Backward doubly stochastic Volterra integral equations and their applications

We consider a least square-type method to estimate the drift parameters for the mean-reverting Ornstein–Uhlenbeck process of the second kind {Xt,t ≥ 0} defined as dXt = &#x1d703;(μ + Xt)dt + dYt,G(1),t ≥ 0...

Parameter estimation for Gaussian mean-reverting Ornstein–Uhlenbeck processes of the second kind: Non-ergodic case

Least Squares Type Estimation for Discretely Observed Non-Ergodic Gaussian Ornstein-Uhlenbeck Processes

Anticipated backward stochastic differential equations with quadratic growth

In this paper, we investigate a kind of partial information linear-quadratic optimal control problem driven by a backward stochastic differential equation, where the state equation and the cost functional contain diffusion terms. Using maximum principle, we derive the corresponding Hamiltonian system, which is a conditional mean-field forward-backward stochastic differential equation. By the backward separation approach and the filtering technique, we get two Riccati equations, and a backward and a forward optimal filtering equations. Then a feedback form of optimal control is obtained.We also extend thecontrol problem to the case of mean-field backward stochastic differential equation under partial information.A corresponding feedback form of optimal control is also obtained.

A partial information linear-quadratic optimal control problem of backward stochastic differential equation with its applications

Berry-Esséen bounds for parameter estimation of general Gaussian processes

In this paper, we focus on mean-field anticipated backward stochastic differential equations (MF-BSDEs, for short) driven by fractional Brownian motion with Hurst parameter H>1/2. First, the existence and uniqueness of this new type of BSDEs are established using two different approaches. Then, a comparison theorem for such BSDEs is obtained. Finally, as an application of this type of equations, a related stochastic optimal control problem is studied and the related sufficient maximum principle is obtained.

Mean-field anticipated BSDEs driven by fractional Brownian motion and related stochastic control problem

Hermite Ornstein--Uhlenbeck processes mixed with a Gamma distribution

Let $Z:=\{Z_t,t\geq0\}$ be a stationary Gaussian process We study two estimators of $\mathbb{E}[Z_0^2]$, namely $\widehat{f}_T(Z):= \frac{1}{T} \int_{0}^{T} Z_{t}^{2}dt$, and $\widetilde{f}_n(Z) :=\frac{1}{n} \sum_{i =1}^{n} Z_{t_{i}}^{2}$, where $ t_{i} = i \Delta_{n}$, $ i=0,1,\ldots, n $, $\Delta_{n}\rightarrow 0$ and $ T_{n} := n \Delta_{n}\rightarrow \infty$ We prove that the two estimators are strongly consistent and establish Berry-Esseen bounds for a central limit theorem involving $\widehat{f}_T(Z)$ and $\widetilde{f}_n(Z)$ We apply these results to asymptotically stationary Gaussian processes and estimate the drift parameter for Gaussian Ornstein-Uhlenbeck processes

Soukaina Douissi

Papers

Berry-Esséen bounds for parameter estimation of general Gaussian processes

Mean-field anticipated BSDEs driven by fractional Brownian motion and related stochastic control problem

Mean-field anticipated BSDEs driven by fractional Brownian motion and related stochastic control problem

Hermite Ornstein--Uhlenbeck processes mixed with a Gamma distribution

Berry-Esseen bounds of second moment estimators for Gaussian processes observed at high frequency