Probability and Stochastic Analysis - University of Bonn
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Research papers

[75] Gradient Flows for Semiconvex Functions on Metric Measure Spaces - Existence, Uniqueness and Lipschitz Continuity, arXiv:1410.3966. PDF
[74] Metric Measure Spaces with Variable Ricci Bounds and Couplings of Brownian Motions, arXiv:1405.0459. PDF
[73] Ricci Tensor for Diffusion Operators and Curvature-Dimension Inequalities under Conformal Transformations and Time Changes, arXiv:1401.0687. PDF
[72] Optimal maps and exponentiation on finite dimensional spaces with Ricci curvature bounded from below, with Nicola Gigli and Tapio Rajala. PDF
[71] On the equivalence of the Entropic curvature-dimension condition and Bochner’s inequality on metric measure spaces, with Matthias Erbar and Kazumasa Kuwada, arXiv:1303.4382. PDF
[70] The space of spaces: curvature bounds and gradient flows on the space of metric measure spaces, arXiv:1208.0434. PDF
[69] Non-branching geodesics and optimal maps in strong CD (K, ∞)-spaces, with Tapio Rajala. Appeared in Calc. Var. PDEs. PDF
[68] Bochner-Weitzenböck formula and Li-Yau estimates on Finsler manifolds, with Shin-ichi Ohta. Adv. Math., 252:429–448, 2014. PDF
[67] Monotonicity of time-dependent transportation costs and coupling by reflection, with Kazumasa Kuwada. Potential Anal., 39(3):231–263, 2013. PDF
[66] CDloc (K,N) IMPLIES MCP(K,N), with Fabio Cavaletti. Journal of Functional Analysis, 262, n° 12, 5110-5127, 2012. PDF
[65] Generalized Orlicz Spaces and Wasserstein Distances for convex-concave Scale Functions. Bulletin des Sciences Mathématiques, 135, n° 6-7, 795-802, 2011 . PDF
[64] Optimal transport from Lebesgue to Poisson, with Martin Huesmann. Ann. Probab., 41(4):2426–2478, 2013. PDF
[63] Non-contraction of heat flow on Minkowski spaces, with Shin-ichi Ohta. Archive for Rational Mechanics and Analysis, 204. n° 3, 917-944, 2012. PDF
[62] A Monotone Approximation to the Wasserstein Diffusion. In "Singular Phenomena and Scaling in Mathematical Models" (ed. M. Griebel), pages 3–23, Springer, 2014. PDF
[61] Localization and Tensorization Properties of the Curvature-Dimension Condition for Metric Measure Spaces II, with Qintao Deng. Journal of Functional Analysis vol. 260 n° 12, 3718-3725, 2011 PDF
[60] Localization and Tensorization Properties of the Curvature-Dimension Condition for Metric Measure Spaces, with Kathrin Bacher. Journal of Functional Analysis, 259 Issue 1, 28-56, 2010. PDF
[59] Ricci bounds for euclidean and spherical cones, with Kathrin Bacher. In "Singular Phenomena and Scaling in Mathematical Models" (ed. M. Griebel), pages 3–23, Springer, 2014. PDF
[58] Mass Transportation and rough curvature bounds for discrete spaces, with Anca-Iuliana Bonciocat. Journal of Functional Analysis, 256, n° 9, 2944-2966, 2009. PDF
[57] Entropic Measure on Multidimensional Spaces. Stochastic analysis, random fields and applications VI. Progress in Probability. Birkhäuser, 2010. PDF
[56] Heat flow on Finsler manifolds, with Shin-ichi Ohta. Comm. Pure Appl. Math. , Vol. 62, n° 10, 1386-1433, 2009. PDF
[55] Wasserstein spaces over Wiener spaces, with S. Fang and J. Shao. Probab. Theory and related Fields, Vol. 146, Numbers 3-4, 535-565, 2010. PDF
[54] Entropic Measure and Wasserstein Diffusion, with Max-Konstantin von Renesse. Ann. Prob. , Vol. 37, Number 3, 1114-1191, 2009. PDF
[53] On a Liouville type theorem for harmonic maps to convex spaces via Markov chains, with Kazuhiro Kuwae. In proceedings of RIMS Workshop on Stochastic Analysis and Applications, RIMS Kkyroku Bessatsu, B6, pages 177-191. Res. Inst. Math. Sci. RIMS, Kyoto, 2008. PDF
