Stochastic differential equations for random matrices processes in the nonlinear framework

• Autorzy: Stihi S. , Boutabia H. , Meradji S

Identyfikatory

DOI

10.7494/OpMath.2018.38.2.261

• Języki publikacji: EN

Abstrakty

EN

In this paper, we investigate the processes of eigenvalues and eigenvectors of a symmetric matrix valued process Xt, where Xt is the solution of a general SDE driven by a G-Brownian motion matrix. Stochastic differential equations of these processes are given. This extends results obtained by P. Graczyk and J. Malecki in [Multidimensional Yamada-Watanabe theorem and its applications to particle systems, J. Math. Phys. 54 (2013), 021503].

Słowa kluczowe

EN

G-Brownian motion matrix; G-stochastic differential equations; random matrices; eigenvalues; eigenvectors

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2018
• Tom: Vol. 38, no. 2
• Strony: 261--283
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Stihi S.

• LaPS Laboratory, Badji-Mokhtar University PO BOX 12, Annaba 23000, Algeria

autor

Boutabia H.

• LaPS Laboratory, Badji-Mokhtar University PO BOX 12, Annaba 23000, Algeria

autor

Meradji S

• LaPS Laboratory, Badji-Mokhtar University PO BOX 12, Annaba 23000, Algeria

Bibliografia

• [1] G.W. Anderson, A. Guionnet, O. Zeitouni, An Introduction to Random, Matrices, Cambridge University Press, 2009.
• [2] X.P. Bai, Y.Q. Lin, On the existence and uniqueness of solutions to stochastic differential equations driven by G-Brownian motion with integral-Lipschitz coefficients, Acta Math. Appl. Sin. Engl. Ser. 30 (2014), 589-610.
• [3] F. Faizullah, A note on the caratheodory approximation scheme for stochastic differential equations under G-Brownian motion, Z. Naturforsch. 67a (2012), 699-704.
• [4] F. Gao, Pathwise properties and homeomorphic flows for stochastic differential equation driven by G-Brownian motion, Stochastic Process. Appl. 119 (2009), 3356-3382.
• [5] P. Graczyk, J. Malecki, Multidimensional Yamada-Watanabe theorem and its applications to particle systems, J. Math. Phys. 54 (2013), 021503.
• [6] M. Katori, H. Tanemura, Symmetry of matrix-valued stochastic processes and noncolliding diffusion particle systems, J. Math. Phys. 45 (2004), 3058-3085.
• [7] X. Li, S. Peng, Stopping times and related Ito's calculus with G-Brownian motion, Stochastic Process. Appl. 121 (2011), 1492-1508.
• [8] Q. Lin, Local time and Tanaka formula for the G-Brownian motion, J. Math. Anal. Appl. 398 (2012), 315-334.
• [9] S. Peng, G-expectation, G-Brownian motion and related stochastic calculus of ltd type, Stochastic Analysis and Applications (2007), Abel Symp., 2, Springer, Berlin, 541-567.
• [10] S. Peng, Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation, Stochastic Process. Appl. 118 (2008), 2223-2253.
• [11] S. Peng, A. Bensoussan, J. Sung, Real Options, Ambiguity, Risk and Insurance, IOS Press, Amsterdam-Berlin-Tokyo-Washington DC, 2013.
• [12] P. Wu, Z. Chen, Invariance principles for the law of the iterated logarithm under G-framework, Sci. China Math. 58 (2011), 1251-1264.

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).