Integral representation of renormalized self-intersection local times (2008)
Hu, Yaozhong, Nualart, David, Song, Jian
In this paper we apply Clark-Ocone formula to deduce an explicit integral representation for the renormalized self-intersection local time of the $d$% -dimensional fractional Brownian motion with...
A singular stochastic differential equation driven by fractional Brownian motion (2007)
Hu, Yaozhong, Nualart, David, Song, Xiaoming
In this paper we study a singular stochastic differential equation driven by an additive fractional Brownian motion with Hurst parameter $H>\frac 12$. Under some assumptions on the drift, we show...
Fractional martingales and characterization of the fractional Brownian motion (2007)
Hu, Yaozhong, Nualart, David, Song, Jian
In this paper we introduce the notion of $\alpha$-martingale as the fractional derivative of order $\alpha$ of a continuous local martingale, where $ \alpha\in (-\frac 12, \frac 12)$, and we show...
Stochastic Heat Equation Driven by Fractional Noise and Local Time (2007)
The aim of this paper is to study the $d$-dimensional stochastic heat equation with a multiplicative Gaussian noise which is white in space and it has the covariance of a fractional Brownian motion...
A Delayed Black and Scholes Formula I (2006)
Arriojas, Mercedes, Hu, Yaozhong, Mohammed, Salah-Eldin, Pap, Gyula
In this article we develop an explicit formula for pricing European options when the underlying stock price follows a non-linear stochastic differential delay equation (sdde). We believe that the...
A Delayed Black and Scholes Formula II (2006)
Arriojas, Mercedes, Hu, Yaozhong, Mohammed, Salah-Eldin, Pap, Gyula
This article is a sequel to [A.H.M.P]. In [A.H.M.P], we develop an explicit formula for pricing European options when the underlying stock price follows a non-linear stochastic delay equation with...
Rough Path Analysis Via Fractional Calculus (2006)
Using fractional calculus we define integrals of the form $% \int_{a}^{b}f(x_{t})dy_{t}$, where $x$ and $y$ are vector-valued H\"{o}lder continuous functions of order $\displaystyle \beta \in...
Renormalized self-intersection local time for fractional Brownian motion (2005)
Let B_t^H be a d-dimensional fractional Brownian motion with Hurst parameter H\in(0,1). Assume d\geq2. We prove that the renormalized self-intersection local...
Renormalized self-intersection local time for fractional Brownian motion (2005)
Let BtH be a d-dimensional fractional Brownian motion with Hurst parameter H∈(0,1). Assume d≥2. We prove that the renormalized self-intersection local time...
Some Processes Associated with Fractional Bessel Processes (2004)
Let $B=\{(B_{t}^{1},..., B_{t}^{d}), t\geq 0\}$ be a $d$-dimensional fractional Brownian motion with Hurst parameter $H$ and let $R_{t}=% \sqrt{(B_{t}^{1})^{2}+... +(B_{t}^{d})^{2}}$ be the...
Discrete-time approximations of stochastic delay equations: The Milstein scheme (2004)
Hu, Yaozhong, Mohammed, Salah-Eldin A., Yan, Feng
In this paper, we develop a strong Milstein approximation scheme for solving stochastic delay differential equations (SDDEs). The scheme has convergence order 1. In order to establish the scheme, we...
Hu, Yaozhong, Oksendal, B, Zhang, TS
We present a white noise calculus for d-parameter fractional Brownian motion B-H (x, omega); x is an element of R-d, omega is an element of Omega with general d-dimensional Hurst parameter H =...
Discrete-Time Approximations Of Stochastic Delay Equations: The Milstein Scheme (2003)
In this paper, we develop a strong Milstein approximation scheme for solving stochastic delay dierential equations (SDDE's). The scheme has convergence order 1. In order to establish the scheme, we...
Chaos expansion of local time of fractional Brownian motions (2002)
We find the chaos expansion of local time l(T)((H))(x, (.)) of fractional Brownian motion with Hurst coefficient H is an element of (0, 1) at a point x is an element of R-d. As an application we show...
Chaos expansion of heat equations with white noise potentials (2002)
The asymptotic behavior as t --> infinity of the solution to the following stochastic heat equations [GRAPHICS] is investigated, where w is a space-time white noise or a space white noise. The use of...
Probability Structure Preserving and Absolute Continuity (2001)
The concept of probability structure preserving mapping is introduced. The idea is applied to define stochastic integral for fractional Brownian motion (fBm) and to obtain an anticipative Girsanov...
Stochastic calculus for fractional Brownian motion - I. Theory (2000)
Duncan, Tyrone E, Hu, Yaozhong, Pasik-Duncan, Bozenna
In this paper a stochastic calculus is given for the fractional Brownian motions that have the Hurst parameter in (1/2, 1). A stochastic integral of Ito type is defined for a family of integrands so...
Ito-Wiener chaos expansion with exact residual and correlation, variance inequalities (1997)
We give a formula of expanding the solution of a stochastic differential equation (abbreviated as SDE) into a finite Ito-Wiener chaos with explicit residual. And then we apply this formula to obtain...
Une inégalité d'interpolation sur l'espace de Wiener (1995)
Laurent Decreusefond, Yaozhong Hu, Ali Suleyman
In this note we prove an interpolation inequality in L p -norm between the Sobolev spaces of order 0 and 2 on the Wiener space. R'esum'e Dans cette note nous d'emontrons une in'egalit'e...
Optimal time to invest when the price processes are geometric Brownian motions
Let $X_1(t)$, $\cdots$, $X_n(t)$ be $n$ geometric Brownian motions, possibly correlated. We study the optimal stopping problem: Find a stopping time $\tau^*