It is well-known that Control Theory was founded by N. Wiener in 1948 ([349]). After that, this
theory was greatly extended to various complicated setting and widely used in sciences and …

The main purpose of this paper is to survey some recent progresses on control theory for
stochastic distributed parameter systems, ie, systems governed by stochastic differential …

In this work, we study two final value problems for fractional reaction equation with standard
Brownian motion W (t) and fractional Brownian motion BH (t), for H∈(1 4, 1 2)∪(1 2, 1) …

We study an inverse scattering problem associated with a Schrödinger system where both
the potential and source terms are random and unknown. The well-posedness of the forward …

We are concerned with the direct and inverse scattering problems associated with a time-
harmonic random Schrödinger equation with unknown source and potential terms. The …

This paper is devoted to establishing global Carleman estimates for some forward and
backward stochastic degenerate parabolic equations. First, two Carleman estimates for the …

In this paper, we study the null controllability for some linear and semi-linear parabolic
SPDEs involving both the state and the gradient of the state. To start with, an improved …

In this paper, we establish two Carleman estimates for a stochastic degenerate parabolic
equation. The first one is for the backward stochastic degenerate parabolic equation with …

Stochastic parabolic equations are widely used to model many random phenomena in
natural sciences, such as the temperature distribution in a noisy medium, the dynamics of a …

In this paper, we derive a Carleman estimate for a stochastic wave equation. Then we apply
the Carleman estimate to solve an inverse source problem of determining two kinds of …