For a backward stochastic differential equation (BSDE, for short), when the generator is not progressively measurable, it might admit adapted solutions, shown by an example. However, Volterra integral equations (BSVIEs, generators are allowed to be anticipating. This gives, among other things, essential difference between BSDEs and BSVIEs. Under some proper conditions, well-posedness of such BS...

2 Young’s integrals and stochastic differential equations driven by fractional Brownian motions 4 2.1 Young’s integral and basic estimates . . . . . . . . . . . . . . . . . . 4 2.2 Stochastic differential equations driven by a Hölder path . . . . . . . 7 2.3 Multidimensional extension . . . . . . . . . . . . . . . . . . . . . . . 11 2.4 Fractional calculus . . . . . . . . . . . . . . . . . . . ...

This paper is devoted to a construction of the stochastic Itô integral with respect to infinite dimensional cylindrical Wiener process. The construction given is an alternative one to that introduced by DaPrato and Zabczyk [3]. The connection of the introduced integral with the integral defined by Walsh [9] is provided as well.

For a one-parameter process of the form X, = X0 + & (b, d W, + & & ds, where W is a Wiener process and I+ d W is a stochastic integral, a twice continuously differentiable function f(X,) is again expressible as the sum of a stochastic integral and an ordinary integral via the Ito differentiation formula. In this paper we present a generalization for the stochastic integrals associated with a tw...

This paper presents a new optimization algorithm to design an optimal proportional, integral, derivative (PID) controller in hydro-turbine generator governor for damping output frequency oscillations. In this research, we utilize a stochastic and optimal based PID controller to control frequency-response of the hydro turbine. The proposed algorithm is employed to design an optimal PID controlle...

In this paper we propose a new approach to fuzzy stochastic integrals of Itô and Aumann type. Then a fuzzy equation with fuzzy stochastic integrals is investigated. The existence and uniqueness of solution is proven. Some typical properties of the solution are also obtained. Similar results to set-valued stochastic integral equations are stated.

We connect some basic issues of survival analysis in biostatistics with estimation and convergence theories of stochastic ltering. Viewing censored data problems through a ltering perspective, we can derive estimators expressed using stochastic integral/diierential equations. We then study statistical asymptotics using convergence theory of stochastic equations. We will illustrate such a progra...