Stohastičke metode u matematičkoj analizi

UNIRI-plus projekt 2019 (uniri-pr-prirod-19-16)


 Sažetak:

Matematička analiza je jedno od najznačajnijih područja matematike s primjenama u mnogim prirodnim i društvenim znanostima. Cilj ovog projekta je upotrijebiti stohastičke metode u proučavanju određenih analitičkih problema u više grana moderne matematičke analize, poput dinamičkih sustava, specijalnih funkcija, statističke teorije distribucije i teorije ekstremnih vrijednosti. Mnogi fenomeni, kako u svakodnevnom životu, tako i u raznim područjima znanosti, pokazuju svojstvo slučajnosti, kao npr. u osiguranju i financijama, klimatologiji, biologiji i geologiji. Takve slučajnosti se najprikladnije analiziraju stohastičkim metodama, koje su razvijene unutar okvira teorije vjerojatnosti, posebice teorije slučajnih procesa. Problemi koje u okviru ovog projekta planiramo proučiti su teorijske i primijenjene prirode, te su, osim za područja stručnosti članova tima, značajni i za druge discipline, poput statističke fizike i teorije signala. Preciznije, planiramo ispitati funkcionalnu konvergenciju parcijalnih suma i maksimuma za neke klase slučajnih procesa, proučiti neka statistička svojstva hiperboličkih dinamičkih sustava, dobiti nove spektralne karakterizacije hiperboličkog ponašanja neautonomnih dinamika, istražiti WKS sampling rekonstruiranje determinističkih i stohastičkih signala, te poboljšati određene formule u statističkoj teoriji distribucija. Cilj projekta je i povezati istraživače sa Sveučilišta u Rijeci čiji se znanstveni rad odvija u području teorije vjerojatnosti ili u srodnim granama matematike, odnosno koji u svom radu koriste stohastičke metode. Time će se formirati novi istraživački tim i inicirati kolaboracija članova tima koja prethodno nije postojala. Kako će u aktivnostima projekta biti uključeni i brojni inozemni stručnjaci, ovim projektom planiramo doprinijeti i većoj međunarodnoj vidljivosti sastavnica s kojih dolaze članovi tima (Odjel za matematiku i Pomorski fakultet), ali i općenito Sveučilišta u Rijeci. 

 Voditelj projekta: izv. prof. dr. sc. Danijel Krizmanić (Fakultet za matematiku Sveučilišta u Rijeci) 

 Istraživački tim:  
prof. dr. sc. Tibor Pogány (Pomorski fakultet Sveučilišta u Rijeci)
izv. prof. dr. sc. Davor Dragičević (Fakultet za matematiku Sveučilišta u Rijeci)
Emma Šepić (Fakultet za matematiku Sveučilišta u Rijeci)

