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The long time behavior of the fractional Ornstein-Uhlenbeck process with linear self-repelling drift
Let BH be a fractional Brownian motion with Hurst index \({1 \over 2} \le H < 1\) 1 ...
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The Laws of Large Numbers Associated with the Linear Self-attracting Diffusion Driven by Fractional Brownian Motion and Applications
Let \(B^H\) B H
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Forward and symmetric Wick-Itô integrals with respect to fractional Brownian motion
Let BH = {B t H , t ⩾ 0} be a fractional Brownian motion with Hurst index H ∈ (0, 1). Inspired by pathwise integrals and Wick product, in this paper, we consider the ...
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Open AccessQuadratic covariations for the solution to a stochastic heat equation with space-time white noise
Let u(t,x)\(u(t,x)\) be the solution to a stochastic heat equation ∂∂tu=12∂2∂x2u+∂2∂t∂xX(t,x),t≥0,x∈R$$ \frac{\partial }{\partial t}u=\frac{1}{2} \frac{\partial ^{2}}{\partial x^{2}}u+ \frac{\partial ^{2}}{\partial...
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The Least Squares Estimation for the α-Stable Ornstein-Uhlenbeck Process with Constant Drift
In this paper, we consider the least squares estimators of the Ornstein-Uhlenbeck process with a constant drift dXt=(θ1−θ2Xt)dt+dZt$$dX_{t}=(\theta_{1}-\theta_{2}X_{t})dt+dZ_{t} $$with X0 = x0, where θ1, θ2 are t...
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Asymptotic Behavior for High Moments of the Fractional Heat Equation with Fractional Noise
In this paper, we investigate the large time behavior of the solution to the fractional heat equation $$\begin{aligned} \frac{\partial...
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Ergodicity and Stationary Solution for Stochastic Neutral Retarded Partial Differential Equations Driven by Fractional Brownian Motion
In this paper, we discuss a class of neutral retarded stochastic functional differential equations driven by a fractional Brownian motion on Hilbert spaces. We develop a
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Open Accesspth mean almost periodic solutions to neutral stochastic evolution equations with infinite delay and Poisson jumps
In this paper, we investigate the pth mean almost periodic solution to a neutral stochastic evolution equation with infinite delay and Poisson jumps. We give a sufficient condition for the existence and uniquenes...
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Open AccessA law of iterated logarithm for the subfractional Brownian motion and an application
Let S H ...
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Large Deviation Principle for a Space-Time Fractional Stochastic Heat Equation with Fractional Noise
In this paper, we consider the large deviation principle for a class of space-time fractional stochastic heat equation $$\partial _t^\beta {u^...
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Open AccessControllability of a stochastic functional differential equation driven by a fractional Brownian motion
Let U, V and W be three Hilbert spaces and let B ...
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Global attracting sets and stability of neutral stochastic functional differential equations driven by Rosenblatt process
We are concerned with a class of neutral stochastic partial differential equations driven by Rosenblatt process in a Hilbert space. By combining some stochastic analysis techniques, tools from semigroup theory...
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Open AccessSome properties of the solution to fractional heat equation with a fractional Brownian noise
In this paper, we consider the stochastic heat equation of the form ...
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Open AccessOn a semilinear mixed fractional heat equation driven by fractional Brownian sheet
In this paper, we consider the stochastic heat equation of the form ...
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Open AccessThe quadratic variation for mixed-fractional Brownian motion
Let W = λ B ...
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Approximation of the Rosenblatt Sheet
In this paper, we obtain an approximation theorem for the Rosenblatt sheet, using martingale differences. The proof involves the tightness and identification of finite dimensional distributions.
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Open AccessTemporal variation for fractional heat equations with additive white noise
Let u ( t , ...
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The fractional derivative for fractional Brownian local time with Hurst index large than 1 / 2
Let \(B^H\) B H ...
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Article
Open AccessSolving a stochastic heat equation driven by a bi-fractional noise
In this paper, we consider a stochastic heat equation with multiplicative bi-fractional Brownian sheet. Using the technique of Feynman-Kac formula and Malliavin calculus, we give an explicit formula of the wea...
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Solving a Nonlinear Fractional Stochastic Partial Differential Equation with Fractional Noise
In this article, we will prove the existence, uniqueness and Hölder regularity of the solution to the fractional stochastic partial differential equation of the form
