. Wakolbinger, A Poisson model for gapped local alignments. Statist. Probab. Lett. 60 (2002), no. 1, 91-100 [pdf 165k] [ps 230k]

  • A. Greven, A. Klenke, A. Wakolbinger, Interacting diffusions in a random medium: comparison and longtime behavior, Stoch. Proc. Appl. 98 (1) (2002) 23-41.

  • D.Metzler, R.Fleißner , A. Wakolbinger, A.v.Haeseler, Assessing variability by joint sampling of alignments and mutation rates. J. Mol. Evol. 53 (2001) 660-669 [pdf 310k] [ps 1150k]

  • D. Dawson , L. Gorostiza, A. Wakolbinger, Occupation time fluctuations in branching systems. J. Theoretical Probab. 14 (2001) 729-796.

  • A. Greven, A.Klenke, A. Wakolbinger, Interacting Fisher-Wright diffusions in a catalytic medium , Probab Theory Relat Fields 120 (2001) 1, 85-117

  • J.A. López-Mimbela, A. Wakolbinger, A probabilistic proof of non-explosion of a non-linear pde system, J. Appl. Prob 37 (2000) 635-641.

  • M. Birkner, A. Wakolbinger, A Comparison of Free Branching and Stepping Stone Models, in: "Stochastic Models" (L. Gorostiza, B.G. Ivanoff, eds), pp. 15-23, CMS Conference Proceedings vol 26, AMS 2000.

  • A. Greven, A. Klenke, A. Wakolbinger, The longtime behavior of branching random walk in a catalytic medium, Electronic Journal of Probability, Vol 4 (1999) , paper 12, pages 1-80.

  • V. Vatutin, A. Wakolbinger, Spatial branching populations with long individual lifetimes, Theory Probab. Appl. 43 (1998) 620-632.

  • J.A. López-Mimbela, A. Wakolbinger, Length of Galton-Watson trees and blow up of semilinear systems, J. Appl. Probab. 35 (1998) 802 - 811.

  • K. Matthes, R. Siegmund-Schultze, A. Wakolbinger, Recurrence of ancestral lines and offspring trees in time stationary branching populations, Math. Nachr. 185 (1997), 163-211.

  • J.A. López-Mimbela, A. Wakolbinger, Which critically branching populations persist? in: Classical and Modern Branching Processes (K. B. Athreya, P. Jagers, eds), IMA Vol. in Math. and its Appl. 84, p. 203-216, Springer 1997.

  • G. Leha, G. Ritter, A. Wakolbinger, An improved Lyapunov-function approach to the behavior of diffusion processes in Hilbert spaces, Stoch. Anal. Appl. 15 (1997) 59-89.

  • J.A. López-Mimbela, A. Wakolbinger, Clumping in Multitype-Branching Trees, Adv. Appl. Probab. 28 (1996) 1034-1050.

  • L.G. Gorostiza , K. Hochberg, A. Wakolbinger, Persistence of a critical super-2 process, J. Appl. Probab. 32 (1995) 534-540.

  • A. Wakolbinger, Limits of spatial branching populations, Bernoulli 1(1/2) (1995) 171-189.

  • K. Hochberg, A. Wakolbinger, Non-persistence of two-level branching particle systems in low dimensions, in: A. Etheridge (ed.), Stochastic Partial Differential Equations, London Math. Soc. Lecture Note Series 216 (1995), 126-140.

  • A. Wakolbinger, Poblaciones aleatorias ramificadas y sus equilibrios, Notas de investigación 9, Sociedad Matemática Mexicana 1994.

  • L.G. Gorostiza, A. Wakolbinger, Long time behavior of critical branching particle systems and applications, in: "Measure-Valued Processes, Stochastic Partial Differential Equations, and Interacting Systems" (D. A. Dawson, ed.), pp. 119 - 137, CMS Conference Proceedings vol 5, AMS 1994.

  • A. Stöckl, A. Wakolbinger, On clan recurrence and -transience in time stationary branching Brownian particle systems, in: "Measure-Valued Processes, Stochastic Partial Differential Equations, and Interacting Systems" (D. A. Dawson, ed.), pp. 213 - 219, CMS Conference Proceedings vol 5, AMS 1994.

  • L.G. Gorostiza, A. Wakolbinger, Asymptotic behavior of a reaction-diffusion system. A probabilistic approach. Random&Computational Dynamics 1 (1993), 445-463.

  • K. Matthes, R. Siegmund-Schultze, A. Wakolbinger, Equilibrium distributions of age-dependent Galton Watson processes II, Math. Nachr. 160 (1993) 313-324.

  • K. Matthes, R. Siegmund-Schultze, A. Wakolbinger, A spatial zero-one law for equilibria of branching particle systems, J. Theor. Probab. 6 (1993) 699-711.

  • A. Wakolbinger, Schrödinger Bridges from 1931 to 1991, in: E. Cabaña et al. (eds) , Proc. of the 4th Latin American Congress in Probability and Mathematical Statistics, Mexico City 1990, Contribuciones en probabilidad y estadística matemática 3 (1992) , pp. 61-79.

  • L.G.Gorostiza, S. Roelly, A. Wakolbinger, Persistence of critical multitype particle and measure branching processes, Probab. Theory Relat. Fields 92 (1992), 313-335.

  • K. Matthes, R. Siegmund-Schultze, A. Wakolbinger, Equilibrium distributions of age dependent Galton Watson processes I , Math. Nachr. 156 (1992), 233 - 267.

  • L. G. Gorostiza, A. Wakolbinger, Convergence to equilibrium of critical branching particle systems and superprocesses, and related nonlinear partial differential equations, Acta Applicandae Mathematicae 27 (1992), 269-291.