 Objavljeni radovi:
  1. T. K. Pogány, On one-step extrapolation error of vector time series, Bulletin of Kerala Mathematics Association 16 (2019), No. 2, 69-76.
  2. R. K. Parmar, T. K. Pogány, On Mathieu-type series for the unified Gaussian hypergeometric functions, Applicable Analysis and Discrete Mathematics 14 (2020), 138-149.
  3. A. K. Rathie, T. K. Pogány, Novel reductions of Kampé de Fériet function, Scientia. Series A: Mathematical Sciences 30 (2020), 27-41.
  4. D. Dragičević, Barbashin-type conditions for exponential stability of linear cocycles, Monatshefte für Mathematik 19 (2020), 813-826.
  5. L. Backes, D. Dragičević, Quasi-shadowing for partially hyperbolic dynamics on Banach spaces, Journal of Mathematical Analysis and Applications 492 (2020), 124445
  6. D. Dragičević, Y. Hafouta, Limit theorems for random expanding or Anosov dynamical systems and vector-valued observables, Annales Henri Poincare 21 (2020), 3869-3917.
  7. D. Dragičević, N. Jurčević Peček, N. Lupa, Admissibility and general dichotomies for evolution families, Electronic Journal of Qualitative Theory of Differential Equations 2020 (2020), 58, 19pp.
  8. T. K. Pogány, S. Nadarajah, Explicit forms for three integrals in Wand et al., Mathematical Communications 26 (2021), 101-105.
  9. R. K. Parmar, G. V. Milovanović, T. K. Pogány, Multi-parameter Mathieu, and alternating Mathieu series, Applied Mathematics and Computation 400 (2021), 27pp.
  10. D. Jankov Maširević, T. K. Pogány, On a second type Neumann series of modified Bessel functions of the first kind, Integral Transforms and Special Functions 32 (2021), No. 2, 105-112.
  11. K. Górska, A. Horzela, T. K. Pogány, Non-Debye relaxations: smeared time evolution, memory effects, and the Laplace exponents, Communications in Nonlinear Science and Numerical Simulation 99 (2021), Art. No. 105837, 11pp.
  12. M. Ali, M. Ghayasuddin, T. K. Pogány, Integrals with two-variable generating function in the integrand, Montes Taurus Journal of Pure and Applied Mathematics 3 (2021) No. 3, 95-103.
  13. K. Górska, A. Horzela, A. Lattanzi, T. K. Pogány, On complete monotonicity of three parameter Mittag-Leffler function, Applicable Analysis and Discrete Mathematics 15 (2021) No. 1, 118-128.
  14. K. Mehrez, T. K. Pogány, Integrals of ratios of Fox-Wright and incomplete Fox-Wright functions with applications, Journal of Mathematical Inequalities 15 (2021) No. 3, 981-1001.
  15. D. Jankov Maširević, T. K. Pogány, CDF of non-central 𝜒2 distribution revisited. Incomplete hypergeometric type functions approach, Indagationes Mathematicae 32 (2021) No. 4, 901-915.
  16. L. Backes, D. Dragičević, Shadowing for infinite dimensional dynamics and exponential trichotomies, Proceedings of the Royal Society of Edinburgh Section A: Mathematics 151 (2021), 863-884.
  17. D. Dragičević, Hyers-Ulam stability for nonautonomous semilinear dynamics on bounded intervals, Mediterranean journal of mathematics 18 (2021), 9pp.
  18. D. Dragičević, M. Pituk, Shadowing for nonautonomous difference equations with infinite delay, Applied Mathematics Letters 120 (2021), 107284, 8pp.
  19. L. Backes, D. Dragičević, A general approach to nonautonomous shadowing for nonlinear dynamics, Bulletin des Sciences Mathematiques 170 (2021), 102996, 30pp.
  20. D. Dragičević, Hyers-Ulam stability for a class of perturbed Hill's equations, Results in Mathematics 76 (2021), 11pp.
  21. L. Backes, D. Dragičević, K. J. Palmer, Linearization and Holder Continuity for Nonautonomous Systems, Journal of Differential Equations 297 (2021), 536-574.
  22. K. Górska, A. Horzela, T. K. Pogány, Non-Debye relaxations: The characteristic exponent in the excess wings model, Communications in Nonlinear Science and Numerical Simulation 103 (2021), Paper No. 106006, 11pp.
  23. D. Dragičević, Y. Hafouta, Almost Sure Invariance Principle for Random Distance Expanding Maps with a Nonuniform Decay of Correlations, Thermodynamic Formalism-CIRM Jean Morlet Chair Fall 2019, Lecture Notes in Mathematics, vol. 2290, 177-204.
  24. L. Backes, D. Dragičević, On the spectral radius of compact operator cocycles, Stochastics and Dynamics 21 (2021), 2150026, 16pp.
  25. L. Backes, D. Dragičević, Hyers-Ulam stability for hyperbolic random dynamics, Fundamenta mathematicae 255 (2021), 69-90.
  26. D. Dragičević, On the Hyers-Ulam stability of certain nonautonomous and nonlinear difference equations, Aequationes Mathematicae 95 (2021), 829-840.
  27. D. Dragičević, Y. Hafouta, Almost sure invariance principle for random dynamical systems via Gouezel's approach, Nonlinearity 34 (2021), 6773-6798.
  28. D. Krizmanić, Maxima of linear processes with heavy-tailed innovations and random coefficients, Journal of Time Series Analysis 43 (2022), 238-262.
  29. D. Krizmanić, A functional limit theorem for moving averages with weakly dependent heavy-tailed innovations, Brazilian Journal of Probability and Statistics 36 (2022), 138-156.
  30. D. Dragičević, A. L. Sasu, B. Sasu, On Stability of Discrete Dynamical Systems - From Global Methods to Ergodic Theory Approaches, Journal of Dynamics and Differential Equations 34 (2022), 1107-1137.
  31. D. Dragičević, A. L. Sasu, B. Sasu, Input-Output Criteria for Stability and Expansiveness of Dynamical Systems, Applied Mathematics and Computation 414 (2022), 126574, 22pp.
  32. L. Backes, D. Dragičević, L. Singh, Shadowing for nonautonomous and nonlinear dynamics with impulses, Monatshefte für Mathematik 198 (2022), 485-502.
  33. D. Dragičević, Global smooth linearization of nonautonomous contractions on Banach spaces, Electronic Journal of Qualitative Theory of Differential Equations (2022), 19pp.
  34. D. Dragičević, W. Zhang, L. Zhou, Admissibility and nonuniform exponential dichotomies, Journal of Differential Equations 326 (2022), 201-226.
  35. D. Dragičević, A. L. Sasu, B. Sasu, On Polynomial Dichotomies of Discrete Nonautonomous Systems on the Half-Line, Carpathian Journal of Mathematics 38 (2022), 663-680.
  36. M. Ali, J. Paneva-Konovska, T. K. Pogány, On multi-index Whittaker function, related integrals and inequalities, Journal of Mathematical Inequalities 16 (2022), No. 2, 513-527.
  37. Y. A. Brychkov, D. J. Maširević, T. K. Pogány, New expression for CDF of 𝜒'𝜈2(λ) distribution and Marcum Q1 function, Results in Mathematics 77 (2022), Article number: 102, 11pp.
  38. T. K. Pogány, S. Nadarajah, On the probability density function of the Hartman-Watson distribution, Mathematical Communications 27 (2022), No. 1, 101-107.
  39. K. Górska, A. Horzela, D. Jankov Maširević, T. K. Pogány, Observations on the McKay I𝜈 Bessel distribution, Journal of Mathematical Analysis and Applications 516 (2022), No. 1, Article No. 124681, 14pp.
  40. L. Backes, D. Dragičević, A generalized Grobman-Hartman theorem for nonautonomous dynamics, Collectanea Mathematica 73 (2022), 411-431.
  41. D. Dragičević, A. L. Sasu, B. Sasu, L. Singh, Nonuniform Input-Output Criteria for Exponential Expansiveness of Discrete Dynamical Systems and Applications, Journal of Mathematical Analysis and Applications 515 (2022), 126436.
  42. L. Backes, D. Dragičević, M. Pituk, L. Singh, Weighted shadowing for delay differential equations, Archiv der Mathematik 119 (2022), 539-552.
  43. D. Dragičević, A. L. Sasu, B. Sasu, Admissibility and Polynomial Dichotomy of Discrete Nonautonomous Systems, Carpathian Journal of Mathematics 38 (2022), 737-762.
  44. R. K. Parmar, G. V. Milovanović, T. K. Pogány, Extension of Mathieu series and alternating Mathieu series involving Neumann function Y𝜈 , Periodica Mathematica Hungarica 86 (2023), No. 1, 191-209.
  45. D. Jankov Maširević, T. K. Pogány, Functional bounds for Exton's double hypergeometric X function, Journal of Mathematical Inequalities 17 (2023), No. 1, 259-267.
  46. T. K. Pogány, N. Laraqi, On Neumann series of Macdonald functions, Integral Transforms and Special Functions 34 (2023), No. 7, 552-561.
  47. D. Krizmanić, Joint functional convergence of partial sums and maxima for moving averages with weakly dependent heavy-tailed innovations and random coefficients, ALEA Latin American Journal of Probability and Mathematical Statistics 20 (2023), 1247-1270.
  48. D. Krizmanić, A functional limit theorem for self-normalized linear processes with random coefficients and i.i.d. heavy-tailed innovations, Lithuanian Mathematical Journal 63 (2023), 305-336. 

