arXiv subjects

László Bondici

Publications and source records attributed to László Bondici.

2 recordsLinked to original sources

arXiv2022

Example of a Dirichlet process whose zero energy part has finite p-variation

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.

math.PR↗

arXiv2022

On the lack of semimartingale property

In this work we extend the characterization of semimartingale functions in Cinlar et al. (1980) to the non-Markovian setting. We prove that if a function of a semimartingale remains a semimartingale, then under certain conditions the function must have intervals where it is a difference of two convex functions. Under suitable conditions this property also holds for random functions. As an application, we prove that the median process defined in Prokaj et al. (2011) is not a semimartingale. The same process appears also in Hu and Warren (2000) where the question of the semimartingale property is raised but not settled.

math.PR↗