具有Hölder系数的奇异随机Volterra方程的道路唯一性

Strong well-posedness of McKean-Vlasov stochastic differential equation with H{ö}lder drift

In this paper, we prove pathwise uniqueness for stochastic systems of McKean-Vlasov type with singular drift, even in the measure argument, and uniformly non-degenerate Lipschitz diffusion matrix. Our proof is based on Zvonkin's transformation \cite{zvonkin\_transformation\_1974} and so on the regularization properties of the associated PDE, which is stated on the space $[0,T]\times \R^d\times \mathcal{P}\_2(\R^d)$, where $T$ is a positive number, $d$ denotes the dimension equation and $\mathcal{P}\_2(\R^d)$ is the space of probability measures on $\R^d$ with finite second order moment. Especi…

带跳跃和非Lipschitz系数的随机Volterra方程的非负解

On non-negative solutions of stochastic Volterra equations with jumps and non-Lipschitz coefficients

本文研究带跳跃和非Lipschitz系数的随机Volterra方程，建立非负解强存在与路径唯一性条件，并应用于Lévy驱动方程，定义alpha稳定CIR过程的Volterra扩展。

Fractional calculus and path-wise integration for Volterra processes driven by Lévy and martingale noise

We introduce a pathwise integration for Volterra processes driven by Lévy noise or martingale noise. These processes are widely used in applications to turbulence, signal processes, biology, and in environmental finance. Indeed they constitute a very flexible class of models, which include fractional Brownian and Lévy motions and it is part of the so-called ambit fields. A pathwise integration with respect of such Volterra processes aims at producing a framework where modelling is easily understandable from an information perspective. The techniques used are based on fractional calculus and in…

Stochastic Volterra equations driven by fractional Brownian motion with Hurst parameter H > 1/2

In this note we prove an existence and uniqueness result of solution for stochastic Volterra integral equations driven by a fractional Brownian motion with Hurst parameter H > 1/2, showing also that the solution has finite moments. The stochastic integral with respect to the fractional Brownian motion is a pathwise Riemann-Stieltjes integral.

Regularity of stochastic Volterra equations by functional calculus methods

We establish pathwise continuity properties of solutions to a stochastic Volterra equation with an additive noise term given by a local martingale. The deterministic part is governed by an operator with an $H^\infty$-calculus and a scalar kernel. The proof relies on the dilation theorem for positive definite operator families on a Hilbert space.

Large and moderate deviations for stochastic Volterra systems

We provide a unified treatment of pathwise Large and Moderate deviations principles for a general class of multidimensional stochastic Volterra equations with singular kernels, not necessarily of convolution form. Our methodology is based on the weak convergence approach by Budhijara, Dupuis and Ellis. We show in particular how this framework encompasses most rough volatility models used in mathematical finance and generalises many recent results in the literature.

随机Volterra积分的一个BDG不等式

A BDG inequality for stochastic Volterra integrals

本文为随机Volterra积分建立了Burkholder-Davis-Gundy型不等式，给出有限与无限区间上的上界，并用于量化不同核的方程间路径距离及均值回归方程的均匀时间界。

Existence, uniqueness and regularity for a class of semilinear stochastic Volterra equations with multiplicative noise

We consider a class of semilinear Volterra type stochastic evolution equation driven by multiplicative Gaussian noise. The memory kernel, not necessarily analytic, is such that the deterministic linear equation exhibits a parabolic character. Under appropriate Lipschitz-type and linear growth assumptions on the nonlinear terms we show that the unique mild solution is mean-$p$ Hölder continuous with values in an appropriate Sobolev space depending on the kernel and the data. In particular, we obtain pathwise space-time (Sobolev-Hölder) regularity of the solution together with a maximal type bou…

带有Volterra高斯噪声的非线性随机滤波

Nonlinear Stochastic Filtering with Volterra Gaussian noises

本文针对受Volterra高斯过程驱动的信号-观测系统，建立了涵盖两种 regime 的非线性滤波理论，推导了相关公式，在一维情形下刻画了未归一化条件密度并证明其适定性，最终证明信号条件分布具有光滑密度。

随机Volterra方程的Wong--Zakai收敛性与FNO学习

Wong--Zakai Convergence and FNO Learning for Stochastic Volterra Equations

该研究针对描述带记忆随机系统的随机Volterra积分方程，建立Wong--Zakai收敛性，将镜像填充傅里叶神经算子的解算子学习框架扩展至该类方程，经数值实验验证其预测精度与泛化能力。

体制切换的Volterra算子：模态稳定性与淬火放大

Regime-Switching Volterra Operators: Modal Stability and Quenched Amplification

针对有限维、体制依赖的Volterra方程，建立算子理论框架，证明全局适定性、模态稳定性阈值及非正态体制下的路径有限幂律放大机制。