[52] Counterexample for the Optimality of Kendall-Cranston Coupling, with Kazuhiro Kuwae. Electron. Comm. Probab. 12:66-72, 2007. PDF
[51] Expectations and Martingales in Metric Spaces, with Tom Christiansen. Stochastics, 801:1-17, 2008. PDF
[50] On the geometry of metric measure spaces II. Acta Math. 196, no. 1, 133-177 2006. PDF
[49] A curvature-dimension condition for metric measure spaces. C. R. Math. Acad. Sci. Paris 342, no. 3, 197-200 2006. PDF
[48] Generalized Ricci curvature bounds and convergence of metric measure spaces. C. R. Acad. Sci. Paris, Ser. I 340,235-238 2005. PDF
[47] On the geometry of metric measure spacesin Acta Math. 196, no.1, 65-131 2006. PDF
[46] Convex functionals of probability measures and nonlinear diffusions on manifolds J. Math. Pures. Appl. 84, 149-168 2005. PDF
[45] Coupling, regularity and curvature In "Interacting Stochastic Systems", edt. J.-D. Deuschel and A. Greven. Springer 2004. PDF
[44] Maximal Coupling of Euclidean Brownian Motions, with Elton Hsu. Com. Math. Stat., 1(1), 2014. PDF
[43] Construction of Diffusion Processes on Fractals, d-sets, and general Metric Measure Spaces, with Takashi Kumagai. J. Math. Kyoto Univ., 452:307-327, 2005 PDF
[42] Transport Inequalities, Gradient Estimates, Entropy and Ricci Curvature, with Max-Konstantin von Renesse. In Comm. Pure Appl. Math. 68,923-940 2005. PDF
[41] Probability Measures on Metric Spaces of Nonpositive Curvature. In 'Heat Kernels and Analysis on Manifolds, Graphs, and Metric Spaces', Lecture Notes from a quarter program on heat kernels, random walks, and analysis on manifolds and graphs, April 16- July 13, 2002 Paris, France. Edts. P. Auscher et al. Providence, RI: American Mathematical Society AMS. Contemp. Math. 338, 2003. PDF
[40] Discretization and Convergence for Harmonic Maps into Trees, with Martin Hesse and Martin Rumpf. Calc. Var. 21, 113-136 2004. PDF
[39] A semigroup approach to harmonic maps. Potential Analysis. 23,225-277 2005. PDF
[38] Harmonic map heat flow generated by Markovian semigroups.In: Evolution equations: applications to physics, industry, life sciences and economics. Proceedings of the 7th international conference on evolution equations and their applications, EVEQ2000 conference, Levico Terme, Italy, October 30-November 4, 2000. Herausgeg. von M. Iannelli et al. Basel: Birkhuser. Prog. Nonlinear Differ. Equ. Appl. 55, 359-373 (2003).
[37] Markov semigroups and harmonic maps.In ”Nichtlineare partielle Differentialgleichungen und geometrische Analysis”, herausgeg. von S. Hildebrandt und H. Karcher, pp 487- 504. Springer 2002
[36] Nonlinear martingale theory for processes with values in metric spaces of nonpositive curvature.Annals of Probability 30 (2002), 1195-1222
[35] Nonlinear Markov operators associated with symmetric Markov kernels.Calc. Var. 12 (2001), 317-357
[34] Nonlinear Markov operators, discrete heat flow, and harmonic maps between singular spaces.Potential Analysis 16 (2002), 305-340
[33] Dirichlet forms and their applications in stochastics, analysis and geometry.Bulletin of the International Statistical Institute, 52nd Session, Invited Papers, 1999
[32] mit W. Stummer: On exponentials of additive functionals of Markov processes.Stochast. Proc. and their Appl. 85 (2000), 45-60
[31] The geometric aspect of Dirichlet forms.In: ”New directions in Dirichlet forms.” (Ed. by J. Jost, W. Kendall, U. Mosco, M. Röckner, K.T. Sturm) International Press and AMS 1998.
