Prof. Dr. Harald Luschgy

Ehem. Professor an der Universität Trier

Fachbereich IV - Mathematik

E-Mail: luschgyuni-trierde  

Forschungsschwerpunkte

  • Statistics of Stochastic Processes
  • Quantization for Probability Distributions
  • Invariance Structures in Probability and Statistics

Bücher

  • H. LUSCHGY (2012) Martingale in diskreter Zeit. Springer.
  • H. LUSCHGY and S. GRAF (2000) Foundations of Quantization for Probability Distributions. Lecture Notes in Mathematics 1730, Springer.
  • E. HÄUSLER and H. LUSCHGY (2014) Stable Convergence and Stable Limit Theorems.(Forthcoming)
  • H. LUSCHGY and G. PAGÈS (2013) Functional Quantization of Stochastic Processes. (In Progress)

Publikationen

  • H. LUSCHGY (1974). Anmerkung zu einem Konvergenzsatz für Martingale mit nach links filtrierender Indexmenge.
    Z. Wahrsch. Verw. Gebiete, 171-172
     
  • H. LUSCHGY (1978). Extreme invariant positive operators on Lp-spaces.
    Proc. Amer. Math. Soc.72, 301-304
     
  • H. LUSCHGY (1978). Sur l'existence d'une plus petite sous-tribu exhaustive par paire.
    Ann. Inst. H. Poincare Sect. B 14, 391-398
     
  • H. LUSCHGY (1978). Invariant extensions of positive operators for right amenable semigroups.
    Archiv Math. 3, 356-358
     
  • H. LUSCHGY (1980). Invariant extensions of positive operators and extreme points.
    Math. Z. 171, 75-81
     
  • H. LUSCHGY (1982). Extreme invariant extensions of probability measures and probability contents.
    Illinois J. Math. 26, 27-40
     
  • H. LUSCHGY (1982). Minimax character of the two-sample chi-square-test.
    Statistica Neerlandica 36, 129-134
     
  • H. LUSCHGY and W. THOMSEN (1983). Extreme points in the Hahn-Banach-Kantorovich setting.
    Pacific J. Math. 105, 387-398
     
  • H. LUSCHGY (1984). Invariant least favourable distributions and most stringent tests.
    Statistics and Decision 2, 293-313
     
  • H. LUSCHGY (1985). Measurable selections of limit points.
    Archiv Math. 45, 350-353
     
  • H. LUSCHGY and D. MUSSMANN (1985). Equivalent properties and completion of statistical experiments.
    Sankhya 47, Series A, 174-195
     
  • H. LUSCHGY (1985). Statistical characterization of Gaussian measures on a Hilbert space.
    Probab. Math. Statist. 6, 151-159
     
  • H. LUSCHGY (1986). Decomposition of charges and measures.
    Proc. Amer. Math. Soc. 96, 121-125
     
  • H. LUSCHGY and D. MUSSMANN (1986). Products of majorized statistical experiments.
    Statistics and Decisions 4, 321-335
     
  • H. LUSCHGY (1987). Elimination of randomization and Hunt-Stein type theorems in invariant statistical decision problems.
    Statistics 18, 99-111
     
  • H. LUSCHGY and D. MUSSMANN (1987). A characterization of weakly dominated experiments by compactness of the set of decision-rules.
    Sankhya 49, Series A, 388-394
     
  • H. LUSCHGY (1987). Comparison of shift experiments on a Banach space.
    Mathematical Statistics and Probability Theory, Vol. A (M.L. Puri et al., eds.), 217-230. D. Reidel
     
  • H. LUSCHGY (1988). A note on majorized statistical experiments.
    Sankhya 50, Series A, 149-150
     
  • H. LUSCHGY (1988). Pairwise sufficiency and invariance.
    Osaka J. Math. 25, 785-794
     
  • H. LUSCHGY, D. MUSSMANN, and S. YAMADA (1988). Minimal L-space and Halmos-Savage criterion for majorized experiments.
    Osaka J. Math. 25, 795-803
     
  • H. LUSCHGY (1988). Asymptotic almost equidistribution on a Banach space.
    Trans. Tenth. Prague Conf. Information Theory, Statist. Dec. Functions, Random Processes, Vol. B, 155-163. Reidel
     
  • H. LUSCHGY (1989). Integral representation in the set of transition kernels.
    Probab. Math. Statist. 10, 75-92
     
