Convergence to convex compact sets in infinite dimensions

Journal of Mathematical Analysis and Applications

Volumn 284, Issue 2, 2003, Pages 471-480

  Artstein, Zvi ^a   Gaitsgory, Vladimir ^b  

^a WEIZMANN INSTITUTE OF SCIENCE   (Israel)

^b UNIVERSITY OF SOUTH AUSTRALIA   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0041852620     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-247X(03)00334-2     Document Type: Article

References (14)

1. Z. Artstein, G.C. Hansen, Convexification in limit laws of random sets in Banach spaces, Ann. Probab. 13 (1985) 307-309.
2. Z. Artstein, R.A. Vitale, A strong law of large numbers for random compact sets, Ann. Probab. 3 (1975) 879-882.
3. V. Gaitsgory, A. Leizarowitz, Limit occupational measures set for a control system and averaging of singularly perturbed control systems, J. Math. Anal. Appl. 233 (1999) 461-475.
4. V. Gaitsgory, M.-T. Nguyen, Multiscale singularly perturbed control systems: Limit occupational measures sets and averaging, SIAM J. Control Optim. 41 (2002) 954-974.
5. G. Grammel, Averaging of singularly perturbed systems, Nonlinear Anal. 28 (1997) 1851-1865.
6. J. Hale, Theory of Functional Differential Equations, 2nd ed., Springer, New York, 1977.
7. J.C. Hansen, P. Hulse, Subadditive ergodic theorems for random sets in infinite dimensions, Statist. Probab. Lett. 50 (2000) 409-416.
8. F. Hiai, Strong laws of large numbers for multivalued random variables, in: G. Salinetti (Ed.), Multifunctions and Integrands, Stochastic Analysis, Approximation and Optimization, in: Lecture Notes in Math., Vol. 1091, Springer, Berlin, 1984, pp. 160-172.
9. E. Klein, A.C. Thompson, Theory of Correspondences, Wiley-Interscience, New York, 1984.
10. V.V. Nemytskii, V.V. Stepanov, Qualitative Theory of Differential Equations, Princeton Univ. Press, Princeton, NJ, 1960.
11. M.L. Puri, D.A. Ralescu, Limit theorems for random compact sets in Banach space, Math. Proc. Cambridge Philos. Soc. 97 (1985) 151-158.
12. R.L. Taylor, H. Inoue, A strong law of large numbers for random sets in Banach spaces, Bull. Inst. Math. Acad. Sinica 13 (1985) 403-409.
13. R.L. Taylor, H. Inoue, Laws of large numbers for random sets, in: J. Goutsias, R.P.S. Mahler, H.T. Nguyen (Eds.), Random Sets: Theory and Applications, in: IMA Vol. Math. Appl., Vol. 97, Springer, New York, 1997, pp. 347-360.
14. R.L. Taylor, A.N. Vidyashankar, Y. Chen, Limit theorems for exchangeable random elements and random sets, in: M.L. Puri (Ed.), Asymptotics in Statistics and Probability, Papers in honor of George Gregory Roussas, VSP, Zeist, The Netherlands, 2000, pp. 367-378.