Quelques resultats d'entropie sur l'espace de Wiener
Tóm tắt
One studies three problems related to entropy phenomenon in the classical Wiener space. In particular, the minoration of the Wiener measure for the set {x∈X/ϕ(x)⩽ε} is given where ϕ is a Sobolev norm in the Wiener spaceX.
Tài liệu tham khảo
Airault H. et Malliavin P.: Intégration géométrique sur l'espace de Wiener,Bull. Sci. Math., 2e série, tome 112 (1988), p. 3–52.
Fang S.: Non-dégénérescence des pseudo-normes de Sobolev sur l'espace de Wiener,Bull. Sci. Math., 2e série, tome 115 (1991), p. 223–234.
Goodman V.: Characteristics of normal samples,Annals of Prob. 16(3) (1988), pp. 1281–1290.
Kolmogorov A. N. et Tihomirov V. M.: ε-entropy and ε-capacity of sets in functional spaces,American Math. Society Translation. Serie 2, Vol. 17 (1961), pp. 277–364.
Malliavin, P.: Stochastic differential equations and cylindrical vector valued martingales (Dedicated to Leopoldo Nachbin) in J. A. Barroso (éd.),Aspect of Mathematics and Its Applications, (1986), pp. 583–599.
Takeda M.: (r, p)-capacity on the Wiener space and properties of Brownian motion,Z.W. 68 (1984), pp. 149–162.
Watanabe S.:Lecture on Stochastic Differential Equations and Malliavin Calculus, Berlin, Springer (1984) (Tata Institute of fundamental research lectures on mathematics, 73).
Fang S.: Sur un résultat d'entropie de l'espace de Wiener,C.R.A.S. 312, série I (1991), p. 995–998.