Alexander Yu. Veretennikov
We establish the large deviation principle for stochastic differential equations with averaging in the case when all coefficients of the fast component depend on the slow one, including diffusion.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Using Zvonkin's transform and the Poisson equation in $R^d$ with a parameter, we prove the averaging principle for stochastic differential equations with time-dependent Hölder continuous coefficients. Sharp convergence rates with order $(α\wedge1)/2$ in the strong sense and $(α/2)\wedge1$ in the weak sense are obtained, considerably extending the existing results in the literature. Moreover, we prove that the convergence of the multi-scale system to the effective equation depends only on the regularity of the coefficients of the equation for the slow variable, and does not depend on the regula…
Wellposedness and averaging principle for conditional distribution dependent SDEs driven by standard Brownian motions and fractional Brownian motions
本文研究了由标准Brown运动和分数阶Brown运动驱动的条件分布依赖型随机微分方程，通过不动点定理证明了解的存在唯一性，并建立了其解可由平均方程逼近的平均原理。
Conditional McKean-Vlasov SDEs with jumps and Markovian regime-switching: wellposedness, propagation of chaos, averaging principle
本文研究带跳和马尔可夫机制切换的条件McKean-Vlasov随机微分方程，利用L2-Wasserstein距离证明强适定性，建立平均场粒子系统的混沌传播及显式收敛速率，并针对双时间尺度情形建立平均化原理。
Averaging principles for time-inhomogeneous multi-scale SDEs with partially dissipative coefficients
本文研究时间非齐次多尺度随机微分方程的平均化原理，针对快速分量漂移仅部分耗散的情形，分别建立了慢分量强收敛与弱收敛结果，并基于演化测度系的存在唯一性证明。
Averaging principles for time-inhomogeneous multi-scale SDEs via nonautonomous Poisson equations
本文研究时间非齐次多尺度随机微分方程的渐近行为，通过分析马尔可夫半群测度演化与非自治泊松方程性质，推导了两类带显式收敛速率的强弱平均原理，并通过算例验证了有效性。
Stochastic averaging for a class of stochastic differential equations (SDEs) with fractional Brownian motion, of the Hurst parameter H in the interval (1/2, 1), is investigated. An averaged SDE for the original SDE is proposed, and their solutions are quantitatively compared. It is shown that the solution of the averaged SDE converges to that of the original SDE in the sense of mean square and also in probability. It is further demonstrated that a similar averaging principle holds for SDEs under stochastic integral of pathwise backward and forward types. Two examples are presented and numerica…
By comparing the original equations with the corresponding stationary ones, the moderate deviation principle (MDP) is established for unbounded additive functionals of several different models of distribution dependent SDEs, with non-degenerate and degenerate noises.
Large Deviation Principle for complex solution to squared Bessel SDE
本文研究了平方Bessel SDE复数解与Schramm-Loewner演化的联系，证明了当维数参数趋于负无穷时该解的大偏差原理。
The large deviations principles are established for a class of multidimensional degenerate stochastic differential equations with reflecting boundary conditions. The results include two cases where the initial conditions are adapted and anticipated.
Let O the basin of attraction of the unique stable equilibrium of a dynamical system, which is the law of large numbers limit of a Poissonian SDE. We consider the law of the exit point from O of that Poissonian SDE. We adapt the approach of M. Day (1990) for the same problem for a Brownian SDE. For that purpose, we will use the Large deviation for the Poissonian SDE reflected at the boundary of O studied in our recent work Pardoux and Samegni (2018).
This paper establishes a Freidlin-Wentzell large deviation principle for stochastic differential equations(SDEs) under locally weak monotonicity conditions and Lyapunov conditions. We illustrate the main result of the paper by showing that it can be applied to SDEs with non-Lipschitzian coefficients, which can not be covered in the existing literature. These include the interesting biological models like stochastic Duffing-van der Pol oscillator model, stochastic SIR model, etc.
We establish a large deviation principle for a reflected Poisson driven SDE. Our motivation is to study in a forthcoming paper the problem of exit of such a process from the basin of attraction of a locally stable equilibrium associated with its law of large numbers. Two examples are described in which we verify the assumptions that we make to establish the large deviation principle.