 Radovi prihvaćeni za objavljivanje:
  1. D. Dragičević, J. Sedro, Statistical stability and linear response for random hyperbolic systems, Ergodic Theory and Dynamical Systems
  2. D. Dragičević, On the robustness property of nonuniform exponential dichotomies, Proceedings of the ICDEA 2021 - Advances in Discrete Dynamical Systems, Difference Equations and Applications, Springer Proceedings in Mathematics & Statistics
  3. L. Backes, D. Dragičević, On the linearization of infinite-dimensional random dynamical systems, Mathematische Nachrichten
  4. T. K. Pogány, Whittaker-type derivative sampling and (p, q)-order weighted differential operator, in Stephen D. Casey, M. Maurice Dodson, Paulo J. S. G. Ferreira, Ahmed Zayed (EDS.), Sampling, Approximation, and Signal Analysis (Harmonic Analysis in the Spirit of J. Rowland Higgins), Birkhäuser, 2022, 8pp.
  5. D. J. Maširević, T. K. Pogány, Bounds for confluent Horn function of Φ2 deduced by McKay I𝜈 Bessel law, Rad Hrvatske akademije znanosti i umjetnosti, Matematicke znanosti (2022), 11pp.
  6. D. Dragičević, N. Jurčević Peček, Hyers-Ulam-Rassias stability for nonautonomous dynamics, Rocky Mountain Journal of Mathematics
  7. L. Backes, D. Dragičević, Multiscale linearization of nonautonomous dynamics, Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  8. D. Dragičević, Y. Hafouta, J. Sedro, A vector-valued almost sure invariance principle for random expanding on average cocycles, Journal of Statistical Physics
  9. D. Dragičević, P. Giulietti, J. Sedro, Quenched linear response for smooth expanding on average cocycles, Communications in Mathematical Physics
  10. L. Backes, D. Dragičević, M. Pituk, M. Onitsuka, Conditional Lipschitz shadowing for ordinary differential equations, Journal of Dynamics and Differential Equations
  11. T. K. Pogány, Truncation error upper bounds in derivative Whittaker-type plane sampling reconstruction, Montes Taurus Journal of Pure and Applied Mathematics (2023), 12pp.
  12. G. V. Milovanović, R. K. Parmar, T. K. Pogány, Bounds for the (p,v)-extended Beta function and certain consequences, Journal of Mathematical Inequalities 

