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Jinlong Wei

Publications and source records attributed to Jinlong Wei.

At least 19 recordsLinked to original sources
arXiv2026

Strong solutions and sharp Euler--Maruyama approximations for SDEs with Lebesgue--Dini drift

We investigate the strong approximation of stochastic differential equations whose drift is square-integrable in time and Dini continuous in space, while the diffusion coefficient is non-constant and uniformly elliptic. Using a refined Itô--Tanaka trick combined with parabolic regularity estimates, we first establish strong well-posedness and the stochastic flow property. Under additional Lipschitz regularity of the diffusion matrix, we then analyze a polygonal-type Euler--Maruyama scheme and prove the strong error estimate \[ \Big\|\sup_{0\le t\le1}|X_t-X_t^n|\Big\|_{L^p(Ω)} \le C n^{-\frac12}\log(n)^{\frac32}, \quad p\ge2. \] We further show that this rate is sharp: even under smooth and uniformly elliptic diffusion coefficients with vanishing drift, the convergence order $1/2$ cannot be improved. These results provide the first sharp quantitative strong convergence estimates in a Lebesgue--Dini drift framework.

math.PR↗
arXiv2025

SDEs with subcritical Lebesgue--Hölder drift and driven by $α$-stable processes

We obtain the unique weak and strong solvability for time inhomogeneous stochastic differential equations with the drift in subcritical Lebesgue--Hölder spaces $L^p([0,T];{\mathcal C}_b^β({\mathbb R}^d;{\mathbb R}^d))$ and driven by $α$-stable processes for $α\in (0,2)$. The weak well-posedness is derived for $β\in (0,1)$, $α+β>1$ and $p>α/(α+β-1)$ through Prohorov's theorem, Skorohod's representation and the regularity estimates of solutions for a class of fractional parabolic partial differential equations. The pathwise uniqueness and Davie's type uniqueness are proved for $β>1-α/2$ by using Itô--Tanaka's trick. Moreover, we give a counterexample to the pathwise uniqueness for the supercritical Lebesgue--Hölder drifts to explain the present result is sharp.

math.PR↗
arXiv2025

Fokker-Planck equation for stochastic heat equations

This work is devoted to the study of the Fokker--Planck equation for a stochastic heat equation with an additive $Q$-Wiener noise and non-homogeneous boundary conditions. We explicitly construct the probability density function and establish the associated Fokker--Planck equation by applying the eigenfunction expansion technique. Moreover, the Feynman--Kac formula is used to obtain the probabilistic representation of the solution. The analysis is further extended to cases with multiplicative noise involving nonlocal diffusion operators under homogeneous boundary conditions, as well as the corresponding Kardar--Parisi--Zhang (KPZ) equation. Notably, the evolution of the probability density function for the stochastic heat equation depends critically on the spatial location.

math.PR↗
arXiv2025

The Euler-Maruyama method for SDEs with low-regularity drift

We study the strong $L^p$-convergence rates of the Euler-Maruyama method for stochastic differential equations driven by Brownian motion with low-regularity drift coefficients. Specifically, the drift is assumed to be in the Lebesgue-Hölder spaces $L^q([0,T]; {\mathcal C}_b^α({\mathbb R}^d))$ with $α\in(0,1)$ and $q\in (2/(1+α),\infty]$. For every $p\geq 2$, by using stochastic sewing and/or the Itô-Tanaka trick, we obtain the $L^p$-convergence rates: $(1+α)/2$ for $q\in [2,\infty]$ and $(1-1/q)$ for $q\in (2/(1+α),2)$. Moreover, we prove that the unique strong solution can be constructed via the Picard iteration.

math.PR↗
arXiv2025

Notes on Multiple Periodic Solutions for Second-order Discrete Hamiltonian System