Large and Moderate deviation principles for the Multivalued McKean-Vlasov SDEs with jumps
本文通过弱收敛方法研究了具有非利普希茨系数的多值麦克-瓦拉斯随机微分方程的大偏差和中等偏差原理，并利用比希-里不等式解决非利普希茨条件带来的困难。
In this paper, using Zvonkin type transform, the large deviation principle is proved for stochastic differential equations with Dini continuous drifts, where the existed methods for large deviation principle are unavailable. The method and result are new in related fields. Moreover, the result is also extended to a class of degenerate stochastic differential equations with Dini continuous drifts.
We establish an averaging principle for a family of solutions$(X^{\varepsilon}, Y^{\varepsilon})$ $ :=$ $(X^{1,\,\varepsilon},\,X^{2,\,\varepsilon},\, Y^{\varepsilon})$ of a system of SDE-BSDEwith a null recurrent fast component $X^{1,\,\varepsilon}$. Incontrast to the classical periodic case, we can not rely on aninvariant probability and the slow forward component$X^{2,\,\varepsilon}$ cannot be approximated by a diffusion process.On the other hand, we assume that the coefficients admit a limit in aCesaro sense. In such a case, the limit coefficients may havediscontinuity. We show that we can…
Strong averaging principle for multiscale time-inhomogeneous SDEs with multiplicative $α$-stable noises
本文针对乘性α-稳定噪声驱动的多尺度非齐次时间随机系统，基于Khasminskii离散化方法建立强平均原理，证明慢子系统向两类平均系统的强收敛性，并将结果应用于气候-天气系统。
Averaging principle for McKean-Vlasov SDEs driven by multiplicative fractional noise with highly oscillatory drift coefficient
针对含乘性分数噪声与高振荡漂移的 McKean-Vlasov SDE，本文借助 Khasminskii 离散化证明原系统在两种拓扑下强收敛于平均系统。
We establish the large deviation principle for solutions of one-dimensional SDEs with discontinuous coefficients. The main statement is formulated in a form similar to the classical Wentzel--Freidlin theorem, but under the considerably weaker assumption that the coefficients have no discontinuities of the second kind.
Cramér-type moderate deviations for Euler-Maruyama scheme for SDE
本文研究了SDE的Euler-Maruyama格式，建立了标准化与自标准化Cramér型中偏差，由此推导出Berry-Esseen界限与中偏差原理，并改进了相关近期工作。
Large Deviations for SDE driven by Heavy-tailed Lévy Processes
本文研究了一类由有界漂移和重尾Lévy过程驱动的一维随机微分方程，在无指数可积性条件下证明了其满足具有离散速率函数和对数速度的弱大偏差原理，但不满足完整的大偏差原理。
Localized sufficient conditions for the large deviation principle of the given stochastic differential equations will be presented for stochastic differential equations with non-Lipschitzian and time-inhomogeneous coefficients, which is weaker than those relevant conditions existing in the literature. We consider at first the large deviation principle when $\int_0^t\sup_{x\in\mathbb{R}^d}||σ(s,x)||\vee|b(s,x)|ds=:C_t<\infty$ for any fixed $t$, then we generalize the conclusion to unbounded case by using bounded approximation program.
We consider a general class of epidemic models obtained by applying a random time change to a collection of Poisson processes and we show the large deviation principle for such models. We generalize to a more general situation the approach followed by Dolgoaschinnykh [3] in the case of the SIR epidemic model. Thanks to an assumption which is satisfied in many examples, we simplify the recent work by P. Kratz and E. Pardoux [8].
