Last Update: March 31, 2011
Southern Illinois University, Carbondale
Professor Dr. rer. nat. Henri Schurz

PUBLICATIONS (ONLY REFEREED, ALREADY ACCEPTED OR PUBLISHED ONES):

List of Publications: monographs and textbooks

• [72]. 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).
• [71]. 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.
• [70]. P.E. Kloeden, E. Platen, H. Schurz: `Numerical solution of stochastic differential equations through computer experiments', Universitext, Springer-Verlag, New York, pp. 292, 1997 (Second edition, first edition 1994, third corrected reprinting 2003, Advanced Textbook, ISBN 3-540-57074-8).

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

• [69]. S. Gan, H. Schurz and H. Zhang: `Mean square convergence of stochastic theta-methods for nonlinear neutral stochastic differential delay equations', Int. J. Numer. Anal. Model. 8 (2011), no. 2, 201-213.
• [68]. H. Schurz: `Stochastic wave equations with cubic nonlinearity and Q-regular additive noise in R^2', DCDS, p. 1-10, 2011 (accepted).
• [67]. H. Schurz: `Almost sure convergence and asymptotic stability of systems of linear stochastic difference equations in R^d driven by L^2-martingales', JDEA, p. 1-11, 2011 (accepted).
• [66]. H. Schurz: `Basic concenpts of numerical analysis of stochastic differential equations explained by balanced implicit Theta methods', Special Volume "Stochastic Differiential Equations and Processes", Springer, New York, p. 1-131, 2011 (accepted).
• [65]. H. Schurz: `Almost sure asymptotic stability and convergence of stochastic Theta methods applied to systems of linear SDEs in R^d', ROSE, De Gruyter, Berlin, p. 1-19, 2011 (accepted).
• [64]. H. Schurz: `Nonlinear stochastic heat equations with cubic nonlinearities and additive Q-regular noise in R^1', Electron. J. Differ. Equ. Conf. 19, p. 221-233, 2010.
• [63]. H. Schurz: `Algorithmic solution of stochastic differential equations', Algorithms 3 (3), p. 216-223, 2010. (doi:10.3390/a3030216)
• [62]. J.A.D. Appleby, A. Rodkina and H. Schurz: `On an exponential martingale approach to almost sure stability of Ito SDEs in R^1', accepted in DCDIS (2010).
• [61]. J.A.D. Appleby, A. Rodkina and H. Schurz: `Non-positivity and oscillations of solutions of nonlinear stochastic difference equations', J. Difference Equ. Appl. 16 (7), p. 807-830, 2010.
• [60]. H. Schurz: `Analysis and discretization of some quasilinear SPDEs with cubic-type nonlinearities and Q-regular noise', Preprint M-05-009, Department of Mathematics, Carbondale, 2005, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., accepted (2006).
• [59]. J.A.D. Appleby, A. Rodkina and H. Schurz: `On the oscillation of solutions of stochastic difference equations', Mat. Ensen. Univ. (N. S.) 17 (2), p. 1-10, 2009.
• [58]. A. Rodkina and H. Schurz: `On positivity and boundedness of solutions of nonlinear stochastic difference equations', Discrete Contin. Dyn. Syst. - Supplement 2009, p. 640-649, 2009.
• [57]. Z. Liu, Q. Wang and H. Schurz: `Inverse optimal noise-to-state stabilization of stochastic recurrent neural networks driven by noise of unknown covariance', Optimal Control Appl. Methods 30 (2), p. 163-178, 2009.
• [56]. H. Schurz: `New stochastic integrals, oscillation theorems and energy identities', Commun. Appl. Anal. 13 (2), p. 181-194, 2009.
• [55]. H. Schurz: `Verification of Lyapunov functions for the analysis of stochastic Lienard equations', Journal of Sound and Vibration 325, p. 938-949, 2009.
• [54]. I. Bashkirtseva, L. Ryashko and H. Schurz: `Analysis of noise-induced transitions for Hopf system with additive and multiplicative random disturbances', Chaos Solitons Fractals 39 (1), p. 72-82, 2009.
• [53]. A. Rodkina, H. Schurz and L. Shaikhet: `Almost sure stability of some stochastic dynamical systems with memory', Discrete Contin. Dyn. Syst. Ser. A 21 (2) (2008) 571-593.
• [52]. H. Schurz: `How rates of L^p-convergence carry over to numerical approximations of some convex, non-smooth functionals of SDEs', Int. J. Numer. Anal. Model. 5 (1) (2008) 55-72.
• [51]. H. Schurz: `Analysis and discretization of semi-linear stochastic wave equations with cubic nonlinearity and additive space-time noise', Discrete Cont. Dyn. Syst. Ser. S 1 (2) (2008) 353-363.
• [50]. E. Moro and H. Schurz: `Boundary preserving semi-analytical numerical algorithms for stochastic differential equations', SIAM J. Sci. Comput. 29 (4) (2007) 1525-1549.
• [49]. H. Bessaih and H. Schurz: `Upper bounds on the rate of convergence of truncated stochastic infinite-dimensional differential systems with H-regular noise', J. Comput. Appl. Math. 208 (2) (2007) 354-361.
• [48]. H. Schurz: `A numerical method for nonlinear stochastic wave equations in R^1', Dynam. Contin. Discr. Impul. Syst. A 14 (S2) (2007) 74-78.
