Stummer Publications
Selected Publications / Preprints
| M. Broniatowski, W. Stummer: Some theoretical foundations of bare-simulation optimization of some directed distances between fuzzy sets respectively basic belief assignments. Entropy 26, 312, 2024. https://doi.org/10.3390/e26040312 | |
| M. Broniatowski, W. Stummer: A precise bare simulation approach to the minimization of some distances. II. Further Foundations. arXiv:2402.08478v1 (77 pages) |
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| M. Broniatowski, W. Stummer: A precise bare simulation approach to the minimization of some distances. I. Foundations.
IEEE Transactions on Information Theory 69(5), May 2023, pp. 3062-3120, https://doi.org/10.1109/TIT.2022.3215496. See also arXiv:2107.01693v3 (71 pages). An earlier, extended, differently structured version can be found under the slightly different title „A precise bare simulation approach to the minimization of some distances. Foundations“ at arXiv:2107.01693v1 (typo-corr. v2), 2021, 94 pages. |
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| M. Broniatowski, W. Stummer: On a cornerstone of Bare-Simulation Distance/Divergence Optimization. In: F. Nielsen and F. Barbaresco (eds.), Geometric Science of Information 2023, Part I, Lecture Notes in Computer Science 14071, Springer, 2023, pp. 105–116. https://doi.org/10.1007/978-3-031-38271-0_11 |
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| M. Broniatowski, W. Stummer: A Unifying Framework for Some Directed Distances in Statistics. In: F. Nielsen, A.S.R. Srinivasa Rao and C.R. Rao (eds.), Handbook of Statistics Vol. 46, Academic Press/Elsevier, 2022, pp. 145-223. https://doi.org/10.1016/bs.host.2022.03.007.
See also arxiv:2203.00863 |
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| W. Stummer: Optimal transport with some directed distances. In: F. Nielsen and F. Barbaresco (eds.), Geometric Science of Information 2021, Lecture Notes in Computer Science 12829, Springer, 2021, pp. 829–840. https://doi.org/10.1007/978-3-030-80209-7_89 | |
| N.B. Kammerer, W. Stummer: Some dissimilarity measures of branching processes and optimal decision making in the presence of potential pandemics. Entropy 22(8), no. 874 (2020); 123 pages. https://doi.org/10.3390/e22080874 | |
| M. Broniatowski, W. Stummer: Some universal insights on divergences for statistics, machine learning and artificial intelligence. In: F. Nielsen (ed.), Geometric Structures of Information, pp. 149-211. Springer, 2019. https://doi.org/10.1007/978-3-030-02520-5_8 |
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| M. Broniatowski, E. Miranda, W. Stummer: Testing the number and nature of the components in a mixture distribution. In: F. Nielsen and F. Barbaresco (eds.), Geometric Science of Information 2019, Lecture Notes in Computer Science 11712, Springer, 2019, pp. 309–318. https://doi.org/10.1007/978-3-030-26980-7_32 | |
| B. Roensch, W. Stummer: Robust estimation by means of scaled power Bregman distances. Part I. Non-homogeneous data. In: F. Nielsen and F. Barbaresco (eds.), Geometric Science of Information 2019, Lecture Notes in Computer Science 11712, Springer, 2019, pp. 319–330. https://doi.org/10.1007/978-3-030-26980-7_33 | |
| B. Roensch, W. Stummer: Robust estimation by means of scaled power Bregman distances. Part II. Extreme Values. In: F. Nielsen and F. Barbaresco (eds.), Geometric Science of Information 2019, Lecture Notes in Computer Science 11712, Springer, 2019, pp. 331–340. https://doi.org/10.1007/978-3-030-26980-7_34 | |
| S. Krömer, W. Stummer: A new toolkit for mortality data analytics. In: A. Steland, E. Rafajlowicz͕, O. Okhrin (eds.), Stochastic Models, Statistics and Their Applications, Springer, 2019, pp. 393–407. https://doi.org/10.1007/978-3-030-28665-1_30 | |
| A.-L. Kißlinger, W. Stummer: A new toolkit for robust distributional change detection. Applied Stochastic Models in Business and Industry 34, pp. 682-699 (2018). https://doi.org/10.1002/asmb.2357 |
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| Cotta, V.A. Reisen, P. Bondon, W. Stummer: Robust estimation of covariance and correlation functions of a stationary multivariate process. Preprint, 2017. | |
| W. Stummer, A.-L. Kißlinger: Some new flexibilizations of Bregman divergences and their asymptotics. In: F. Nielsen and F. Barbaresco (eds.), Geometric Science of Information 2017, Lecture Notes in Computer Science 10589, Springer, 2017, pp. 514–522. https://doi.org/10.1007/978-3-319-68445-1_60 | |
