Limit theorems with applications  Page description

Help  Print 
Back »
 

Details of project

  
Identifier
48544
Type K
Principal investigator Pap, Gyula
Title in Hungarian Határeloszlástételek és alkalmazásaik
Title in English Limit theorems with applications
Panel Mathematics and Computing Science
Department or equivalent Department of Applied Mathematics and Probability Theory (University of Debrecen)
Participants Baran, Sándor
Barczy, Mátyás
Fazekas, István
Gáll, József Mihály
Ispány, Márton
Starting date 2005-01-01
Closing date 2009-12-31
Funding (in million HUF) 9.968
FTE (full time equivalent) 3.48
state closed project





 

Final report

  
Results in Hungarian
Kidolgoztunk egy Heath-Jarrow-Morton típusú diszkrét idejű határidős kamatlábmodellt, melyet egy autoregressziós mező hajt meg, nem pedig egyetlen folyamat, mely realisztikusabb, mint az eredeti modell. Drift-feltételt vezettünk le az arbitrázsmentességre, és különböző statisztikai kérdéseket vizsgáltunk meg, többek között konzisztenciát, valamint a paraméterek becslésének aszimptotikus viselkedését mind stabil, mind pedig instabil esetekben. Sikerült Black-Scholes formulát levezetni késleltetett modellekben is. Levezettünk elégséges feltételeket valószínűségi változókból álló háromszögrendszerre, melynek teljesülése esetén a háromszögrendszerből felépített véletlen lépcsősfüggvények egy (nem feltétlenül időhomogén) diffúziós folyamathoz konvergálnak. Továbbá elégséges feltételeket adtunk arra, hogy véletlen lépcsősfüggvények sztochasztikus integréljainak sorozata konvergáljon egy sztochasztikus integrálhoz, amikor az integrandusok az integrátorok funkcionáljai. Különböző eredményeket értünk el inhomogén diffúziós folyamatok statisztikai kérdéseivel kapcsolatban. Új eredményeink vannak térbeli folyamatok statisztikai viselkedésével kapcsolatban is, mind stabil, mind pedig instabil esetekben, mind diszkrét, mind folytonosidőben. Egzakt formulát kaptunk Heisenberg-csoporton értelmezett Gauss-mérékek Fourier-transzformáltjaira. Új központi határelsozlás-tételeket kaptunk lokálisan kompakt Abel-csoportokon.
Results in English
We worked out a discrete time Heath-Jarrow-Morton type interest rate model driven by an autoregressive random field instead of a single process, which is more realistic than the original one. We derived no-arbitrage drift-condition, and investigated several statistical questions, including consistency and asymptotic behavior of maximum likelihood estimator of the parameters both in stable and unstable cases. We also derived a delayed Black-Scholes formula. We derived sufficient conditions for a triangular array of random vectors such that the sequence of related random step functions converges towards a (not necessarily time homogeneous) diffusion process. Sufficient conditions are also given for convergence of stochastic integrals of random step functions, where the integrands are functionals of the integrators. Several results are achieved concerning statistical inference of time inhomogeneous diffusion processes. There are new results on statistical questions concerning spatial prorecces both in stable and unstable cases, and both in discrete and continuous time. We derived exact formulas for the Fourier transform of Gaussian measures on the Heisenberg group. We obtained new central limit theorems for locally compact Abelian groups.
Full text http://real.mtak.hu/1830/
Decision
Yes





 