• [47]. H. Schurz: `Nonlinear stochastic wave equations in $\R^1$ with power-law nonlinearity and additive space-time noise', Contemporary Math. 440 (2007) 223-242.
• [46]. H. Schurz: `Applications of numerical methods and its analysis for systems of stochastic differential equations', Bull. Karela Math. Soc. 4 (1) (2007) 1-85.
• [45]. H. Schurz: `Existence and uniqueness of solutions of semilinear stochastic infinite-dimensional differential systems with H-regular noise', J. Math. Anal. Appl. 332 (1) (2007) 334-345.
• [44]. H. Schurz: `Modeling, analysis and discretization of stochastic logistic equations', Int. J. Numer. Anal. Model. 4 (2) (2007) 180-199.
• [43.] C. Kahl and H. Schurz: `Balanced implicit Milstein methods for SDEs', Monte Carlo Methods Appl. 12 (2) (2006) 143-170.
• [42]. J.A.D. Appleby, A. Rodkina and H. Schurz: `Pathwise nonexponential decay rates of solutions of scalar nonlinear stochastic differential equations', Discrete Cont. Dynam. Syst. B 6 (4) (2006) 667-696.
• [41]. H. Schurz: `An axiomatic approach to numerical approximations of stochastic processes', Int. J. Numer. Anal. Model. 3 (4) (2006) 459-480.
• [40]. H. Schurz: `Stochastic $\alpha$-calculus, a fundamental theorem and Burkholder-Davis-Gundy-type estimates', Dynam. Syst. Applic. 15 (2) (2006) 241-268.
• [39]. H. Schurz and K.R. Schneider: `Waveform relaxation methods for ordinary stochastic differential equations', Int. J. Numer. Anal. Model. 3 (2) (2006) 232-254.
• [38]. E.J. Allen, L.J.S. Allen and H. Schurz: `A comparison of persistence-time estimation for discrete and continuous stochastic population models that include demographic and environmental variability', Math. Biosciences 196 (1), p. 14-38, 2005.
• [37]. A. Rodkina and H. Schurz: `Almost sure asymptotic stability of drift-implicit theta-methods for bilinear ordinary stochastic differential equations in R^1', J. Comput. Appl. Math. 180 (1), p. 13-31, 2005.
• [36]. A. Rodkina and H. Schurz: `On global asymptotic stability of solutions to some in-arithmetic-mean-sense drift-monotone stochastic difference equations', Int. J. Numer. Anal. Model. 2 (3), p. 355-366, 2005.
• [35]. H. Schurz: `Stability of numerical methods for ordinary SDEs along Lyapunov-type and other functions with variable step sizes', Electr. Trans. Numer. Anal. 20, p. 27-49, 2005.
• [34]. H. Schurz: `Convergence and stability of balanced implicit methods for SDEs with variable step sizes', Int. J. Numer. Anal. Model. 2 (2), p. 197-220, 2005.
• [33]. A. Rodkina and H. Schurz: `A theorem on global asymptotic stability of solutions to nonlinear stochastic difference equations with Volterra type noises', Stab. Control Theory Appl. (SACTA) 6 (1), p. 23-34, 2004.
• [32]. A. Rodkina and H. Schurz: `Global asymptotic stability of solutions to cubic stochastic difference equations', Adv. Diff. Equat. 1 (3), p. 249-260, 2004.
• [31]. H. Schurz; `General theorems for numerical approximation of stochastic processes on the Hilbert space $H_2 ([0,T])$', Electr. Trans. Numer. Anal. 16, p. 50-69, 2003.
• [30]. H. Schurz: `Remarks on Taylor series expansions and conditional expectations for (ordinary) Stratonovich stochastic differential equations with V-commutativity', Stochastic Anal. Applic. 21 (4), p. 865-894, 2003.
• [29]. H. Schurz: `Moment attractivity, stability and contractivity exponents of stochastic dynamical systems', Discrete Cont. Dyn. Syst. 7 (3), p. 487-515, 2001.
• [28]. H. Schurz: `On moment-dissipative stochastic dynamical systems', Dynam. Syst. Appl. 10 (1), p. 11-44, 2001.
• [27]. H. Schurz: `Preservation of probabilistic laws through Euler methods for Ornstein-Uhlenbeck process', Stochastic Anal. Appl. 17 (3), p. 463-486, 1999.
• [26]. H. Schurz: `The invariance of asymptotic laws of linear stochastic systems under discretization', Z. Angew. Math. Mech. 79 (6), p. 375-382, 1999.
• [25]. G.N. Mil'shtein, E. Platen, H. Schurz: `Balanced implicit methods for stiff stochastic systems', SIAM J. Numer. Anal. 35 (3), p. 1010-1019, 1998.
• [24]. L.B. Ryashko and H. Schurz: `Mean square stability analysis of some stochastic systems', Dynam. Syst. Appl. 6 (2), p.165-190, 1997.
• [23]. H. Schurz: `Modelling and analysis of stochastic innovation diffusion', Z. Angew. Math. Mech. 76 (Suppl. 3, I-XV), p. 366-369, 1996.
• [22]. H. Schurz: `Numerical regularization for SDEs: Construction of nonnegative solutions', Dynam. Syst. Appl. 5 (1), p. 323-352, 1996.
• [21]. H. Schurz: `Asymptotical mean square stability of an equilibrium point of some linear numerical solutions', Stochastic Anal. Appl. 14 (3), p. 313-354, 1996.
• [20]. 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.
• [19]. 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.
• [18]. 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.
• [17]. 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.
• [16]. 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 volumes