| B. Roensch, W. Stummer: 3D insights to some divergences for robust statistics and machine learning. In: F. Nielsen and F. Barbaresco (eds.), Geometric Science of Information 2017, Lecture Notes in Computer Science 10589, Springer, 2017, pp. 460–469. https://doi.org/10.1007/978-3-319-68445-1_54 |
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| V.A. Reisen, C. Levy-Leduc, H.H.A. Cotta, T.T.A. Albuquerque, W. Stummer: Long-memory models under outliers: an application to air pollution level. In: B.R. Gurjar, P. Kumar, J.N. Govil (eds.), Environmental Science and Engineering, Vol. 3 – Air and Noise Pollution, Studium Press LLC, 2017, pp. 135-166. |
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| A.-L. Kißlinger and W. Stummer: Robust statistical engineering by means of scaled Bregman distances. In: C. Agostinelli, A. Basu, P. Filzmoser, D. Mukherjee (eds.), Recent Advances in Robust Statistics: Theory and Applications, Springer, 2016, pp. 81-113. https://doi.org/10.1007/978-81-322-3643-6_5 | |
| A.-L. Kißlinger and W. Stummer: New model search for nonlinear recursive models, regressions and autoregressions. In: F. Nielsen and F. Barbaresco (eds.), Geometric Science of Information 2015, Lecture Notes in Computer Science 9389, Springer, 2015, pp. 693-701. https://doi.org/10.1007/978-3-319-25040-3_74 | |
| A.-L. Kißlinger and W. Stummer: Some decision procedures based on scaled Bregman distance surfaces. In: F. Nielsen and F. Barbaresco (eds.), Geometric Science of Information 2013, Lecture Notes in Computer Science 8085, Springer, 2013, pp. 479-486. https://doi.org/10.1007/978-3-642-40020-9_52 | |
| W. Stummer and I. Vajda : On Bregman Distances and Divergences of Probability Measures. IEEE Transactions on Information Theory 58(3), pp. 1277-1288 (2012). https://doi.org/10.1109/TIT.2011.2178139 [arXiv:0911.2784] |
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| W. Stummer and W. Lao: Limits of Bayesian decision related quantities of binomial asset price models. Kybernetika 48(4), pp. 750-767 (2012). https://www.kybernetika.cz/content/2012/4/750/paper.pdf [ABSTRACT] |
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| R. Feicht and W. Stummer: An explicit non-stationary stochastic growth model. Chapter 7 of the book: O. de la Grandville (ed.), Economic Growth and Development, Frontiers of Economics and Globalization Vol. 11, 2011, pp. 141-202. Emerald Group Publishing Limited, Bingley UK. http://dx.doi.org/10.1108/S1574-8715(2011)0000011012 |
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| N.B. Kammerer and W. Stummer : Some distance bounds of branching processes and their diffusion limits. Preprint (45 pages) (2010). [arXiv:1005.3758] |
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| W. Stummer and I. Vajda: On divergences of finite measures and their applicability in statistics and information theory. Statistics 44, pp. 169-187 (2010). https://doi.org/10.1080/02331880902986919 |
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| R. Feicht and W. Stummer : Complete closed-form solution to a stochastic growth model and corresponding speed of economic recovery. IWQW Discussion Paper No. 5/2010 (29 pages) (2010). https://www.econstor.eu/bitstream/10419/41470/1/63745314X.pdf https://www.iwf.rw.fau.de/files/2016/03/05-2010.pdf |
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| W. Stummer and I. Vajda : Optimal statistical decisions about some alternative financial models. Journal of Econometrics 137, pp. 441-471 (2007). https://doi.org/10.1016/j.jeconom.2005.10.001 |
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| I. Schäl and W. Stummer : Basel-II compliant mapping of operational risks. Journal of Operational Risk 2(1), pp. 93 – 114 (2007). https://doi.org/10.21314/JOP.2007.021 |
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| W. Stummer : Some Bregman distances between financial diffusion processes. Proc. Appl. Math. Mech. 7, pp. 1050503 – 1050504 (2007). https://doi.org/10.1002/pamm.200700814 |
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| I. Schäl and W. Stummer : Kategorisierung operationeller Risiken im Umfeld von Basel II. FINANZ BETRIEB (now: CORPORATE FINANCE) 7(12), pp. 786-798 (2005). https://research.owlit.de/document/f5231ba2-a493-30aa-a96a-dd8a633a581f |
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| W. Stummer: Exponentials, Diffusions, Finance, Entropy and Information.
