Henri Schurz Assistant Professor Dr. rer. nat.

Carbondale, Illinois Minneapolis, Minnesota Dresden, Germany

Main Scientific Interests:

Current Courses (spring semester 2002)

Math 250 - Calculus II (Spring 2002)

Math 305 - Introduction to Differential Equations (Spring 2002)

Math 582 - Stochastic Differential Equations (Confirmed for Spring 2003)

Math 150 - Calculus I (Fall 2001)

Math 472 - Linear Programming (Fall 2001)

Math 8660 - Topics in Probability: Stochastic Differential Equations (Spring 2001)

Math 5652 - Introduction to Stochastic Processes (Spring 2000)

Math 4242 - Applied Linear Algebra (Fall 1999)

Math 1272 - Calculus II (Spring 2001)

Math 1272 - Calculus II (Spring 2000)

Math 1271 - Calculus I (Fall 2000)

Math 1031 - College Algebra & Probability (Fall 1999)

Past Teaching - Complete Teaching List 1986 - 2002 (in html)

Curriculum Vitae and Teaching Experiences 1986 -- 2001 and Detailed Publication List

Research Results and References (Recommendations) and Summary of Ph.D. Thesis

Academic Career:

• Assistant Professor at Southern Illinois University, Department of Mathematics, Carbondale, USA, since August 2001
• Assistant Professor at University of Minnesota, School of Mathematics, Minneapolis, USA, 1999 - 2001
• Visiting stays at more than 30 academic, research-oriented institutions / universities
• Postdoctoral Research Fellowship sponsored by DFG at University of Kaiserslautern, Department of Mathematics (AG Technomathematics), 1999, Kaiserslautern, Germany
• Reviewer for Annals of Applied Probability since 2001-
• Permanent Reviewer for Zentralblatt of Mathematics since 1998-
• Reviewer for SIAM Journal on Numerical Analysis since 1997-
• Associate Professor (Invited) in Stochastic Processes at Department of Mathematics, University Los Andes, 1997-1999, Bogota, Colombia 
• Part-time Lecturer in Stochastic Numerics, Stochastic Dynamical Systems and Mathematical Modelling at Humboldt University, 1994-1997, Berlin, Germany
• Invited Guest Lecturer on Stochastic Dynamical Systems at University of Innsbruck, Institute for Mechanics, Innsbruck, Austria, 1996.
• Ph. D. in Mathematics (Thesis on 'Stability Theory of Numerical Methods for Systems of Stochastic Differential Equations', Head of Ph.D. Commission: Prof. Dr. Hans Foellmer), 1997.  Humboldt University, Department of Mathematics, Institute for Stochastics, Berlin, Germany
• Member of National Research Foundation Grant 378 ''Quantification and Simulation  of Economical Processes'' of DFG, 1994-1996, Berlin, Germany
• Research Associate at Weierstrass Institute (WIAS), 1992-1996, Berlin, Germany
• Invited Programmer at Murdoch University, Department of Mathematics, 1991, Perth, WestAustralia
• Research Assistant at Academy of Sciences of former GDR, 1989-1991, Berlin, EastGermany
• Master  in Mathematics (Thesis on Control of Discrete Markov Chains, Advisors: Prof. Dr. P.H. Mueller, Dr. G. Maibaum), 1989. Technical University, Department of Mathematics, Dresden, EastGermany

Scientific Interests:

• Análisis estocástico. Ecuaciones diferenciales estocásticas
• Análisis numérico.  Sistemas dinámicos estocásticos
• Matemáticas financieras y marketing, Ingenería estocastica
• Estadística matemática, Probabilidad aplicada
• Modelamiento matemático y aplicaciones. 
• Análisis funcional. Operadores positivos, Teoría de medidas.