  • H. LUSCHGY (1989). Characterizations of infinite dimensional Gaussian shift experiments.
    Statist. Probab. Letters 8, 463-468
     
  • H. LUSCHGY (1990). Choquet type representation of transition kernels and applications.
    Atti Sem. Math. Fis. Univ. Modena 39, 311-320
     
  • H. LUSCHGY (1991). Testind one-sided hypotheses for the mean of a Gaussian process.
    Metrika 38, 179-194
     
  • H. LUSCHGY (1991). Ordering regression models od Gaussian processes.
    Stochastic Orders and Decision under risk. IMS Lecture Notes - Monograph Series, Vol. 19 (K. Mosler and M. Scarsini, eds.), 207-230
     
  • H. LUSCHGY (1991). Multiplicative decomposition of probability measures.
    Proc. Amer. Math. Soc. 111, 197-204
     
  • H. LUSCHGY (1992). Comparison of location models for stochastic processes.
    Prob. Theory Rel. Fields 93, 39-66
     
  • H. LUSCHGY (1992). Approximations and time-discretization in testing one-sided hypotheses of a Gaussian process.
    Metrika 39, 95-105
     
  • H. LUSCHGY (1992). Local asymptotic mixed normality for semimartingale experiments.
    Probab. Theory Rel. Fields 92, 151-177
     
  • H. LUSCHGY and A. RUKHIN (1993). Adaptive tests for stochastic processes in the ergodic case.
    Stochastic Processes Appl. 45, 45-59
     
  • H. LUSCHGY (1993). Second order behaviour of Neyman-Pearson tests for stochastic processes.
    Statistics and Decisions 11, 133-150
     
  • H. LUSCHGY (1993). On a singularity occuring in a self-correcting point process model.
    Ann. Inst. Statist. Math. 45, 445-452
     
  • H. LUSCHGY and A. RUKHIN (1993). Asymptotic properties of tests for a class of diffusion processes: optimality and adaption.
    Math. Methods of Statistics 2, 42-51
     
  • H. LUSCHGY (1994). Asymptotic inference for semimartingale models with singular parameter points.
    J. Statist. Planning and Inference 39, 155-186
     
  • H. LUSCHGY (1994). Asymptotic behaviour of Neyman-Pearson tests for autoregressive processes.
    Scand. J. Statistics 21, 461-473
     
  • H. LUSCHGY (1994). Asymptotic expansions of error probabilities for tests.
    Asymptotic Statistics, Proc. Fifth Prague Conf. (P. Mandl and M. Huskova, eds.), 369-377. Physica-Verlag
     
  • H. LUSCHGY and S. GRAF (1994). Consistent estimation in the quantization problem for random vectors.
    Trans. Twelth Prague Conf. Information Theory, Statist. Decision Functions, Random Processes, 84-87
     
  • H. LUSCHGY (1995). Linear estimaters and radonifying operators.
    Theory Probab. Appl. 40, 205-213
     
  • H. LUSCHGY (1995). Local asymptotic quadrcity of stochastic pocess models based on stopping times.
    Stochastic Processes Appl. 57, 305-317
     
  • H. LUSCHGY and S. GRAF (1997). The quantization of the Cantor distribution.
    Math. Nachrichten 183, 113-133
     
  • H. LUSCHGY (1998). Minimaxity and equivariance in infinite dimensions.
    Theory Probab. Appl. 43, 540-560
     
  • H. LUSCHGY (1999). Complete families of invariant distributions.
    Statistics and Decisions 17, 87-99
     
  • H. LUSCHGY and S. GRAF (2001). Asymptotoics of the quantization errors for self-similar probabilities.
    Real Analysis Exchange 26,2, 795-810
     
  • H. LUSCHGY and S. GRAF (2002). The quantization dimension of self-similar probabilities.
    Math. Nachrichten 241, 103-109
     
  • H. LUSCHGY and S. GRAF (2002). Rates of convergence for the empirical quantization error.
    Ann. Probab. 30, 874- 897.
     
  • H. LUSCHGY and G. PAGÈS (2002). Functional quantization of Gaussian processes.
    J. Functional Analysis 196, 486-531
     
  • H. LUSCHGY, S. GRAF and G. PAGÈS (2003). Functional quantization and small ball probabilities for Gaussian processes.
    Journal of Theoretical Probability 16, 1047-1062
     
  • H. LUSCHGY and S. GRAF (2004). Sharp asymptotics of the metric entropy for ellipsoids.
    Journal of Complexity 20, 876-882.
     