We design numerical schemes for a class of slow-fast systems of stochastic differential equations, where the fast component is an Ornstein-Uhlenbeck process and the slow component is driven by a fractional Brownian motion with Hurst index $H>1/2$. We establish the asymptotic preserving property of the proposed scheme: when the time-scale parameter goes to $0$, a limiting scheme which is consistent with the averaged equation is obtained. With this numerical analysis point of view, we thus illustrate the recently proved averaging result for the considered SDE systems and the main differences wit…
Averaging principle and normal deviation for multi-scale SDEs with polynomial nonlinearity
本文研究含多项式非线性的多尺度SDE，证明强平均、泛函中心极限型正态偏差、吸引子收敛及第二Bogolyubov定理。
Uniform large deviation principles for SDEs under locally weak monotonicity conditions
本文在局部弱单调与Lyapunov条件下，利用弱收敛方法建立了随机微分方程的一致大偏差原理，并将其推广到多项式增长系数、退化噪声及随机Hamilton系统。
In this paper, we consider McKean-Vlasov stochastic differential equations (MVSDEs) driven by Lévy noise. By identifying the right equations satisfied by the solutions of the MVSDEs with shifted driving Lévy noise, we build up a framework to fully apply the weak convergence method to establish large and moderate deviation principles for MVSDEs. In the case of ordinary SDEs, the rate function is calculated by using the solutions of the corresponding skeleton equations simply replacing the noise by the elements of the Cameron-Martin space. It turns out that the correct rate function for MVSDEs i…
Smoluchowski-Kramers Approximation Meets Khasminskii Averaging Principles in Nonequilibrium Random Environments I
研究一类二阶随机微分方程在非平衡随机环境中的Smoluchowski-Kramers近似和Khasminskii平均原理，通过路径积分分部公式等分析，在特定尺度下慢过程收敛到有效动力学。
Central Limit Type Theorem and Large Deviation Principle for Multi-Scale McKean-Vlasov SDEs
本文研究多尺度McKean-Vlasov随机系统的渐近行为，利用Poisson方程与弱收敛方法证明了中心极限型定理，并建立了Freidlin-Wentzell大偏差原理。
The primary goal of this paper is to prove a near-martingale optional stopping theorem and establish solvability and large deviations for a class of anticipating linear stochastic differential equations. We prove the existence and uniqueness of solutions using two approaches: (1) Ayed-Kuo differential formula using an ansatz, and (2) a novel braiding technique by interpreting the integral in the Skorokhod sense. We establish a Freidlin-Wentzell type large deviations result for solution of such equations.
Averaging principle for SDEs with singular drifts driven by $α$-stable processes
本文针对由 $\alpha$-稳定过程驱动的奇异漂移 SDEs，利用 Besov-Hölder 空间中的 Schauder 估计，建立了平均化原理的强收敛速率，并在特定参数范围内获得最优速率及鞅解的收敛性。
We prove an large deviation principle for multivalued sdes
We present the validity of stochastic averaging principle for non-autonomous slow-fast stochastic differential equations (SDEs) whose fast motions admit random periodic solutions. Our investigation is motivated by some problems arising from multi-scale stochastic dynamical systems, where configurations are time dependent due to nonlinearity of the underlying vector fields and the onset of time dependent random invariant sets. Averaging principle with respect to uniform ergodicity of the fast motion is no longer available in this scenario. Lyapunov second method together with synchronous coupli…
Under a Lipschitz condition on distribution dependent coefficients, the central limit theorem and the moderate deviation principle are obtained for solutions of McKean-Vlasov type stochastic differential equations, which extend from the corresponding results for classical stochastic differential equations to the distribution dependent setting.
In this article we prove the existence and uniqueness for degenerate stochastic differential equations with Sobolev (possibly singular) drift and diffusion coefficients in a generalized sense. In particular, our result covers the classical DiPerna-Lions flows and, we also obtain the well-posedness for degenerate Fokker-Planck equations with irregular coefficients. Moreover, a large deviation principle of Freidlin-Wenzell type for this type of SDEs is established.
