arXiv subjects

Weilin Xiao

Publications and source records attributed to Weilin Xiao.

5 recordsLinked to original sources

arXiv2026

Boundary Inference for Mixed Fractional Models under High-Frequency Observation Critical LAN and Score Tests at $H=3/4$

We study boundary inference at $H=3/4$ for mixed fractional Brownian motion and mixed fractional Ornstein--Uhlenbeck models under high-frequency observation. This boundary is economically important because it separates the critical and supercritical regimes of mixed fractional dynamics. We make three contributions. First, we identify the exact critical first-order scaling and show that, after removing the explicit linear component in the $H$-score, the transformed $(σ,H)$ block is already non-degenerate. Second, we establish critical score central limit theorems (CLT) and derive local asymptotic normality (LAN) with fully explicit leading information constants for both models. Third, we construct boundary-calibrated one-sided score tests for detecting entry into the supercritical region $H>3/4$ and discuss feasible implementation through restricted nuisance estimation. Monte Carlo evidence shows that the feasible statistic has the correct directional power but conservative null calibration. Finally, an intraday illustration on one-minute SPY data finds no persistent evidence in favor of $H>3/4$.

math.ST↗

arXiv2024

Global Feature Pyramid Network

The visual feature pyramid has proven its effectiveness and efficiency in target detection tasks. Yet, current methodologies tend to overly emphasize inter-layer feature interaction, neglecting the crucial aspect of intra-layer feature adjustment. Experience underscores the significant advantages of intra-layer feature interaction in enhancing target detection tasks. While some approaches endeavor to learn condensed intra-layer feature representations using attention mechanisms or visual transformers, they overlook the incorporation of global information interaction. This oversight results in increased false detections and missed targets.To address this critical issue, this paper introduces the Global Feature Pyramid Network (GFPNet), an augmented version of PAFPN that integrates global information for enhanced target detection. Specifically, we leverage a lightweight MLP to capture global feature information, utilize the VNC encoder to process these features, and employ a parallel learnable mechanism to extract intra-layer features from the input image. Building on this foundation, we retain the PAFPN method to facilitate inter-layer feature interaction, extracting rich feature details across various levels.Compared to conventional feature pyramids, GFPN not only effectively focuses on inter-layer feature information but also captures global feature details, fostering intra-layer feature interaction and generating a more comprehensive and impactful feature representation. GFPN consistently demonstrates performance improvements over object detection baselines.

cs.CV↗

arXiv2021

Mixed sub-fractional Brownian motion and drift estimation of related Ornstein-Uhlenbeck process

In this paper, we will first give the numerical simulation of the sub-fractional Brownian motion through the relation of fractional Brownian motion instead of its representation of random walk. In order to verify the rationality of this simulation, we propose a practical estimator associated with the LSE of the drift parameter of mixed sub-fractional Ornstein-Uhlenbeck process, and illustrate the asymptotical properties according to our method of simulation when the Hurst parameter $H>1/2$.

math.PR↗

arXiv2020

Maximum likelihood estimation for mixed fractional Vasicek processes

The mixed fractional Vasicek model, which is an extended model of the traditional Vasicek model, has been widely used in modelling volatility, interest rate and exchange rate. Obviously, if some phenomenon are modeled by the mixed fractional Vasicek model, statistical inference for this process is of great interest. Based on continuous time observations, this paper considers the problem of estimating the drift parameters in the mixed fractional Vasicek model. We will propose the maximum likelihood estimators of the drift parameters in the mixed fractional Vasicek model with the Radon-Nikodym derivative for a mixed fractional Brownian motion. Using the fundamental martingale and the Laplace transform, both the strong consistency and the asymptotic normality of the maximum likelihood estimators have been established for all $H\in(0,1)$, $H\neq 1/2$.

math.PR↗

arXiv2020

Simulation of Integro-Differential Equation and Application in Estimation of Ruin Probability with Mixed Fractional Brownian Motion

In this paper, we are concerned with the numerical solution of one type integro-differential equation by a probability method based on the fundamental martingale of mixed Gaussian processes. As an application, we will try to simulate the estimation of ruin probability with an unknown parameter driven not by the classical Lévy process but by the mixed fractional Brownian motion.

math.PR↗