Publication List (see Curriculum Vitae Icon above)

List of Publications: monographs and textbooks

• [36]. H. Schurz: `An introduction to analytical and numerical methods for (ordinary) stochastic differential equations', monograph in progress, Carbondale, 2001.
• [35]. H. Schurz: `Stability, stationarity, and boundedness of some implicit numerical methods for stochastic differential equations and applications', Logos-Verlag, Berlin, pp. 288, 1997 (Research Monograph, ISBN 3-931216-94-2).
• [34]. S.S. Artemiev, Y.G. Michaylichenko, H. Schurz, I.O. Shkurko, M.A. Yakunin: `Numerical integration of ordinary SDEs with 'Dynamics and Control' (Computer Manual), Computer Center, Russian Academy of Sciences, Siberian Division, Novosibirsk, 1997.
• [33]. P.E. Kloeden, E. Platen, H. Schurz: `Numercial solution of stochastic differential equations through computer experiments', Universitext, Springer-Verlag, New York, pp. 292, 1997 (Second edition, first edition 1994, Advanced Textbook, ISBN 3-540-57074-8).

List of Publications: refereed papers in international journals (status: in preparation or submitted)

• [32]. H. Schurz: A brief introduction to numerical analysis of SDEs without tears, Preprint m-01-005 (2001), 1-177, Department of Mathematics, SIU, Carbondale, 2001.
• [31]. H. Schurz: `Qualitative analysis of (balanced) stochastic Theta methods', Manuscript, SIU, Carbondale, 2001.
• [30]. H. Schurz; `General theorems for numerical approximation of stochastic processes on the Hilbert space $H_2 ([0,T])$', Preprint m-01-006 (2001), 1-19, Department of Mathematics, SIU, Carbondale, 2001.
• [29]. K.R. Schneider and H. Schurz: `Waveform relaxation methods for stochastic differential equations', Report 1733, IMA, University of Minnesota, Minneapolis, 2000 (submitted).
• [28]. H. Schurz: `Partial- and linear-implicit numerical methods for nonlinear stochastic differential equations', Manuscript, University of Minnesota, Minneapolis, 2000.
• [27]. H. Schurz: `On the numerical approximation of some functionals of SDEs with application to mathematical finance', Manuscript, University of Minnessota, Minneapolis, 2000.
• [26]. H. Schurz: `On Taylor series expansions and conditional expectations for (ordinary) Stratonovich stochastic differential equations with V-commutativity', Report 1671, IMA, University of Minnesota, Minneapolis, 1999 (to be resubmitted).
• [25]. H. Schurz: `General principles for numerical approximation of stochastic processes on stochastically weak Banach spaces', Report 1669, IMA, University of Minnesota, Minneapolis, 1999 (in revision).

List of Publications: refereed papers in international journals (status: accepted or appeared)

• [24]. H. Schurz: `Moment attractivity, stability and contractivity exponents of stochastic dynamical systems', Discrete Cont. Dyn. Syst. 7 (3), 487-515 (2001), also Report 1741, IMA, University of Minnesota, 2000, also earlier version `Moment contractivity and stability exponents of nonlinear stochastic dynamical systems', Technical Report No. 215, University of Kaiserslautern, 1999, Report 1656, IMA, University of Minnesota, Minneapolis, 1999.
• [23]. H. Schurz: `On moment-dissipative stochastic dynamical systems', Dyn. Syst. Appl. 10 (1), 11-44, (2001), Technical Report No. 214, University of Kaiserslautern, 1999.
• [22]. H. Schurz: `Preservation of probabilistic laws through Euler methods for Ornstein-Uhlenbeck process', Stochastic Anal. Appl. 17 (3), p. 463-486, 1999.
• [21]. H. Schurz: `The invariance of asymptotic laws of stochastic systems under discretizaction', Z. Angew. Math. Mech. 79 (6), p. 375-382, 1999.
• [20]. G.N. Mil'shtein, E. Platen, H. Schurz: `Balanced implict methods for stiff stochastic systems', SIAM J. Numer. Anal. 35 (3), p. 1010-1019, 1998.
• [19]. L.B. Ryashko and H. Schurz: `Mean square stability analysis of some stochastic systems', Dyn. Syst. Appl. 6 (2), p.165-190, 1997.
• [18]. H. Schurz: `Modelling and analysis of stochastic innovation diffusion', ZAMM 76 (Suppl. 3, I-XV), p. 366-369, 1996.
• [17]. H. Schurz: `Numerical regularization for SDEs: Construction of nonnegative solutions', Dyn. Syst. Appl. 5 (1), p. 323-352, 1996.
• [16]. H. Schurz: `Asymptotical mean square stability of an equilibrium point of some linear numerical solutions', Stochastic Anal. Appl. 14 (3), p. 313-354, 1996.
• [15]. P.E. Kloeden, E. Platen, H. Schurz, M. Sorensen: `On effects of discretization on estimators of drift parameters for diffusion processes', J. Appl. Prob. 33, p. 1061-1076, 1996.
• [14]. Karmeshu, H. Schurz: `Effects of distributed delay on the stability of structures under seismic excitation and multiplicative noise', SADHANA 20 (2-4), p. 451-474, 1995.
• [13]. S.S. Artemiev, H. Schurz: `Stiff systems of stochastic differential equations with small noise and their numerical solution' (in Russian), Report No. 1039, Vychisl. Tsentr Ross. Akad. Nauk Sib. Otd., Novosibirsk, p. 1-24, 1995.
• [12]. T.A. Averina, S.S. Artem'ev, H. Schurz: `Numerical analysis of stochastic auto-oscillating systems', Bull. Novosib. Comput. Cent., Ser. Numer. Anal. 6, p. 9-27, 1995.
• [11]. P.E. Kloeden, E. Platen, H. Schurz: `The numerical solution of nonlinear stochastic dynamical systems: a brief introduction', J. Bifur. Chaos 1 (2), p. 227-286, 1991.

