7 citations · 16 across the 5 of their papers we have counts for
4 papers · 1 filter
Single jump filtrations and local martingales
Alexander A. Gushchin
A single jump filtration generated by a random variable with values in on a probability space $(Ω,{\mathscr{F}…
Integrated quantile functions: properties and applications
Alexander A. Gushchin, Dmitriy A. Borzykh
In this paper we provide a systematic exposition of basic properties of integrated distribution and quantile functions. We define these transforms in such a way that they character…
On pathwise counterparts of Doob's maximal inequalities
Alexander A. Gushchin
In this paper, we present pathwise counterparts of Doob's maximal inequalities (on the probability of exceeding a level) for submartingales and supermartingales.
Processes that can be embedded in a geometric Brownian motion
Alexander Gushchin, Mikhail Urusov
The main result is a counterpart of the theorem of Monroe [\emph{Ann. Probability} \textbf{6} (1978) 42--56] for a geometric Brownian motion: A process is equivalent to a time chan…