By a new orthogonal direct sum decomposition $E_{M} = Y \oplus Z$, which $Z$ is related to $Δu_i(i=1,2,3,....,M)$, and a new functional $I(u)$, the method in [2] is improved to obtain new multiple periodic solutions with negativity hypothesis on $F$ for a second-order discrete Hamiltonian system. Moreover, we exhibit an instructive example to make our result more clear, which hasn't been solved by the known results.

math.AP↗
arXiv2025

Uniqueness of strong solutions for SDEs with Hölder diffusions

This paper is concerned with the Itô stochastic differential equations with $\mR^{d\times k}$ diffusions in class of Hölder spaces and continuous $\mR^d$ drifts. We derive a uniqueness result of strong solutions for $\cC^α\ (α\geq \frac{1}{2})$ coefficients and this result is new. Our proof is supported by Itô's formula and a finer analysis on cut-off and smoothing techniques.

math.AP↗
arXiv2025

Frequency-Domain Joint Monitoring of Differential Group Delay and Dependent Loss of Optical Singleand Few-Mode Fiber Channels Based on CAZAC Sequences

This paper addresses the challenges of monitoring optical-fiber channels subject to complex, multidimensional impairments-such as dynamic interference across polarization or modal dimensions-where conventional methods suffer from high equipment costs, poor impairment discrimination and limited scalability. We propose an in-service, frequency-domain joint monitoring scheme based on constant-amplitude zero-autocorrelation (CAZAC) sequences. Exploiting their flat spectra and ideal autocorrelation, we model the channel as a multi-input multi-output (MIMO) system and estimate its frequency response to extract both differential group delay (DGD) and dimension-dependent loss (DL) regardless of dimensionality. Experimental validation in polarization-division-multiplexing (PDM) and mode-division-multiplexing (MDM) scenarios demonstrates robust performance: in a 2x2 PDM setup, polarization-dependent loss (PDL) error stays below 0.3 dB and polarization-mode dispersion (PMD) accuracy is 0.3 ps; in a 4x4 MDM system, mode-dependent loss (MDL) and differential mode-group delay (DMGD) errors remain around 0.3 dB and 0.3 ps, respectively. Fully compatible with existing coherent DSP without additional hardware, the scheme enables continuous, cost-effective, real-time monitoring of multidimensional optical channels.

physics.optics↗
arXiv2024

A new maximal regularity for parabolic equations and an application

We introduce the Lebesgue--Hölder--Dini and Lebesgue--Hölder spaces $L^p(\mathbb{R};{\mathcal C}_{\vartheta,ς}^{α,ρ}({\mathbb R}^n))$ ($\vartheta\in \{l,b\}, \, ς\in \{d,s,c,w\}$, $p\in (1,+\infty]$ and $α\in [0,1)$), and then use a vector-valued Calderón--Zygmund theorem to establish the maximal Lebesgue--Hölder--Dini and Lebesgue--Hölder regularity for a class of parabolic equations. As an application, we obtain the unique strong solvability of the following stochastic differential equation \begin{eqnarray*} X_{s,t}(x)=x+\int\limits_s^tb(r,X_{s,r}(x))dr+W_t-W_{s}, \ \ t\in [s,T], \ x\in \mathbb{R}^n, \ s\in [0,T], \end{eqnarray*} for the low regularity growing drift in critical Lebesgue--Hölder--Dini spaces $L^p([0,T];{\mathcal C}^{\frac{2}{p}-1,ρ}_{l,d}({\mathbb R}^n;{\mathbb R}^n))$ ($p\in (1,2]$), where $\{W_t\}_{0\leq t\leq T}$ is a $n$-dimensional standard Wiener process. In particular, when $p=2$ we give a partially affirmative answer to a longstanding open problem, which was proposed by Krylov and Röckner for $b\in L^2([0,T];L^\infty({\mathbb R}^n;{\mathbb R}^n))$ based upon their work ({\em Probab. Theory Relat. Fields 131(2): 154--196, 2005}).

