# Publications

**(a) Books**

- [1]
*Generalized diffusion operators*, Akademie Verlag Berlin/Wiley VCH, ``Mathematical Research", Vol.**75**(1993), 120 pp. (ISBN 3-05-501617-3, ISSN 0138-3019) - [2]
*Econometrics, Mathematical Theory and Applications (German: Ökonometrie, Mathematische Theorie und Anwendungen)*, Verlag Vieweg Wiesbaden/Springer (2001), VIII+330 pp. (ISBN 352803176X)

**(b) Diploma, Ph.D., Habilitation (second Ph.D. degree) Theses**

- [3]
*On the rate of convergence of the distribution of the integrated periodogram to the normal distribution*(germ.), Diploma thesis, Dresden University of Technology (1983), 79 p. - [4]
*Generalized second order differential operators and nonconservative one-dimensional quasi- diffusion processes*(germ.), Ph.D. thesis, University of Jena (1988), 105 p. - [5]
*Linear operators, bilinear forms, and Markov processes*, Habilitation thesis, University of Jena (1996), 166 p.

**(c) Articles in Journals**

- [6]
A class of procedures to compute the optimal value function in a Markovian decision problem,
*Optimization***17**3 (1986), 399-409. - [7]
Generalized second order differential operators,
*Mathematische Nachrichten***152**(1991), 229-245. - [8]
Classification of boundaries of diffusions (russ.),
*Ukrainian Mathematical Journal***43**5, (1991), 626-631. - [9]
Constructions and generators of one-dimensional quasidiffusions with applications to selfaffine diffusions and
Brownian motion on the Cantor set,
*Stochastics and Stochastic Reports***42**(1993), 93-114. - [10]
Geometrical structures induced by continuous strong Markov processes associated with generalized second order elliptic
differential operators,
*Stochastics and Stochastic Reports***47**(1994), 103-120. - [11]
(with N.I. Portenko) On a class of perturbations of the generator of the stable process,
*Theory of Probability and Mathematical Statistics***52**(1995), 102-111. - [12]
(with L. Ritter) The limiting power of the Durbin-Watson test,
*Communications in Statistics: Theory and Methods***29**(2000), 2665 - 2676. - [13] A clat Copy of the Ornstein-Uhlenbeck operator on the path space over a Riemannian manifold,
*Infinite Dimensional Analysis and Quantum Probability***5**, No. 3 (2002) 351-394. World Scientific - [14]
Closability of positive symmetric bilinear forms with applications to classical and stable forms,
*Osaka Journal of Mathematics***40**, No. 3 (2003) 563-594. OJM - [15]
(with Uta Freiberg) Zeros of the eigenfunctions of a class of generalized second order differential operators on the
Cantor set,
*Mathematische Nachrichten***265**(2004) 3-14. Wiley Online Library - [16]
A class of processes on the path space over a compact Riemannian manifold with unbounded diffusion,
*Transactions of the American Mathematical Society***356**, No. 9 (2004), 3751-3767. American Mathematical Society - [17]
A Stationary Fleming-Viot type Brownian particle system,
*Mathematische Zeitschrift*,**263**, No. 3 (2009), 541-581. SpringerLink - [18]
Weak Convergence of n-Particle Systems Using Bilinear Forms,
*Milan Journal of Mathematics***81**, No. 1 (2013), 37-77. SpringerLink , arxiv, pdf - [19]
Absolute Continuity under Time Shift for Ornstein-Uhlenbeck type Processes with Delay or Anticipation,
*Communications in Stochastic Analysis***8**, No. 4 (2014), 439-448. COSA , arxiv, pdf

- [20]
(with John Karlsson) A class of infinite dimensional stochastic processes with
unbounded diffusion,
*Stochastics***87**, No. 3 (2015), 424-457. Taylor & Francis , arxiv, pdf - [21]
Mosco Type Convergence of Bilinear Forms and Weak Convergence of n-Particle
Systems,
*Potential Analysis***43**, No. 2 (2015), 241-267. SpringerLink , arxiv, pdf - [22]
(with John Karlsson) Infinite dimensional Ornstein-Uhlenbeck processes with unbounded diffusion - Approximation,
quadratic variation, and Itô formula,
*Mathematische Nachrichten***289**, No. 17-18 (2016), 2192-2222. Wiley Online Library , arxiv, pdf - [23]
Absolute Continuity under Time Shift of Trajectories and Related Stochastic Calculus,
*Memoirs of the American Mathematical Society***249**, No. 1185 (2017), 135 pp. American Mathematical Society , arxiv, pdf - [24] Boundedness of the Stationary Solution to the Boltzmann Equation with Spatial Smearing, Diffusive Boundary Conditions,
and Lions' Collision Kernel,
*SIAM Journal on Mathematical Analysis (SIMA)***50**, No. 6 (2018), 5761-5782. SIAM , arxiv, pdf - [25] Knudsen Type Group for Time in R and Related Boltzmann Type Equations,
*Communications in Contemporary Mathematics*, published electronically 09 - 2021,**25**, No. 03, 2150072 (2023), 72 pp. World Scientific , arxiv, pdf - [26] Quasi-Invariance under Flows Generated by Non-Linear PDEs,
*Analysis and Applications*, Vol. 22, No 01, 179-277 (2024) World Scientific ; version 2021 86 pp. arxiv, pdf

