We give a brief survey on the Itô calculus and white noise theory with the aim to extend the
Itô theory of stochastic integration to stochastic processes which may not be adapted. The …

We review a new stochastic integral for adapted and instantly independent stochastic
processes and show that it is well-defined. Then we prove a unified Itô formula for the new …

Stochastic differential equations with adapted integrands and initial conditions are well
studied within Itô's theory. However, such a general theory is not known for corresponding …

A stochastic process Xt is called a near-martingale with respect to a filtration {Ft} if E [Xt| Fs]=
E [Xs| Fs] for all s≤ t. It is called a nearsubmartingale with respect to {Ft} if E [Xt| Fs]≥ E [Xs …

Exponential processes in the Itô theory of stochastic integration can be viewed in three
aspects: multiplicative renormalization, martingales, and stochastic differential equations. In …

Full article: On the Ayed-Kuo stochastic integration for anticipating integrands Skip to Main
Content Taylor and Francis Online homepage Taylor and Francis Online homepage Log in …

In this paper, we study the solutions of a stochastic differential equation with various
anticipating initial conditions. We show that the conditional expectation of the solution of …

We study the new stochastic integral introduced by Ayed and Kuo in [1]. Our main results are
two Itô formulas that extend the one presented in [1]. We generalize the notion of the Itô …

Stochastic differential equations can be specified with anticipatory initial value constraints
(IVC) which is useful in many applications where future filtration is known. However, such …

We study the concept of translation of a Brownian motion by an anticipative term given by a
Lebesgue integral of an instantly independent stochastic process. We introduce an …