Parameter estimations for linear parabolic fractional SPDEs with jumps

Authors

  • Wilfried GRECKSCH Martin-Luther-University Halle-Wittenberg Faculty of Natural Sciences II, Institute of Mathematics 06099 Halle (Saale), Germany, e-mail: wilfried.grecksch@mathematik.uni-halle.de
  • Hannelore LISEI Babe¸s-Bolyai University Faculty of Mathematics and Computer Sciences 1, Kog˘alniceanu Street 400084 Cluj-Napoca, Romania, e-mail: hanne@math.ubbcluj.ro https://orcid.org/0000-0003-1934-6274
  • Jens LUEDDECKENS Martin-Luther-University Halle-Wittenberg Faculty of Natural Sciences II, Institute of Mathematics 06099 Halle (Saale), Germany, e-mail: jlueddeckens@web.de

DOI:

https://doi.org/10.24193/subbmath.2019.2.12

Keywords:

Parameter estimation, SPDE, cylindrical fractional Brownian motion, cylindrical Poisson process.

Abstract

We give an unbiased and consistent estimator for the drift coefficient of a linear parabolic stochastic partial differential equation driven by a multiplicative cylindrical fractional Brownian motion with Hurst index 1/2 < h < 1 and a cylindrical centered Poisson process, if the observations of the solution process are given in discrete time points. The presented method is based on mean square estimations.

Mathematics Subject Classification (2010): 60H15, 62F12, 60G22.

References

Bertin, K., Torres, S., Tudor, C. A., Maximum-likelihood estimators and random walks in long memory models, Statistics, 45(2011), no. 4, 361-374.

Cialenco, I., Parameter estimation for SPDEs with multiplicative fractional noise, Stoch. Dyn., 10(2010), no. 4, 561-576.

Gichman, I.I., Skorochod, A.W., Stochastische Differentialgleichungen, Akademie- Verlag, 1971.

Kozachenko, Y., Melnikov, A., Mishura, Y., On drift parameter estimation in models with fractional Brownian motion, Statistics, 49(2015), no. 1, 35-62.

Long, H., Parameter estimation for a class of stochastic differential equations driven by small stable noises from discrete observations, Acta Math. Sci. Ser. B (Engl. Ed.), 30(2010), no. 3, 645-663.

Lototsky, S.V., Rozovsky, B.L., Stochastic partial differential equations, Springer, 2017. [7] Lueddeckens, J., Fraktale stochastische Integralgleichungen im White-Noise-Kalku¨l, Dissertation Martin-Luther-Universit¨at Halle-Wittenberg, April 2017.

Maslowski, B., Tudor, C.A., Drift parameter estimation for infinite-dimensional fractional Ornstein–Uhlenbeck process, Bull. Sci. Math., 137(2013), no. 7, 880-901.

Nualart, D., Stochastic calculus with respect to fractional Brownian motion, Ann. Fac. Sci. Toulouse Math. (6), 15(2006), no. 1, 63-78.

Protter, Ph., Stochastic Integration and Differential Equations, Springer, 1990.

Xiao, W., Zhang, W., Zhang, X., Parameter identification for discretely observed geometric fractional Brownian motion, J. Stat. Comput. Simul., 85(2015), no. 2, 269-283.

STUDIA UBB MATHEMATICA, Volume 64 (LXIV), No. 2, June 2019

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Published

2019-06-30

How to Cite

GRECKSCH, W., LISEI, H., & LUEDDECKENS, J. (2019). Parameter estimations for linear parabolic fractional SPDEs with jumps. Studia Universitatis Babeș-Bolyai Mathematica, 64(2), 279–289. https://doi.org/10.24193/subbmath.2019.2.12

Issue

Volume 64, No. 2, June 2019

Section

Articles

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Copyright (c) 2019 Studia Universitatis Babeș-Bolyai Mathematica

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This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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