In this paper, a linear combination of quadratic modified hat functions is proposed to solve
stochastic Itô–Volterra integral equation with multi-stochastic terms. All known and unknown …

We study the existence, uniqueness, and approximation of solutions of general stochastic
differential equations (SDEs) with two time-dependent reflecting barriers driven by optional …

It is well-known that modern stochastic calculus has been exhaustively developed under
usual conditions. Despite such a well-developed theory, there is evidence to suggest that …

In this paper, we study SDEs with respect to optional semimartingales or optional SDEs. Our
leading idea is to explore the concept and technique of local time of optional processes to …

This paper is devoted to the question of existence and uniqueness of strong solutions of
stochastic differential equations with respect to optional semimartingales. Optional …

What makes an optional stochastic exponential a true optional martingale in a probability
space where the underlying filtration is not right continuous nor complete. In this paper, we …

In the first part of this paper, we pose and solve a new version of Skorokhod problem with
jumps, reflected in the half line R^+ R+ and associated to a right limited and left limited …

ABSTRACT The classical Doob–Meyer decomposition and its uniform version the optional
decomposition are stated on probability spaces with filtrations satisfying the usual …

In this work, we introduce a new Skorokhod problem with two reflecting barriers when the
trajectories of the driven process and the barriers are right and left limited. We show that this …

This paper is devoted to comparison of strong solutions of stochastic equations with respect
to optional semimartingales. Optional semimartingales have right and left limits but are not …