List of Publications: refereed papers in special volumnes

• [10]. H. Schurz: `Numerical analysis for SDE without tears' (invited chapter), in V. Lakshmikantham, D. Kannan, Handbook of Stochastic Analysis and Applications, Marcel Dekker, Basel, October 2001, 239-361.
• [9]. Karmeshu, H. Schurz: `Moment evolution of the outflow-rate from nonlinear conceptual reservoirs', in Surface Water-Hydrology 1, ed. by V.P. Singh and B. Kumar, Kluwer Academic Publishers, Dordrecht, p. 403-413, 1996.
• [8]. Karmeshu, H. Schurz: `Stochastic stability of structures under active control with distributed time delays', Applications of Statistics and Probability: Civil Engineering Reliability and Risk Analysis, ed. by M. Lemaire, J.-L. Favre, A. Mebarki, A.A. BALKEMA Publishers, Rotterdam, p. 1111-1119, 1995.
• [7]. P.E. Kloeden, E. Platen, H. Schurz: `Higher order approximate Markov chain filters´, in Stochastic Processes: A Festschrift in Honour of Gopinath Kallianpur, ed. by S. Cambanis et al, Springer, New York, p. 181-190, 1993.
• [6]. P.E. Kloeden, E. Platen, H. Schurz: `Effective simulation of optimal trajectories in stochastic control', in Optimazation: Techniques and Applications, ed. by K.H. Phua et al., Vol. 2, World Scientific, Singapore, p. 633-644, 1992.

List of Publications: papers in proceedings

• [5]. H. Schurz: 'Stability analysis of (balanced) stochastic Theta methods', in Proc. Stochastic Numerics Workshop 2001, ETH, Zurich, pp. 32, 2001. 
• [4]. H. Schurz: `Remarks on preservation of asymptotical mean square and pathwise properties of bilinear SDE by numerical methods', in Proc. AMCA-95, Internat. Conf. Advanced Mathematics, Computations and Applications (Novosibirsk, June 1995), NCC Publisher, Novosibirsk, p. 291-292, 1995. 
• [3]. H. Schurz: `Mean square stability analysis of some numerical methods solving bilinear SDEs', in Proc. Workshop on Stochastics and Finance (Berlin, September 1994), Sonderdruck at Humboldt University, Berlin, p. 77-78, 1994.
• [2]. H. Schurz: `Approximate Markov chain filtering', in Proc. 1st Workshop on Stochastic Numerics (Gosen, September 1992), in Report No. 21, IAAS, Berlin, p. 83-84, 1992.
• ([1]. P.E. Kloeden, E. Platen, N. Hofmann, H. Schurz: `The stochastic Taylor formula and higher order numerical schemes for stochastic differential equations', in Proc. New Computation Methods in Turbulent Mixing, Loughborough, 1991.)