math.PR↗
arXiv2023

Stochastic equations with low regularity drifts

By using the Itô-Tanaka trick, we prove the unique strong solvability as well as the gradient estimates for stochastic differential equations with irregular drifts in low regularity Lebesgue-Hölder space $L^q(0,T;{\mathcal C}_b^α({\mathbb R}^d))$ with $α\in(0,1)$ and $q\in (2/(1+α),2$). As applications, we show the unique weak and strong solvability for stochastic transport equations driven by the low regularity drift with $q\in (4/(2+α),2$) as well as the local Lipschitz estimate for stochastic strong solutions.

math.PR↗
arXiv2021

Multi-Rate Nyquist-SCM for C-Band 100Gbit/s Signal over 50km Dispersion-Uncompensated Link

In this paper, to the best of our knowledge, we propose the first multi-rate Nyquist-subcarriers modulation (SCM) for C-band 100Gbit/s signal transmission over 50km dispersion-uncompensated link. Chromatic dispersion (CD) introduces severe spectral nulls on optical double-sideband signal, which greatly degrades the performance of intensity-modulation and direct-detection systems. Based on the prior knowledge of the dispersive channel, Nyquist-SCM with multi-rate subcarriers is proposed to keep away from the CD-caused spectral nulls flexibly. Signal on each subcarrier can be individually recovered by a digital signal processing, including the feed-forward equalizer with no more than 31 taps, a two-tap post filter, and maximum likelihood sequence estimation with one memory length. Combining with entropy loading based on probabilistic constellation shaping to maximize the capacity-reach, the C-band 100Gbit/s multi-rate Nyquist-SCM signal over 50km dispersion-uncompensated link can achieve 7% hard-decision forward error correction limit and average normalized generalized mutual information of 0.967 at received optical power of -4dBm and optical signal-to-noise ratio of 47.67dB. In conclusion, the multi-rate Nyquist-SCM shows great potentials in solving the CD-caused spectral distortions.

cs.IT↗
arXiv2021

Stochastic transport equation with bounded and Dini continuous drift

The results established by Flandoli, Gubinelli and Priola ({\it Invent. Math.} {\bf 180} (2010) 1--53) for stochastic transport equation with bounded and Hölder continuous drift are generalized to bounded and Dini continuous drift. The uniqueness of $L^\infty$-solutions is established by the Itô--Tanaka trick partially solving the uniqueness problem, which is still open, for stochastic transport equation with only bounded measurable drift. Moreover the existence and uniqueness of stochastic diffeomorphisms flows for a stochastic differential equation with bounded and Dini continuous drift is obtained.

math.PR↗
arXiv2021

Eulerian collinear configuration for 3-body problem

For 3-body problem with any given masses $m_1, \,m_2,\,m_3>0$, there exist only Eulerian collinear central configuration and Lagrangian equilateral-triangle central configuration, and in this paper, for planar 3-body problem, we prove that there exists another non-collision trajectory $q$, which is not the variational minimizer of the Lagrangian action on the loop space $\overline{Λ_1}$, is also an Eulerian collinear central configuration at any instant. Moreover, we do not need the restriction condition on the winding number $deg(q_i-q_j)\neq0 \,(i\neq j)$.

math.DS↗
arXiv2021

Strong solutions of stochastic differential equations with square integrable drift

We prove the existence and uniqueness of strong solutions for stochastic differential equations in which the drift coefficient is square integrable in time variable and Hölder continuous in space variable. Moreover, we prove that the unique strong solution has a continuous modification, which is $β$-Hölder continuous in space variable for every $β\in (0,1)$, and as an $L^2(Ω\times (0,T))$ valued function, it is differentiable as well.

math.AP↗
arXiv2020

Practical Solutions for 400 Gbit/s Data Center Transmission

We review three solutions for low-cost data center interconnects with a target reach of up to 80 km. Directly detected DMT, PAM-4 and multi-band CAP are promising modulation schemes, enabling 400 Gbit/s by combining eight channels of 56 Gbit/s.

eess.SP↗