**(d) Conference Proceedings**

- [27]
Generalized second order differential operators and nonconservative
quasidiffusions with natural boundaries, in H.J. Engelbert, W. Schmidt
(eds.) Stochastic Differential Systems, Lecture Notes in Control and
Information Sciences
**96**, 164-175, Springer: Berlin Heidelberg New York London Paris Tokyo (1987). - [28]
Generators and geometrical structures of continuous strong
Markov processes in
*R*^{d}, in M. Dozzi, H.J. Engelbert, D. Nualart (eds.) Stochastic Processes and Related Topics, Mathematical Research**61**, 81-87, Akademie Verlag Berlin (1991). - [29] (with G. Müller, M. Roth und A. Stock) Mathematical models of plasmid partitioning in unicellular bacteria and streptomyces, in D. Noak, H. Krügel, S. Baumberg (eds.) Genetics and Product Formation in Streptomyces, 315-320, Plenum Publishing Corp., New York and London (1991).
- [30]
Multidimensional continuous strong Markov processes with
transition densities, in H.J. Engelbert, I. Karatzas, M.
Röckner (eds.) Stochastic Processes and Optimal Control,
Stochastics Monographs
**7**, 115-136, Gordon and Breach Science Publishers (1993). - [31]
Generalized second order partial differential operators in
analysis and probability, in H.J. Engelbert, H. Föllmer, J.
Zabczyk (eds.) Stochastic Processes and Related Topics,
Stochastics Monographs
**10**, 49-60, Gordon and Breach Science Publishers (1996). - [32] (with Uta Freiberg) On the Zeros of Eigenfunctions of the Generator of a Gap Diffusion, in S. Albeverio, Z.-M. Ma, M. Röckner (eds.) Recent Developments in Stochastic Analysis and related topics, Proceedings of the First Sino-german meeting on stochastic analysis - satellite conference of the ICM, Bejing, PR China, 2002, 182-198, World Scientific (2004).
- [34] Boltzmann Equation and Knudsen Group - Boundary Shape and Boundary Conditions,
*Journal of Physics: Conference Series***2701**(2024), Art. No. 012118, 11 pp. JPCS

**(f) Research Reports**

- [34] (with J. Groh) Über nichtkonservative verallgemeinerte Differentialoperatoren zweiter Ordnung, Forschungsergebnisse FSU, N/85/3, 20 pp.
- [35] (with J. Groh) Darstellung linearer Operatoren als verallgemeinerte Differentialoperatoren zweiter Ordnung, Forschungsergebnisse FSU, N/85/27, 20 pp.
- [36]
Linear local operators satisfying the local maximum principle
and associated Markov processes and geometrical structures in
in
*R*^{d}I-IV, Forschungsergebnisse FSU, Math/91/4, 85 pp. - [37]
Closability of positive symmetric bilinear forms under non-
regularity assumptions and its probabilistic counterpart, Publikationen
des SFB 256 (Bonn)
**394**(1995), 50 pp.

Lectures and Posters

**(a) Lectures at Conferences**

**August 1990**2nd World Congress of the Bernoulli Society, Uppsala (Sweden)**September 1990**19th Conference on Stochastic Processes and their Applications, Eisenach (Germany)**September 1991**(with G. Müller, M. Roth, and A. Stock, lecture delivered by G. Müller): 7th VAAM Workshop ``Biology of Streptomyces" Stuttgart Hohenheim (Germany)**January 1992**3rd European Symposium on Analysis and Probability, Paris (France)**June 1993**22nd Conference on Stochastic Processes and their Applications, Amsterdam (Netherlands)**October 1994**5th European Symposium on Analysis and Probability, Bonn (Germany)**April 1996**International Conference on Stochastic Differential Geometry and Infinite Dimensional Analysis, Hangzhou (China)**January 2000**AMS Conference, Washington D.C. (USA)**June 2001**International Conference on Stochastic Analysis, Lvov (Ukrain)**July/August 2002**4th IMS Probability Symposium, Banff (Canada)**July 2004**6th World Congress of the Bernoully Society for Mathematical Statistics and Probability and 67th Annual Meeting of the Institute of Mathematical Statistics, Barcelona (Spain)**June 2005**30th Conference on Stochastic Processes and their Applications, Santa Barbara, CA (USA)**October 2013**Conference on Stochastic Analysis and Applications, Hammamet (Tunisia)**May 2015**Conference Probability and Analysis, Bedlewo (Polen)**July 2017**39th Conference on Stochastic Processes and their Applications, Moscow (Russia)**July 2019**41st Conference on Stochastic Processes and their Applications, Evanston/Chicago, IL (USA)**August 2023**12th International Conference on Mathematical Modeling in Physical Sciences, Belgrade (Serbia)

**May 1986**5th IFIP Working Conference ``Stochastic Differential Systems", Eisenach (Germany)

numerous talks presented at workshops, meetings, etc.

**(b) Posters**

**May 1990**(with G. Müller, M. Roth, and A. Stock): Genetics and Product Formation in Streptomyces, Erfurt (Germany)**August 1991**(with G. Müller, M. Roth, and A. Stock, presented by M. Roth): International Symposium on Biology of Actinomycetes, (ISBA 1991) Madison, WI (USA)

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Last updated: 2024-02-29