The exact values of average σ_B width and infinite dimensional σ_G width of Sobolev class B\+r\-p(R) in the metric L\-p(R)(1≤p≤∞) are obtained and the exact (σ∈N) and strong asymptotic (σ>1) results of infinit...
Project supported by the Science Fund of the Chinese Academy of Sciences.
The author discusses a variational equation which has a solution of even function, i.e.a differential equation with some inequality constraints.This problem originated from adiscounted cost problem in singular stochas...
Project supported by the National Natural Science Foundation of China
Concerning the study of Banach support for the sample space of a random process, the idea can go back to the penetrating investigation of R. Dudley, V.N. Sudaso and X. Fernique, about Gaussian cylindrical measure. Gro...
Many authors have discussed how large the increments of a Wiener process can be and also investigated how small the increments of a 1-parameter Wiener process can be. But there had not been seen an exhaustive study of...
In this letter, information uncertainty principle is deducted from the Shannon-Wiener formula. It is proved that Heisenberg’s uncertainty principle is its special case. The Shannon-Wiener formula shows that the maxim...
Malliavin Calculus for two-parameter Wiener functionals has been established by Nualart and Sanz. Under some condition they have proved that the solution of S. D. E. has smooth density in the plane, but the condition ...
<正> We consider a dam model of capacity Ⅴ units and make the following assumptions: (ⅰ) Let X(t) be the water input into the dam during the time interval (0, t], then {X(t):t≥0} is a Wiener process with nonnegativ...
Ⅰ. INTRODUCTION Of late years, Gsrg and other scholsrs studied the questions on increments of the Wiener process extensively and obtained many results. Letting W(t), t≥0 be a standard Wiener process, Hanson and Russ...
The a.s. behavior of increments of partial sums of i. i. d. random variables can be obtained by the increments of Wiener process with the help of the invariance principles. For independent, but not necessarily i.i.d, ...