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Article
Wavelet-based Bayesian approximate kernel method for high-dimensional data analysis
Kernel methods are often used for nonlinear regression and classification in statistics and machine learning because they are computationally cheap and accurate. The wavelet kernel functions based on wavelet a...
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Article
Nonlinear McKean-Vlasov Diffusions under the Weak Hörmander Condition with Quantile-Dependent Coefficients
In this paper, the strong existence and uniqueness for a degenerate finite system of quantile-dependent McKean-Vlasov stochastic differential equations are obtained under a weak Hörmander condition. The approa...
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Article
Matching upper and lower moment bounds for a large class of stochastic PDEs driven by general space-time Gaussian noises
In this paper, we obtain matching upper and lower moment bounds for the solution to stochastic partial differential equation driven by a general Gaussian noise, giving a complete answer to the open problem of ...
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Solvability of Parabolic Anderson Equation with Fractional Gaussian Noise
This paper provides necessary as well as sufficient conditions on the Hurst parameters so that the continuous time parabolic Anderson model $$...
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Backward Euler method for stochastic differential equations with non-Lipschitz coefficients driven by fractional Brownian motion
We study the traditional backward Euler method for stochastic differential equation driven by fractional Brownian motion whose drift coefficient satisfies the one-sided Lipschitz condition. The backward Euler ...
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Article
Driver-in-the-Loop Handling Stability Control of 4WID-EV
An eight-degree-of-freedom vehicle dynamic model with electromechanical coupling was established for a four-wheel-independent-drive electric vehicle (4WID-EV). Based on the single-point preview optimal curvatu...
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Estimation of all parameters in the fractional Ornstein–Uhlenbeck model under discrete observations
Let the Ornstein–Uhlenbeck process \((X_t)_{t\ge 0}\) ( ...
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Article
Generalized moment estimators for \(\alpha \)-stable Ornstein–Uhlenbeck motions from discrete observations
We study the parameter estimation problem for discretely observed Ornstein–Uhlenbeck processes driven by \(\alpha \)α-stable Lévy motions. A method of moments via ergodic theory and via sample characteristic func...
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Article
Higher-Order Derivative of Intersection Local Time for Two Independent Fractional Brownian Motions
In this article, we obtain sharp conditions for the existence of the high-order derivatives (k-th order) of intersection local time $$...
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Article
Preface
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Article
Joint Hölder Continuity of Parabolic Anderson Model
We obtain the Holder continuity and joint Hölder continuity in space and time for the random field solution to the parabolic Anderson equation ...
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Article
Some Recent Progress on Stochastic Heat Equations
This article attempts to give a short survey of recent progress on a class of elementary stochastic partial differential equations (for example, stochastic heat equations) driven by Gaussian noise of various c...
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Article
On the Necessary and Sufficient Conditions to Solve A Heat Equation with General Additive Gaussian Noise
In this note, we consider stochastic heat equation with general additive Gaussian noise. Our aim is to derive some necessary and sufficient conditions on the Gaussian noise in order to solve the corresponding ...
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Article
Parameter estimation for fractional Ornstein–Uhlenbeck processes of general Hurst parameter
This paper studies the least squares estimator (LSE) for the drift parameter of an Ornstein–Uhlenbeck process driven by fractional Brownian motion, whose observations can be made either continuously or at disc...
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Identification of the miRNA-mRNA regulatory network of antler growth centers
Antler growth is a unique event compared to other growth and development processes in mammals. Antlers grow extremely fast during the rapid growth stage when growth rate peaks at 2 cm per day. Antler growth is...
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Article
Antler extracts stimulate chondrocyte proliferation and possess potent anti-oxidative, anti-inflammatory, and immune-modulatory properties
The Sika deer antler is well known for its unique ability to regenerate repeatedly and grow rapidly. Furthermore, it is a precious traditional Chinese medicine and has been widely used for more than 20 centuri...
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Article
Intermittency for the stochastic heat equation driven by a rough time fractional Gaussian noise
This paper studies the stochastic heat equation driven by time fractional Gaussian noise with Hurst parameter \(H\in (0,1/2)\) ...
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Chapter and Conference Paper
Parabolic Anderson Model with Rough Dependence in Space
This paper studies the one-dimensional parabolic Anderson model driven by a Gaussian noise which is white in time and has the covariance of a fractional Brownian motion with Hurst parameter
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Article
Two-point Correlation Function and Feynman-Kac Formula for the Stochastic Heat Equation
In this paper, we obtain an explicit formula for the two-point correlation function for the solutions to the stochastic heat equation on ...
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Chapter and Conference Paper
Nonlinear Young Integrals via Fractional Calculus
For Hölder continuous functions W(t, x) and \(\varphi _t\) ...