Poisson Equation and Application to Multi-Scale SDEs with State-Dependent Switching
本文通过研究马尔可夫链相关泊松方程及其解的正则性，证明了带状态依赖切换的多尺度随机微分方程的三个平均原理与两个中心极限定理结果，并验证所得收敛阶均为最优。
General large deviations and functional iterated logarithm law for multivalued McKean-Vlasov stochastic differential equations
本文针对多值McKean-Vlasov随机微分方程，在非Lipschitz系数下利用弱收敛方法建立了一般大偏差和中偏差原理，并由此推导出解的泛函迭代对数律。
We study large deviation properties of systems of weakly interacting particles modeled by Itô stochastic differential equations (SDEs). It is known under certain conditions that the corresponding sequence of empirical measures converges, as the number of particles tends to infinity, to the weak solution of an associated McKean-Vlasov equation. We derive a large deviation principle via the weak convergence approach. The proof, which avoids discretization arguments, is based on a representation theorem, weak convergence and ideas from stochastic optimal control. The method works under rather mil…
Multi-Scale McKean-Vlasov SDEs: Moderate Deviation Principle in Different Regimes
本文研究多尺度McKean-Vlasov随机微分方程在不同时间尺度分离机制下的中度偏差原理，发现快分量噪声对速率函数有显著影响，并给出显式速率函数公式。
Small time asymptotics for kinetic SDEs with singular drift
该研究针对动力学Kato类中带奇异漂移的动力学随机微分方程，建立小时间大偏差原理并证明其转移密度的逐点Varadhan型渐近，为相关渐近分析提供理论支撑。
Convergence of Numerical Time-Averaging and Stationary Measures via Poisson Equations
本文利用关联的泊松方程，对随机微分方程（SDE）的数值时间平均估计器进行误差分析，证明数值方法的稳态行为收敛于SDE的稳态行为，该方法简单且通用。
Uniform large deviation principles and averaging principles for stochastic Burgers type equations with reflection
本文针对带反射的随机Burgers型方程，利用等连续一致Laplace原理和时间离散化方法，证明了有界集上的一致大偏差原理、紧集上的一致大偏差原理以及平均原理。
We study the large deviations principle (LDP) for stationary solutions of a class of stochastic differential equations (SDE) in infinite time intervals by the weak convergence approach, and then establish the LDP for the invariant measures of the SDE by the contraction principle. We further point out the equivalence of the rate function of the LDP for invariant measures induced by the LDP for stationary solutions and the rate function defined by quasi-potential. This fact gives another view of the quasi-potential introduced by Freidlin and Wentzell.
Poisson Equations with locally-Lipschitz coefficients and Uniform in Time Averaging for Stochastic Differential Equations via Strong Exponential Stability
本文针对系数超线性增长的完全耦合快慢 SDE，利用 Markov 半群的强指数稳定性建立首个带收敛速率的时间一致平均结果，并发展相应非紧空间 Poisson 方程理论。
Strong Averaging Principle and Long-Time Dynamics for Fast-Slow SDEs with Increasing Time-Scale Separation and Degenerate Noise
针对带时变尺度分离参数且满足 $\u03b5_t \to 0$ 的快慢随机微分方程，本文利用冻结快动力学的耗散性建立强平均原理，证明慢变量与平均常微分方程的最大 $L^p$ 估计，给出其收敛到渐近稳定平衡点的判据。
We prove a large deviation principle of Freidlin-Wentzell's type for the multivalued stochastic differential equations with monotone drifts, which in particular contains a class of SDEs with reflection in a convex domain.
We prove a large deviation principle (LDP) for a general class of Banach space valued stochastic differential equations (SDE) that is uniform with respect to initial conditions in bounded subsets of the Banach space. A key step in the proof is showing that a uniform large deviation principle over compact sets is implied by a uniform over compact sets Laplace principle. Because bounded subsets of infinite dimensional Banach spaces are in general not relatively compact in the norm topology, we embed the Banach space into its double dual and utilize the weak-$\star $ compactness of closed bounded…
The characteristic equation for a linear delay differential equation (DDE) has countably infinite roots on the complex plane. We deal with linear DDEs that are on the verge of instability, i.e. a pair of roots of the characteristic equation (eigenvalues) lie on the imaginary axis of the complex plane, and all other roots have negative real parts. We show that, when the system is perturbed by small noise, under an appropriate change of time scale, the law of the amplitude of projection onto the critical eigenspace is close to the law of a certain one-dimensional stochastic differential equation…
Ruin Theory Problems in Simple SDE Models with Large Deviation Asymptotics
该研究针对风险理论与养老基金资产负债模型中的问题，用Wentzell-Freidlin方法推导OU过程和GBM关于指数边界的击中概率等的大偏差对数渐近性，并借助GBM的闭式解数值验证了方法精度。
We study the asymptotic behavior for an inhomogeneous multiscale stochastic dynamical system with non-smooth coefficients. Depending on the averaging regime and the homogenization regime, two strong convergences in the averaging principle of functional law of large numbers type are established. Then we consider the small fluctuations of the system around its average. Nine cases of functional central limit type theorems are obtained. In particular, even though the averaged equation for the original system is the same, the corresponding homogenization limit for the normal deviation can be quite …
This article studies the dynamics of the strong solution of a SDE driven by a discontinuous Lévy process taking values in a smooth foliated manifold with compact leaves. It is assumed that it is \textit{foliated} in the sense that its trajectories stay on the leaf of their initial value for all times a.s.. % Such a system is called a \textit{foliated Lévy diffusion}. Under a generic ergodicity assumption for each leaf, % and a continuous variation of the ergodic measures among each others, we determine the effective behaviour of the system subject to a small smooth perturbation of order $\e>0$…
We obtain asymptotic expansions for the large deviation principle (LDP) for continuous time stochastic processes with weakly dependent increments. As a key example, we show that additive functionals of solutions of stochastic differential equations (SDEs) satisfying Hörmander condition on a $d-$dimensional compact manifold admit these asymptotic expansions of all orders.
