Moment instabilities in multidimensional systems with noise

European Physical Journal B

Volumn 43, Issue 2, 2005, Pages 221-242

  Wilkinson, D M ^a,b  

^a HEWLETT PACKARD LABORATORIES   (United States)

^b STANFORD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; EIGENVALUES AND EIGENFUNCTIONS; LINEAR ALGEBRA; LINEAR SYSTEMS; MULTIVARIABLE SYSTEMS; PERTURBATION TECHNIQUES; WHITE NOISE;

ILL-CONDITIONED SYSTEM; MOMENT INSTABILITIES; MULTIVARIATE ANALYSIS; STOCHASTIC DIFFERENCE SYSTEMS;

RANDOM PROCESSES;

EID: 14744302267     PISSN: 14346028     EISSN: None     Source Type: Journal    
DOI: 10.1140/epjb/e2005-00045-3     Document Type: Article

References (55)

1. J. Guckenheimer, Lect. Applied Math. 17, 187 (1979)
2. C.W. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences, 2nd edn. (Springer-Verlag, Berlin, 1985)
3. J.A. Rice, Mathematical Statistics and Data Analysis, 2nd edn. (Duxbury Press, Belmont, California, 1995)
4. S. Redner, Am. J. Phys. 53, 267 (1990)
5. R.C. Lewontin, D. Cohen, Proc. Nat. Ac. Sci. 62, 1056 (1969)
6. J.N. Tsitsiklis, V.D. Blondel, Mathematics of Control, Signals, and Systems 10, 31 (1997)
7. P. Bougerol, J. Lacroix, Products of Random Matrices with Applications to Schrödinger Operators (Birkhäuser, Boston, 1985)
8. G.W. Stewart, University of Maryland Institute for Advanced Computer Studies, Report No. 91, 2001 (unpublished)
9. J.E. Cohen, C.M. Newman, The Annals of Probability 12, 283 (1984)
10. L. Gurvits, Linear Algebra and its Applications 231, 47 (1995)
11. N.B. Barabanov, Automation and Remote Control 40, 152 (1988)
12. D. Hinrichsen, N.K. Son, in Proceedings of the Third International Conference on Approximation and Optimization, edited by B. Bank et al. (The Electronic Library of Mathematics, 1995)
13. P.R. Kumar, P. Varaiya, Stochastic Systems: Estimation, Identification and Adaptive Control (Prentice-Hall, Englewood Cliffs, New Jersey, 1986)
14. C. Xiao, D.J. Hill, P. Agathoklis, IEEE Transactions on Circuits and Systems 44, 614 (1997)
15. G.V. Moustakidis, Int. J. Adaptive Control and Signal Processing 12, 579 (1998)
16. M. Milisavljević, E.I. Verriest, in Proceedings of the European Control Conference, 1997
17. F. Ma, T.K. Caughey, Int. J. Nonlinear Mech. 16, 139 (1981)
18. F. Kozin, Automatica 5, 95 (1969)
19. W.M. Haddad, V. Chellaboina, S.G. Nersesov, Mathematical Problems in Engineering 8, 493 (2002)
20. T. Hogg, B.A. Huberman, J.M. McGlade, Proceedings of the Royal Society of London B 237, 43 (1989)
21. N.G. van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1992)
22. J.-P. Eckmann, D. Ruelle, Rev. Mod. Phys. 57, 617 (1985)
23. B. Derrida, E. Gardner, J. Phys. France 45, 1283 (1984)
24. B. Derrida, K. Mecheri, J. Pichard, J. Phys. France 48, 733 (1987)
25. N. Zanon, B. Derrida, J. Stat. Phys. 50, 509 (1988)
26. J.B. Pendry, J. Phys. C 15, 4821 (1982)
27. G. Parisi, J. Phys. A 19, L675 (1986)
28. A. Crisanti, G. Paladin, A. Vulpiani, Products of Random Matrices in Statistical Physics (Springer-Verlag, Berlin, 1993)
29. J.P. Bouchaud, A. Georges, D. Hansel, P.L. Doussel, J.M. Maillard, J. Phys. A 19, L1145 (1986)
30. R. Khasminskii, Prikladnaya Matematika i Mekhanika (Journal of Applied Mathematics and Mechanics) 31, 1021 (1967)
31. X. Mao, Stochastic Differential Equations and Applications (Horwood, Chichester, 1997)
32. L. Arnold, M.M. Doyle, N.S. Namachchivaya, Dynamics and Stability of Systems 12, 187 (1997)
33. R. Khasminskii, N. Moschuk, SIAM J. Appl. Math. 58, 245 (1998)
34. A. Abrahams, M.J. Stephen, J. Phys. C 13, L377 (1980)
35. G. Strang, Linear Algebra and Its Applications (Academic Press, New York, 1976)
36. Lyapunov Exponents, Lecture Notes in Mathematics Vol. 1186, edited by L. Arnold, V. Wihstutz (Springer, New York, 1986)
37. A. Herman, M. Neumann, R.J. Stern, Nonnegative Matrices in Dynamic Systems (John Wiley and Sons, New York, 1989)
38. L. Farina, S. Rinaldi, Positive Linear Systems: Theory and Applications (John Wiley and Sons, New York, 2000)
39. Positive Systems, Lecture Notes in Control and Information Sciences Vol. 294, edited by L. Benvenuti, A. de Santis, L. Farina (Berlin, 2003, Springer)
40. L.N. Trefethen, A.E. Trefethen, S.C. Reddy, T.A. Driscoll, Science 261, 578 (1993)
41. R. Bellman, Duke Mathematical J. 21, 491 (1954)
42. H. Furstenberg, H. Kesten, Annals of Mathematical Statistics 31, 457 (1960)
43. G.H. Golub, C.F. van Loan, Matrix Computations, 2nd edn. (The Johns Hopkins University Press, Baltimore, 1989)
44. A. Edelman, Ph.D. dissertation, MIT, 1989
45. H. Minc, Nonnegative Matrices (John Wiley and Sons, New York, 1988)
46. F. Juhasz, Discrete Mathematics 41, 161 (1982)
47. Y.B. Zel'dovich, S.A. Molchanov, A.A. Ruzmaikin, D.D. Sokolov, Uspekhi Fizicheskikh Nauk 152, 3 (1987)
48. Z. Füredi, J. Komlós, Combinatorics 1, 233 (1981)
49. S. Roy, Ph.D. dissertation, MIT, 2003
50. S. Geman, Ann. Prob. 14, 1318 (1986)
51. P.E. Kloeden, E. Platen, Numerical Solution of Stochastic Differential Equations (Springer-Verlag, Berlin, 1992)
52. B.A. Huberman, N.S. Glance, Proc. Natl. Acad. Sci. 90, 7716 (1993)
53. B.K. Øksendal, Stochastic Differential Equations: an Introduction with Applications, 6th edn. (Springer, Berlin, 2003)
54. A. Berman, R.J. Plemmons, Nonnegative Matrices in the Mathematical Sciences (Academic Press, New York, 1979)
55. S. Geman, Ann. Prob. 8, 252 (1980)