arXiv subjects
Publications and source records attributed to Raouf Ghomrasni.
In this paper we extend the recent work of C.A. Braumann \cite{B2007} to the case of stochastic differential equation with random coefficients. Furthermore, the relationship of the Itô-Stratonovich stochastic calculus to studies of random population growth is also explained.
In a recent work \cite{BG}, given a collection of continuous semimartingales, authors derive a semimartingale decomposition from the corresponding ranked processes in the case that the ranked processes can meet more than two original processes at the same time. This has led to a more general decomposition of ranked processes. In this paper, we derive a more general result for semimartingales (not necessarily continuous) using a simpler approach. Furthermore, we also give a generalization of Ouknine \cite{O1, O2} and Yan's \cite{Y1} formula for local times of ranked processes
We show that for a wide class of functions $F$ that: $$ {\lim_{ε\downarrow 0} {\frac{1}ε} \int_0^t \Big\{F(s, X_s) - F(s, X_s - ε)\Big\} d\big _s} = - \int_0^t\int_{\R} F(s, x) d L_s^x $$ where $X_t$ is a continuous semi-martingale, $(L_t^x, x \in \R, t \geq 0)$ its local time process and $(\big _t, t \geq 0)$ its quadratic variation process.