We study the asymptotic behavior of stochastic hyperbolic parabolic equations with slow and fast time scales. Both the strong and weak convergence in the averaging principe are established, which can be viewed as a functional law of large numbers. Then we study the stochastic fluctuations of the original system around its averaged equation. We show that the normalized difference converges weakly to the solution of a linear stochastic wave equation, which is a form of functional central limit theorem. We provide a unified proof for the above convergence by using the Poisson equation in Hilbert …
Weak Existence for Degenerate Distribution Dependent SDEs with multiplicative Noise -- a pathwise regularization approach
本研究将现有弱存在性技术拓展至分布依赖框架，结合路径平均与局部时分解方法，证明了带退化乘性噪声和奇异系数的分布依赖随机微分方程弱解的存在性，揭示了不规则噪声对随机系统退化相关分析难题的正则化作用。
We extend the Erd\H os-R\' enyi law of large numbers to the averaging setup both in discrete and continuous time cases. We consider both stochastic processes and dynamical systems as fast motions whenever they are fast mixing and satisfy large deviations estimates. In the continuous time case we consider flows with large deviations estimates which allow a suspension representation and it turns out that fast mixing of corresponding base transformation suffices for our results.
We study a large deviation principle for a system of stochastic reaction--diffusion equations (SRDEs) with a separation of fast and slow components and small noise in the slow component. The derivation of the large deviation principle is based on the weak convergence method in infinite dimensions, which results in studying averaging for controlled SRDEs. By appropriate choice of the parameters, the fast process and the associated control that arises from the weak convergence method decouple from each other. We show that in this decoupling case one can use the weak convergence method to charact…
Large deviations of the stochastic area for linear diffusions
本文计算了线性随机微分方程（SDEs）中随机面积的生成函数，提取了长时间极限下概率密度主导部分的大偏差函数及有效SDE，并求得与概率流相关的渐近均值和用于判断可逆性的渐近方差。
We introduce a class of Markov chains, that contains the model of stochastic approximation by averaging and non-averaging. Using martingale approximation method, we establish various deviation inequalities for separately Lipschitz functions of such a chain, with different moment conditions on some dominating random variables of martingale differences.Finally, we apply these inequalities to the stochastic approximation by averaging and empirical risk minimisation.
Large deviation for small noise path-dependent stochastic differential equations
本文研究了小噪声路径依赖随机微分方程在参数趋于0时的渐近行为，利用弱收敛方法建立大偏差原理，并应用于小时间区间内泛函的大偏差分析。
In this paper, we study Brinkman's equations with microscale properties that are highly heterogeneous in space and time. The time variations are controlled by a stochastic particle dynamics described by an SDE. The particle dynamics can be thought as particle deposition that often occurs in filter problems. Our main results include the derivation of macroscale equations and showing that the macroscale equations are deterministic. The latter is important for our (also many other) applications as it greatly simplifies the macroscale equations. We use the asymptotic properties of the SDE and the …
This paper investigates a non-autonomous slow-fast system, which is generalized by stochastic differential equations (SDEs) with locally Lipschitz coefficients, subjected to standard Brownian motion (Bm) and fractional Brownian motion (fBm) with Hurst parameter 1/2<H<1. We concentrate on how to handle both types of integrals with respect to Bm and fBm and the locally Lispchitz continuity. The pathwise approach and the Ito stochastic calculus are combined with the technique of stopping time to establish the averaging principle where the averaged equation is defined. Then, the slow component of …
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。