• [15]. H. Schurz: `Numerical analysis of SDEs without tears' (invited chapter), in Handbook of Stochastic Analysis and Applications, ed. by V. Lakshmikantham and D. Kannan, Marcel Dekker, Basel, p. 237-359, 2002.
• [14]. 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.
• [13]. 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.
• [12]. 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.
• [11]. P.E. Kloeden, E. Platen, H. Schurz: `Effective simulation of optimal trajectories in stochastic control', in Optimization: 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

• [10]. H. Schurz: `On estimation of L^p-errors of Ito-Riemann-type numerical quadratures for stochastic integrals along Wiener paths', in Proceedings of Neural, Parallel and Scientific Computations (Atlanta, August 2006), ed. by G.S. Ladde, N.G. Medhin, C. Peng and M. Sambandham, Vol. 3 (Dynamic Publishers, Atlanta, 2006), pp. 221-225, 2006.  
• [9]. H. Schurz: `Rate of convergence of approximations of some convex functionals of stochastic differential equations', in Noise and Fluctuations in Econophysics and Finance, ed. by Derek Abbott, Jean-Philippe Bouchaud, Xavier Gabaix and Joseph L. McCauley, Proc. Soc. Opt. Engg. (Austin, May 2005), SPIE Vol. 5848 (SPIE, Bellingham, WA, 2005), pp. 274-290, 2005.  
• [8]. H. Schurz: `Dynamics of linearly partial-implicit midpoint methods for numerical integration of some infinite systems of ODEs with cubic-type nonlinearity and Q-regular additive noise', in Noise in Complex Systems and Stochastic Dynamics III, ed. by Laszlo B. Kish, Katja Lindenberg and Zoltan Gingl, Proc. Soc. Opt. Engg. (Austin, May 2005), SPIE Vol. 5845 (SPIE, Bellingham, WA, 2005), pp. 182-192, 2005. 
• [7]. H. Schurz: 'Dissipation of mean energy of discretized linear oscillators under random perturbations', in Proc. 5th International Conference on Dynamical Systems and Differential Equations (Pomona, June 2004), ed. Xin Lu, Discr. Cont. Dynam. Syst. B (Suppl. Vol.), AIMS, Pomona, pp. 778-783, 2005. 
• [6]. H. Schurz: 'Two general theorems for numerical approximation of stochastic processes on separable Hilbert spaces', in Proc. SICNPSC (Atlanta, August 2002), Dynamic Publishers, Atlanta, p. 55-58, 2002. 
• [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.

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