Monograph (230 pages, ISBN 3-8322-3186-2). Shaker Verlag (2004). https://www.shaker.de/de/content/catalogue/index.asp?lang=de&ID=8&ISBN=978-3-8322-3186-6 |
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| N. Henze and W. Stummer : Means and middle values in Stochastics. (in German; original title: Mittelwerte und Mitten in der Stochastik). MU 50(5), pp. 18-29 (2004). |
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| W. Stummer : Modern Mathematical Finance for Schools. (in German; original title: Moderne Finanzmathematik für die Schule). In: R. Biehler, J. Engel and J. Meyer, eds., Neue Medien und innermathematische Vernetzungen in der Stochastik, pp. 61 — 75, Verlag Franzbecker Hildesheim/Berlin (2004). |
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| W. Stummer : Nuances of the Non-Arbitrariness of Stock Price Modelling. (in German; original title: Nuancen der Nichtbeliebigkeit von Aktienkurs-Modellierungen). Stochastik in der Schule 23(2), pp. 7-13 (2003). Typo-Corrigenda: In Definition 4.1(ii) there should be >= (greater-than-or-equal-to-symbol) instead of > (greater-than-symbol). |
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| W. Stummer : Some potential means for venture valuation. The Journal of Entrepreneurial Finance (and Business Ventures) 7(3), pp. 39-52 (2002). |
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| W. Stummer : Decision risk reductions for stock indices. Advances and Applications in Statistics 2(1), pp. 79-99 (2002). |
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| W. Stummer : Some divergence properties of asset price models. Entropy 3(5), pp. 300-324 (2001). https://doi.org/10.3390/e3050300 |
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| W. Stummer : A Toolbox for Generalized Relative Entropies, EMM and Contingent Claim Valuation. In: M. Kohlmann and S. Tang, eds., Mathematical Finance, pp. 345-354, Birkhäuser Verlag Basel (2001) |
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| W. Stummer : On a statistical information measure in a generalized Samuelson-Black-Scholes world. Statistics & Decisions (now: Statistics & Risk Modeling) 19(3), pp. 289-314 (2001). https://doi.org/10.1524/strm.2001.19.3.289 |
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| L.C.G. Rogers and W. Stummer : Consistent fitting of one-factor models to interest rate data. Insurance: Mathematics & Economics 27, pp. 45-63 (2000). https://doi.org/10.1016/S0167-6687(00)00039-1 |
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| W. Stummer : On option pricing for non-lognormal perturbations of geometric Brownian motion. ZAMM Z. Angew. Math. Mech. (Applied Mathematics and Mechanics) 80 (S3), S857-S858 (2000). |
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| W. Stummer : On Novikov and arbitrage properties of multidimensional diffusion processes with exploding drift. Statistics & Probab. Letters 46(1), pp. 43-51 (2000). https://doi.org/10.1016/S0167-7152(99)00085-1 |
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| W. Stummer and K.-Th. Sturm : On exponentials of additive functionals of Markov processes. Stochastic Processes Appl. 85, pp. 45-60 (2000). https://doi.org/10.1016/S0304-4149(99)00064-2 |
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| W. Stummer : On a statistical information measure of diffusion processes. Statistics & Decisions (now: Statistics & Risk Modeling) 17(4), pp. 359-376 (1999). https://doi.org/10.1524/strm.1999.17.4.359 |
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| W. Stummer : On arbitrage in the Black-Scholes world – a new sufficient condition. ZAMM Z. Angew. Math. Mech. (Applied Mathematics and Mechanics) 79 (S3), S925-S926 (1999). |
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| W. Stummer : On bounded entropy of solutions of multidimensional stochastic differential equations. Statistics & Probab. Letters 36(4), pp. 327-336 (1998). https://doi.org/10.1016/S0167-7152(97)00079-5 |
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| W. Stummer : On exponential moments of Brownian functionals. Statistics & Probab. Letters 31(3), pp. 233-237 (1997). https://doi.org/10.1016/S0167-7152(96)00035-1 |
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| W. Stummer : The Novikov and entropy conditions of multidimensional diffusion processes with singular drift. Probab. Theory Relat. Fields 97, pp. 515-542 (1993). https://doi.org/10.1007/BF01192962 |
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| A. Wakolbinger and W. Stummer : On Schrödinger processes and stochastic Newton equations. Institutsbericht Nr. 367, Preprint Series of the Department of Mathematics at the Johannes Kepler University Linz, 1988. | |