  • B. Chauvin, A. Rouault, A. Wakolbinger, Growing conditioned trees, Stoch. Processes Appl. 39 (1991), 117-130.

  • M. Pavon, A. Wakolbinger, On free energy, stochastic control, and Schrödinger processes, in:Modeling, Estimation and Control of Systems with Uncertainty, G.B. Di Masi, A. Gombani, A. Kurzhanski (eds.), pp. 334-348 Birkhäuser, Boston, 1991.

  • A. Wakolbinger, On the structure of entrance laws in discrete spatial critical branching processes, Math. Nachr. 151 (1991), 51-57.

  • L. Gorostiza, A. Wakolbinger, Persistence criteria for a class of critical branching particle systems in continuous time, Ann. Probability. 19 (1991), 266-288.

  • D. Dawson, L. Gorostiza, A. Wakolbinger, On Schrödinger processes and large deviations, J. Math. Phys. 31 (10) (1990), 2385-2388.

  • A. Wakolbinger, Interchange of large time and scaling limits in stable Dawson-Watanabe processes: a probabilistic proof, Bol. Soc. Mat. Mexicana, 33 (1990), 45-55.

  • L. Gorostiza , S. Roelly, A. Wakolbinger, Sur la persistance du processus de Dawson-Watanabe stable. L'interversion de la limite en temps et de la renormalisation. In: Seminaire de Probabilité XXIV (Lect. Notes Math., vol. 1426, pp. 275-281), Springer Verlag 1990

  • A. Wakolbinger, Welche kritisch verzweigenden Populationen überleben? Österr. Zeitschrift für Statistik und Informatik 20 (1990), 315-318.

  • A. Wakolbinger, A simplified variational characterization of Schrödinger processes, J. Math.Phys. 30 (12) (1989), 2943-2946.

  • A. Wakolbinger, Los procesos estocásticos de Schrödinger, Ciencia (Revista de la Academia de la Investigación Científica, México) 40 (1989), 199-208.

  • A. Wagner, A. Wakolbinger, E. Glötzl, Towards a method of smog prediction, Österr. Zeitschrift für Statistik und Informatik 19 (1989), 18-29.

  • A. Liemant, K. Matthes, A. Wakolbinger, Equilibrium Distributions of Branching Processes, Akademie Verlag, Berlin, and Kluwer Academic Publishers, Dordrecht, 1988.

  • W. Römisch, A. Wakolbinger, On convergence rates of approximate solutions of stochastic equations, in: H.J. Engelbert, W. Schmidt (Hrsg.) Stochastic Differential Systems, Lecture Notes in Control and Information Sciences 96, pp. 204-212, Springer Verlag, 1987.

  • W. Römisch, A. Wakolbinger, Obtaining convergence rates for approximations in Stochastic Programming, in: J. Guddat (Hrsg.) Parametric Optimization and Related Topics, pp. 327-343, AkademieVerlag Berlin, 1987.

  • E. Lindner, G. Oberaigner und Hj. Wacker, A. Wakolbinger, The hydroelectric storage power plant Partenstein: Forecasting models for the influxand efficiency determination, in: Proc.der 18. Jahrestagung ``Mathematische Optimierung'', Rostock/Diedichshagen, 1986, Seminarbericht Nr. 85 der Humboldt-Univ. zu Berlin, , pp. 59-69 (1986).

  • H. Föllmer, A. Wakolbinger, Time reversal of infinite-dimensional diffusions, Stoch. Processes Appl. 22 (1986), 59-77.

  • H.W. Engl, A. Wakolbinger, Continuity properties of the extension of a locally Lipschitz continuous map to the space of probability measures, Monatshefte f. Math. 100 (1985), 85-103.

  • W. Römisch, A. Wakolbinger, On Lipschitz dependence in systems with differentiated inputs,Math. Ann. 272 (1985), 237-248.

  • A. Wakolbinger, G. Eder, A condition Σλc for point processes, Math. Nachr. 116 (1984),209- 232.

  • A. Wakolbinger, G. Eder, Balance equations and Σ'-type conditions for point processes, Proc. of the 3rd Pannonian Symp. on Math. Statistics, Visegrad, 1982, Akadémiai Kiadó, Budapest, pp. 363-376, 1984

  • H.W. Engl, A. Wakolbinger, On weak limits of probability distributions on Polish spaces, Stoch. Anal. and Appl. 1 (1983), 197-203.

  • M.P. Ershov, A. Wakolbinger, On the existence of Markov processes with given transition functions, Stochastics 6 (1982), 139-145.

  • E. Glötzl, A. Wakolbinger, Bayes estimators and ergodic decomposability with an application to Cox processes, Ann. Probability 6 (1982), 872-876.

  • J. Kerstan, A. Wakolbinger, Ergodic decomposition of probability laws, Z. Wahrscheinlichkeitsth.verw. Gebiete 56 (1981), 399-414.

  • J. Kerstan, A. Wakolbinger, Opérateurs markoviens et l'ensemble de leurs lois de probabilité invariantes, C.R.Acad. Sci. Paris Ser. A., t. 219, 163-166 (1980)

  • B. Rauchenschwandtner, A. Wakolbinger, Some aspects of the Papangelou kernel, in: P. Bártfai and J. Tomkó (eds.), Point Processes and Queuing Problems, North-Holland, Amsterdam-Oxford-New York, pp. 325-336,1981.

  • E. Glötzl, B. Rauchenschwandtner, A. Wakolbinger, On point processes with tail measurable conditional intensity kernels, Math. Nachr. 93 (1979), 151-158.

 
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