Selected Academic Invitations:  

38. Dresden's University of Technology, Dresden, Germany, June 2001, 
37. University of Wisconsin, Milwaukee, USA, March 2001, 
36. Washington State University, Pullman, USA, March 2001, 
35. George Mason University, Fairfax, USA, March 2001, 
34. Clarkson University, Potsdam, USA, March 2001, 
33. Southern Utah University, Cedar City, USA, March 2001, 
32. Southern Illinois University, Carbondale, USA, February 2001, 
31. University of Catania, Catania, Italy, July 2000, 
30. Courant Institute, New York University, New York, USA, May/June 2000, 
29. University of Nebraska, Omaha, USA, February 2000, 
28. Weierstrass Institute (WIAS), Berlin, Germany, June-July 1998, November 1999, January 2000, May-August 2000, January 2001, 
27. Indiana State University, Bloomington, USA, October 1999, 
26. Technical University Cottbus, Cottbus, Germany, May 1999. 
25. University of Freiburg, Freiburg i.B., Germany, May 1999. 
24. The Fields Institute, Toronto, Canada, April 1999. 
23. University of Tennessee, Knoxville, USA, February 1999. 
22. Max-Planck Institute for Demographic Research, Rostock, Germany, February, 1999. 
21. University of Greifswald, Greifswald, Germany, January, 1999. 
20. London School of Economics, London, England, March 1998. 
19. University of North Carolina, Raleigh, USA, March 1998. 
18. University of Braunschweig, Germany, January 1998. 
17. Technical University, Dresden, Germany, January 1998. 
16. Universidad Nacional de Colombia, Colombia, November 1997. 
15. Universidad de Los Andes, Bogota, Colombia, 1997-1999. 
14. University of Edinburgh, Edinburgh, Scotland, April 1997 and June 1997. 
13. Max-Planck Institute for Complex Systems Physics, Dresden, Germany, February 1997. 
12. University of Athens, Greece, July 1996. 
11. ETH, Zurich, Switzerland, November 1995, June 1996 and February 2001, 
10. University of Innsbruck, Institute for Mechanics, Innsbruck, Austria, May-June 1996. 
9. Morehouse College, Atlanta, USA, May 1995. 
8. Massey University at Palmerston North, New Zealand, March 1994. 
7. Jawaharlal Nehru University, New Delhi, India, December 1993. 
6. University of Waterloo, Canada, June 1993. 
5. University of Bremen, Germany, multiple visits 1997, 1994, 1993, 1992. 
4. Ural State University, Ekaterinburg, Russia, November-December 1992. 
3. Australian National University, Canberra, Australia, December 1991. 
2. Murdoch University, Perth, WestAustralia, September-December 1991. 
1. University of Hamburg, Germany, June 1991. 

My thesis students:  
1. Señor Cesar Guzman, Departamento de Ingeniería Industrial, Universidad de Los Andes, Bogotá, on some SDEs with Applications to Mathematical Finance (Exotic Options), 1997-1999 (Master Thesis 1999) 
2. Señor M. Richter, Humboldt University, Berlin, on Stochastic Numerical Analysis, 1996 (Master Thesis 1996) 

Social interests:  practicar todos formas de deporte y  lenguas 

Some Personal Data: Citizenship - Germany, Gender - Male 
Birth Dates: 1964 in Goerlitz (Germany), i.e. I am from Silesia, and not from Saxony! 
Family Status: Married, Two Sons (born in Berlin, 1995, 2000) 
Computational Experiences: with operating systems DOS, UNIX, WINDOWS NT 
Programming Languages: PASCAL, C, FORTRAN, BASIC, HTML 
Workstations: Sun, Dec Alpha (Digital), Silicon Onyx 

                ¡¡¡Vaya con Dios!!! 
       ¡¡¡Dios nos tenga de su mano!!! 
                ¡¡¡Dios te bendiga!!! 

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