List of publications

  
Gáll J; Zuijlen Mv; Pap G: Note on the proportions of financial assets with dependent distributions in optimal portfolios, pp. 339-349 in Proc. 6th International Conference on Applied Informatics (Eger, 2004), vol. II, Eger, B. V. B. Nyomda és Kiadó Kft., 2005
Csukás A; Takai S; Baran S: Adolescent growth in main somatometric traits of Japanese boys: Ogi Longitudinal Growth Study, HOMO Journal of Comparative Human Biology 57(1): 73-86, 2006
Ispány M; Zuijlen Mv; Pap G: Fluctuation limit of branching processes with immigration and estimation of the means, Advances in Applied Probability 37(2): 523-538, 2005
Heyer H; Pap G: Gaussian measures and the embedding problem on a locally compact group, pp. 99-118 in Proc. Infinite Dimensional Harmonic Analysis III (Third German-Japanese Symposium, Tübingen, 2003), World Sci. Publishing, River Edge, NJ., 2005
Barczy M; Pap G: Connection between deriving bridges and radial parts from multidimensional Ornstein-Uhlenbeck processes, Periodica Mathematica Hungarica 50(1-2): 47-60, 2005
Ispány M; Zuijlen Mv; Pap G: Critical branching mechanisms with immigration and Ornstein-Uhlenbeck type diffusions, Acta Scientiarum Mathematicarum (Szeged) 71(3-4): 463-492, 2005
Barczy M; Pap G: Fourier transform of Gauss measures on the Heisenberg group, Annales de l'Institut Henri Poincaré. Probabilités et Statistiques 42(5): 607-633, 2006
Gáll J; Zuijlen Mv; Pap G: Forward interest rate curves in discrete time settings driven by random fields, Computers & Mathematics with Applications 51(3-4): 387-396, 2006
Baran S: A consistent estimator for nonlinear regression models, Metrika 62(1): 1-15, 2005
Chuprunov A; Fazekas I: Inequalities and strong laws of large numbers for random allocations, Acta Mathematica Hungarica 109(1-2): 163-182, 2005
Fazekas I; Kukush A: Kriging and mesurement errors, Discussiones Mathematicae. Probability and Statistics 25(2): 139-159, 2005
Chuprunov A; Fazekas I: Integral analogues of almost sure limit theorems, Periodica Mathematica Hungarica 50(1-2): 61-78, 2005
Fazekas I; Chuprunov A: Asymptotic normality of kernel type density estimators for random fields, Statistical Inference for Stochastic Processes 9(2): 161-178, 2006
Fazekas I: Burkholder's inequality for multiindex martingales, Annales Mathematicae et Informaticae 32: 45-51, 2005
Kukush A; Fazekas I: Kriging and prediction of nonlinear functionals, Austrian Journal of Statistics 34(2): 175-184, 2005
Fazekas I; Chuprunov A: The asymptotic covariance of kernel type density estimators for random fields, pp. 97-108 in Proc. 6th International Conference on Applied Informatics (Eger, 2004), vol. II, Eger, B. V. B. Nyomda és Kiadó Kft., 2005
Fazekas I; Rychlik Z: Almost sure limit theorems for semi-selfsimilar processes, Probability and Mathematical Statistics. 25(2): 241-255, 2005
Fazekas I; Chuprunov A: An almost sure functional limit theorem for the domain of geometric partial attraction of semistable laws, Journal of Theoretical Probability 20(2): 339-353, 2007
Fazekas I; Filzmoser P: A functional central limit theorem for kernel type density estimators, Austrian Journal of Statistics 35(4): 409-418, 2006
Fazekas I: On a general approach to the strong laws of large nunbers, in Proc. 26th Seminar on Stability Problems for Stochastic Models (közlésre elfogadva), 2008
Barczy M; Pap G: Portmanteau theorem for unbounded measures, Statistics & Probability Letters 76(17): 1831-1835, 2006
Becker-Kern P; Pap G: A limit theorem for randomly stopped independent increment processes on separable metrizable groups, Mathematische Nachrichten 280(15): 1664-1680, 2007
Gáll J; Pap G; Peeters W: Random field forward interest rate models, market price of risk and their statistics, Annali dell'Universita di Ferrara Sez. VII Sci. Mat. 53: 233-242, 2007
Baran S; Pap G; Zuijlen, Mv: Parameter estimation of a shifted Wiener sheet, Statistics (közlésre benyújtva), 2009
Baran S; Gáll J; Ispány M; Pap G: Prediction of Hungarian mortality rates using Lee-Carter method, Acta Oeconomica 57(1): 21-34, 2007
