论文标题
零能量部分具有有限的p变差的dirichlet过程的示例
Example of a Dirichlet process whose zero energy part has finite p-variation
论文作者
论文摘要
令$ b^h $为$ \ mathbb {r} $的分数布朗动作，带有hurst参数$ h \ in（0,1）$，$ f $是其路径抗体，$ f（0）= 0 $，让$ b $是标准的布朗尼运动，独立于$ b^h $。我们表明，零能量部分$ a_t = f（b_t） - \ int_0^t f'（b_s）$ f（b）$的db_s $ of $ f（b）$具有正面和有限的$ p $ - 在特殊意义上，对于$ p_0 = \ frac {2} {2} {1+h} $。我们还提供了一些有关某个中位过程的零能量部分的模拟结果，这些结果表明其4/3 $变化是积极且有限的。
Let $B^H$ be a fractional Brownian motion on $\mathbb{R}$ with Hurst parameter $H\in(0,1)$, $F$ be its pathwise antiderivative with $F(0)=0$, and let $B$ be a standard Brownian motion, independent of $B^H$. We show that the zero energy part $A_t=F(B_t)-\int_0^t F'(B_s)dB_s$ of $F(B)$ has positive and finite $p$-variation in a special sense for $p_0=\frac{2}{1+H}$. We also present some simulation results about the zero energy part of a certain median process which suggest that its $4/3$-variation is positive and finite.
