arXiv subjects

R. M. Łochowski

Publications and source records attributed to R. M. Łochowski.

3 recordsLinked to original sources

arXiv2025

The It{ô}-Föllmer formula -- nonstandard cases

The purpose of this note is to prove the It{ô}-Föllmer formula for the càdlàg paths possessing quadratic variation in a possibly ``weakest'' sense along some sequence of partitions. By this we mean, for example, that we do not require the jumps of the quadratic variation to occur exactly at the times when the path itself jumps or that the quadratic variation exists at all time instances. Moreover, we deal with more general partitions than partitions with vanishing mesh used by Föllmer, also relaxing restrictions imposed on a sequence of partitions in other related literature.

math.PR↗

arXiv2021

Moments and tails of hitting times of Bessel processes and convolutions of elementary mixtures of exponential distributions

We present explicit estimates of right and left tails and exact (up to universal, multiplicative constants) estimates of tails and moments of hitting times of Bessel processes. The latter estimates are obtained from more general estimates of moments and tails established for convolutions of elementary mixtures of exponential distributions.

math.PR↗

arXiv2017

Riemann-Stieltjes integrals driven by irregular signals in Banach spaces and rate-independent characteristics of their irregularity

We prove an inequality of the Loéve-Young type for the Riemann-Stieltjes integrals driven by irregular signals attaining their values in Banach spaces and, as a result, we derive a new theorem on the existence of the Riemann-Stieltjes integrals driven by such signals. Also, for any $p\ge1$ we introduce the space of regulated signals $f:[a,b] \rightarrow W$ ($a 0$ by signals whose total variation is of order $δ^{1-p}$ as $δ\rightarrow 0+$ and prove that they satisfy the assumptions of the theorem. Finally, we derive more exact, rate-independent characterisations of the irregularity of the integrals driven by such signals.

math.FA↗