Barczy M: Some questions of probability theory on special topological groups, PhD disszertáció, http://www.inf.unideb.hu/valseg/dolgozok/barczy/disszertaciok_barczy.html, 2006
Arriojas M; Hu Y; Mohammed SE; Pap G: A delayed Black and Scholes formula, Stochastic Analysis and Applications 25(2): 471-492, 2007
Baran S; Pap G; Zuijlen Mv: Asymptotic inference for unit roots in spatial triangular autoregression, Acta Applicandae Mathematicae 96(1-3): 17-42, 2007
Barczy M; Bendikov A; Pap G: Limit theorems on some locally compact Abelian groups, Mathematische Nachrichten 281(12): 1708-1727, 2008
Feinsilver Ph; Pap G: Calculation of Fourier transform of a Brownian motion in the Heisenberg group using splitting formulas, Journal of Functional Analalysis 249(1): 1-30, 2007
Barczy M; Pap G: Weakly infinitely divisible measures on some locally compact Abelian groups, Lithuanian Mathematical Journal 48(1): 17-29, 2008
Bingham M; Pap G: Embeddable probability measures and infinitesimal systems of probability measures on a Moore Lie group, Publicationes Mathematicae (Debrecen) 72(3-4): 293-316, 2008
Becker-Kern P; Pap G: Parameter estimation of selfsimilarity exponents, Journal of Multivariate Analalysis 99(1): 117-140, 2008
Gáll J; Zuijlen, Mv; Pap G: Joint ML estimation of all parameters in a discrete time random field HJM type interest rate model, Econometrica (közlésre elküldve), 2009
Ispány M; Pap G: A note on weak convergence of step processes, Acta Mathematica Hungarica (közlésre benyújtva), 2009
Ispány M: Limit theorems for normalized nearly critical branching processes with immigration, Publicationaes Mathematicae (Debrecen) 72(1-2): 17-34, 2008
Gáll J: Some problems in Discrete Time Financial Market Models, PhD disszertáció, 2007
Györfi L; Ispány M; Zuijlen Mv; Pap G; Varga K: Poisson limit of an inhomogeneous nearly critical INAR(1) model, Acta Scientiarum Mathematicarum (Szeged) 73(3-4): 809-835, 2007
Fülöp E; Pap G: Strong consistency of maximum likelihood estimators for a discrete time random field HJM type interest rate model, Lithuanian Mathematical Journal (közlésre elfogadva), 2009
Fülöp E; Pap G: Asymptotically optimal tests for a discrete time random field HJM type interest rate model, Acta Scientiarum Mathematicarum (Szeged) 73(3-4): 637-661, 2007
Heyer H; Pap G: Truncation inequalities for probability measures on locally compact Abelian groups, Mathematical Inequalities & Applications 11(3): 483-494, 2008
Pap G: The accuracy of merging approximation in generalized St. Petersburg games, Bernoulli (közlésre elküldve), 2009
Baran S; Pap G: On the least squares estimator in a nearly unstable sequence of stationary spatial AR models, Journal of Multivariate Analysis 100(4): 686-698, 2009
Gáll J; Nagy G: A működési kockázat veszteségeloszlás-alapú modellezése (Loss Distribution Approach, LDA), Hitelintézeti Szemle 2007(4): 386-412, 2007
Fazekas I; Chuprunov A: Almost sure limit theorems for random allocations, Studia Scientiarum Mathematicarum Hungarica 42(2): 173-194, 2005
Heyer H; Pap G: Martingale characterizations of increment processes in a commutative hypergroup, Advances in Pure and Applied Mathematics (közlésre elfogadva), 2009
Barczy M; Pap G: Alpha-Wiener bridges: singularity of induced measures and sample path properties, Stochastic Analysis and Applications (közlésre elfogadva), 2009
Barczy M; Pap G: Asymptotic behavior of maximum likelihood estimator for time inhomogeneous diffusion processes, Journal of Statistical Planning and Inference (közlésre benyújtva), 2009
Barczy M; Pap G: Explicit formulas for Laplace transforms of certain functionals of some time inhomogeneous diffusions, Journal of Mathematical Analysis and Applications (közlésre benyújtva), 2009
Fülöp E; Pap G: Note on strong consistency of maximum likelihood estimators for dependent observations, pp. 223-228 in Proc. 7th International Conference on Applied Informatics (Eger, 2007), vol. I, Eger, B. V. B. Nyomda és Kiadó Kft., 2008
Fazekas I: Central limit theorems for kernel type density estimators, pp. 211-222 in Proc. 7th International Conference on Applied Informatics (Eger, 2007), vol. I, Eger, B. V. B. Nyomda és Kiadó Kft., 2008



Back »