[30] Monotone approximation of energy functionals for mappings into metric spaces. II. Potential Analysis 11 (1999), 359-386
[29] Monotone approximation of energy functionals for mappings into metric spaces. I. J. reine angew. Math. 486 (1997), 129-151
[28] Metric spaces of lower bounded curvature. Expo. Math. 17 (1999), 35-48 PDF
[27] Is a diffusion determined by its intrinsic metric? Chaos Solitons Fractals 8 (1997), 1855-1866 PDF
[26] Diffusion processes and heat kernels on length spaces. Annals of Probab. 26 (1998), 1-55
[25] How to construct diffusion processes on metric spaces. Potential Analysis 8 (1998), 149-161
[24] mit Y. Oshima: On the conservativeness of a space-time process. In ”Probability and Mathematical Statistics (Proceedings of the 7th Japan-Russia Symposium 1995)”, ed. by S. Watanabe, M. Fukushima, Yu. V. Prohorov and A. N. Shiryaev. World Scientific 1996
[23] mit R. Höhnle: On the structure of subordinate semigroups. Forum Math. 9 (1997), 641-654
[22] mit E. M. Ouhabaz, P. Stollmann und J. Voigt: The Feller property for absorption semigroups. J. Funct. Anal. 138 (1996), 351-378
[21] Sharp estimates for capacities and applications to symmetric diffusions. Prob. Theory Related Fields 102 (1995), 73-89
[20] mit V. Metz: Gaussian and non-Gaussian estimates for heat kernels on the Sierpinski gasket. In ”Dirichlet Forms and Stochastic Processes (Proceeding of an international conference in Beijing 1993)”, ed. by Z.Ma and M. Röckner, pp. 283-289. De Gruyter 1995
[19] On the geometry defined by Dirichlet forms. In ”Seminar on Stochastic Analysis, Random Fields and Applications (Ascona 1993)” (ed. by E. Bolthausen et al.), pp. 231-242. Birkh¨auser 1995
[18] mit R. Höhnle: Some zero-one-laws for additive functionals of Markov processes. Prob. Theory Related Fields 100 (1994), 407-416
[17] Analysis on local Dirichlet spaces – III. The parabolic Harnack inequality. J. Math. Pures Appl. 75 (1996), 273-297 PDF
[16] Analysis on local Dirichlet spaces – II. Upper Gaussian estimates for the fundamental solutions of parabolic equations. Osaka J. Math. 32 (1995), 275-312 PDF
[15] Schrödinger operators and Feynman-Kac semigroups with arbitrary nonnegative potentials. Expo. Math. 12 (1994), 385-411
[14] Analysis on local Dirichlet spaces – I. Recurrence, conservativeness and Lp- Liouville properties. J. Reine Angew. Math. 456 (1994), 173-196
[13] Harnack’s inequality for parabolic operators with singular low order terms. Math. Z. 216 (1994), 593-611
[12] mit P. Kröger: Hölder continuity of normalized solutions of the Schrödinger equation. Math. Ann. 297 (1993), 663 - 670
[11] On the Lp-spectrum of uniformly elliptic operators on Riemannian manifolds. J. Funct. Anal. 118 (1993), 442 - 453
[10] mit R. Höhnle: A multidimensional analogue to the 0-1-law of Engelbert and Schmidt. Stochastics 44 (1993), 27-41
[9] Schrödinger semigroups on manifolds. J. Funct. Anal. 118 (1993), 309 - 350
[8] Schrödinger operators with arbitrary nonnegative potentials. In ”Operator Calculus and Spectral Theory—Proceedings Conf. Lambrecht 1991” (ed. by M. Demuth, B. Gramsch and B.-W. Schulze), pp. 291 - 306. Birkh¨auser 1992
[7] Schrödinger operators with highly singular, oscillating potentials. Manuscripta Math. 76 (1992), 367 - 395
[6] Heat kernel bounds on manifolds. Math. Ann. 292 (1992), 149 - 162
[5] Measures charging no polar sets and additive functionals of Brownian motion. Forum Math. 4 (1992), 257 - 297
[4] Gauge theorems for resolvents with application to Markov processes. Probab. Th. Rel. Fields. 89 (1991), 387 - 406
[3] Störung von Hunt-Prozessen durch signierte additive Funktionale. Dissertation, Erlangen 1989
[2] Schrödinger equations with discontinuous solutions. In ”Potential Theory” (ed. by J. Král, J. Lukeˇs, I. Netuka and J. Vesel´y), pp. 333-337. Plenum Press 1988
[1] On the Dirichlet-Poisson problem for Schrödinger operators. C. R. Math. Rep. Acad. Sci. Canada 9 (1987), 149-154