 Izlaganja na konferencijama:
  1. T. K. Pogány, Second type Neumann series of generalized Nicholson’s function, Workshop – Conference Vremensko-frekventna analiza sa primenama, Analysis and Acoustics Research – ANACRES, Branch of the Serbian Academy of Sciences and Arts and Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, Novi Sad, Srbija, 6. - 7. svibnja 2020.
  2. T. K. Pogány, Hilbert-type inequalities with non-homogeneous kernel: another view, International scientific online seminar on Analysis, Differential Equations and Mathematical Physics, Southern Federal University, Regional Mathematical Center, Rostov na Donu, Rusija, 15. travnja 2021.
  3. D. Krizmanić, Joint functional convergence of partial sum and maxima processes, 8th European Congress of Mathematics, Portorož, Slovenija, 20. - 26. lipnja 2021.
  4. D. Krizmanić, On joint weak convergence of partial sum and maxima processes, 7th Croatian Mathematical Congress, Split, Hrvatska, 15. - 18. lipnja 2022.
  5. T. K. Pogány, From average sampling to Whittaker sampling, 7th Croatian Mathematical Congress, Split, Hrvatska, 15. - 18. lipnja 2022.
  6. T. K. Pogány, Derivative plane sampling and weighted differential operator, Functional Analysis, Approximation Theory and Numerical Analysis - FAATNA20>22, Matera, Italija, 5. - 8. srpnja 2022.
  7. T. K. Pogány, Observations on truncation error upper bounds in derivative Whittaker-type sampling reconstruction, The 13th Symposium on Generating Functions of Special Numbers and Polynomials and their Applications (GFSNP 2023), Antalya, Turska, 11. - 13. ožujka 2023.
  8. T. K. Pogány, On error analysis in truncation of Whittaker-type derivative sampling series, Harmonic Analysis, Spaces and Operators, Novi Sad, Srbija, 19. - 21. travnja 2023.
  9. D. Krizmanić, Functional convergence of maxima of linear processes with heavy-tailed innovations and random coefficients, 13th International Conference on Extreme Value Analysis, Milano, Italija, 26. - 30. lipnja 2023.
  10. D. Krizmanić, Functional convergence of maxima of linear processes with heavy-tailed innovations and random coefficients, 43rd Conference on Stochastic Processes and their Applications - SPA 2023, Lisabon, Portugal, 24. - 28. srpnja 2023.
  11. T. K. Pogány, Functional inequalities for Bessel and hypergeometric type functions via probabilistic approach, International Workshop on Geometric Function Theory (IWGFT 2023), Department of Mathematics, Indian Institute of Technology, Madras, Chennai, Indija, 18. - 20. kolovoza 2023.
  12. T. K. Pogány, On Rice-Middleton model of probability distribution of sinusoidal signal combined with Gaussian noise, The 29th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications, Ramanujan School of Mathematical Sciences, Pondicherry University, Puducherry, Indija, 21. - 25. kolovoza 2023.