  • H. LUSCHGY and S. GRAF (2004). Quantization for probability measures with respect to the geometric mean error.
    Math. Proc. Cambridge Phil. Soc. 136, 687-717
     
  • H. LUSCHGY and G. PAGÈS (2004). Sharp asymptotics of the functional quantiaztion problem for Gaussian processes.
    Ann. Probability 32, 1574-1599
     
  • H. LUSCHGY and G. PAGÈS (2004). Sharp asymptotics of the Kolmogorov entropy for Gaussian measures.
    J. Functional Analysis 212, 89-120
     
  • H. LUSCHGY and S. SOLECKI (2004). Strong continuity of invariant probability charges.
    Colloquium Math. 101, 135-142.
     
  • H. LUSCHGY, S. DELATTRE, S. GRAF, G. PAGÈS (2004). Quantization of probability distributions under norm-based distortion measures.
    Statistics and Decisions 22, 261-282
     
  • H. LUSCHGY and S. GRAF (2005). The point density measure in the quantization of self-similar probabilities.
    Math. Proc. Cambridge Phil. Soc. 138, 513-531
     
  • H. LUSCHGY and S. GRAF (2005). Entropy-constrained functional quantization of Gaussian measures.
    Proceedings AMS 133, 3403-3409
     
  • H. LUSCHGY, S. DELATTRE, S. GRAF, G. PAGÈS (2006). Quantization of probability distributions under norm-based distortion measures II: self-similar distributions.
    J. Math. Analysis and Applications 318, 507-516
     
  • H. LUSCHGY and G. PAGÈS (2006). Functional quantization of a class of Brownian diffusions: a constructive approach.
    Stochastic Processes and their Applications 116, 310-336
     
  • H. LUSCHGY, S. GRAF, G. PAGÈS (2007). Optimal quantizers for radon random vectors in a Banach Space.
    J. Approximation Theory 144, 27-53.
     
  • H. LUSCHGY and G. PAGÈS (2007). High-resolution product quantization for Gaussian processes under sup-norm distortion.
    Bernoulli 13, 653-671
     
  • H. LUSCHGY, S. GRAF, G. PAGÈS (2008). Distortion mismatch in the quantization of probability measures.
    ESAIM: Probability and Statistics 12, 127-153.
     
  • H. LUSCHGY and G. PAGÈS (2008). Moment estimates for Lévy processes.
    Electronic Communications in Probability 13, 422-434.
     
  • H. LUSCHGY, G. PAGÈS (2008). Functional quantization rate and mean pathwise regularity of processes with an application to Lévy processes.
    Annals of Applied Probability 18, 427-469.
     
  • H. LUSCHGY, S. GRAF (2009). Quantization for probability measures in the Prokhorov metric.
    Theory Probab. Appl. 53, 216-241.
     
  • H. LUSCHGY, G. PAGÈS, B. WILBERTZ (2010). Asymptotically optimal quantization schemes for Gaussian processes.
    ESAIM: Probability and Statistics 14, 93-116.
     
  • H. LUSCHGY, G. PAGÈS, (2009). Expansions for Gaussian processes and Parseval frames.
    Eletronic Journal of Probability 14, 1198-1221.
     
  • H. LUSCHGY, S. GRAF, G. PAGÈS (2011). Fractal functional quantization of mean-regular stochastic processes.
    Math. Proc. Cambridge Phil. Soc. 150, 167-191.
     
  • H. LUSCHGY, S. JUNGLEN (2010). A constructive sharp approach to functional quantization of Stochastic processes.
    J. Applied. Math., Article ID 378519, 32 pages.
     
  • H. LUSCHGY, S. GRAF, G. PAGÈS (2012). The local quantization behaviour of absolutely continuous probabilities.
    Ann. Probability 40, 1795 - 1828.
     
  • H. LUSCHGY, G. PAGÈS (2014). Constructive quadratic functional quantization and critical dimension.
    Electronic Journal of Probability 19, No. 50 19p.

Preprints

  • H. LUSCHGY, G. PAGÈS (2014). Greedy quantization.
     
  • H. LUSCHGY, S. JUNGLEN (2012). The radius problem for optimal functional quantizers of Gaussian processes.
     
  • H. LUSCHGY, S. GRAF, G. PAGÈS (2010). Fractal functional quantization of mean-regular processes: a Haar-type basis approach.
     
  • H. LUSCHGY (2010). Sigma-algebras of invariant sets.