摘要： Suppose that $\{X_i\}$ are i.i.d r.vs with $P(X_i=0)=p, P(X_i=1)=1-p, p\in (0,1).$ Let $X=\sum_{n=1}^\infty\frac{X_n}{2^n}=\sum_{n=1}^\infty Y_n$ and ... 阅读全文

摘要： Let $B^\alpha$ be an $(N,1)$-fractional Brownian motion with index $\alpha\in(0,1).$ Pitt (Local times for Gaussian vector fields, Indiana Univ. Math.... 阅读全文

摘要： Let $0<p=1-q<1$ and $X_1,X_2,\ldots$ be an i.i.d. Bernoulli sequence with $p=\mathbb{P}(X_i=1)=1-\mathbb{P}(X_i=0)$. Denote by $S_n$ the length of the... 阅读全文

摘要： Kronecker’s lemma gives a condition for convergence of partial sums of realnumbers, and for example can be used in the proof of Kolmogorov’s strong la... 阅读全文

摘要： Given $0<s<u<v<1$ and $s<t<v$, one can construct a Cantor set $E\subset [0,1]$ such that $\dim_H E=s, \dim_P E=t, \underline{\dim}_B E=u$ and $\overli... 阅读全文

摘要： Let $X$ be a totally bounded metric space.(1) If $X$ is compact and if $\overline{\dim}_MU\ge s$ for every non-empty open set $U\subset X,$ then $\dim... 阅读全文