Celine Jost
We derive a class of ergodic transformations of self-similar Gaussian processes that are Volterra, i.e. of type X_t = int^t_0 z_X(t,s)dW_s, t>0, where z_X is a deterministic kernel and W is a standard Brownian motion.
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
Maximum likelihood estimation in the ergodic Volterra Ornstein-Uhlenbeck process
本文研究遍历 Volterra Ornstein-Uhlenbeck 过程的漂移参数推断，分别在连续、高频和低频观测下建立 MLE 与矩估计的渐近性质。
This note aims to give an explicit solution for backward stochastic Volterra integral equations with linear time delayed generators. The process $Y$ is expressed by an integral whose kernel is explicitly given. The processes $Z$ is expressed by Hida-Malliavin derivatives involving $Y$.
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.
The aim of this note is to provide some results for stochastic convolutions corresponding to stochastic Volterra equations in separable Hilbert space. We study convolution of the form $W^Ψ(t):=\int_0^t S(t-τ)Ψ(τ)dW(τ)$, $t\geq 0$, where $S(t), t\geq 0$, is so-called {\em resolvent} for Volterra equation considered,$Ψ$ is an appropriate process and $W$ is a cylindrical Wiener process.
We consider a class of semi-linear differential Volterra equations with memory terms, polynomial nonlinearities and random perturbation. For a broad class of nonlinearities, we study statistically steady states of the system and find that they possess regularities compatible with those of the weak solutions. Moreover, if sufficiently many directions in the phase space are stochastically forced, we employ the \emph{generalized coupling} approach to establish the existence and uniqueness of the invariant probability measure to which the system is exponentially attractive. This extends ergodicity…
This is a note on a local ergodic theorem for a symmetric exclusion process defined on an infinite tower of coverings, which is associated with a finitely generated residually finite amenable group.
A note on the uniform ergodicity of diffusion processes
本文针对Itô随机微分方程给出的扩散过程，提出以漂移和扩散系数表示的积分条件来保证转移核在全变差距离下的一致遍历性，并将结果应用于一类从属扩散过程。
In this note, we study the long time behavior of Lotka-Volterra systems whose coefficients vary randomly. Bena{ï}m and Lobry (2015) recently established that randomly switching between two environments that are both favorable to the same species may lead to different regimes: extinction of one species or the other, or persistence of both species. Our purpose here is to describe more accurately the range of parameters leading to these regimes, and the support of the invariant probability measure in case of persistence.
This note is devoted to construct a rough path above a multidimensional fractional Brownian motion $B$ with any Hurst parameter $H\in(0,1)$, by means of its representation as a Volterra Gaussian process. This approach yields some algebraic and computational simplifications with respect to [Stochastic Process. Appl. 120 (2010) 1444--1472], where the construction of a rough path over $B$ was first introduced.
A note on the $\mathcal{W}_2$-convergence rate of the empirical measure of an ergodic $\mathbb{R}^d$-valued diffusion
在强汇合和Lipschitz连续系数假设下，研究遍历扩散过程经验测度在Wasserstein距离下的均方和几乎必然收敛速率。
The classical Birkhoff ergodic theorem states that for an ergodic Markov process the limiting behaviour of the time average of a function (having finite $p$-th moment, $p\ge1$, with respect to the invariant measure) along the trajectories of the process, starting from the invariant measure, is a.s. and in the $p$-th mean constant and equals to the space average of the function with respect to the invariant measure. The crucial assumption here is that the process starts from the invariant measure, which is not always the case. In this paper, under the assumptions that the underlying process is …
Some notes on ergodic theorem for $U$-statistics of order $m$ for stationary and not necessarily ergodic sequences
本文研究了非必然遍历的严格平稳序列上m阶U-统计量的收敛性，给出了其几乎必然收敛及在L^p中收敛的充分条件。
The note is devoted to estimates for convolutions appearing in some class of stochastic Volterra equations. Two maximal inequalities and exponential tail estimate are proved by the fractional method of infinite dimensional stochastic calculus. The paper extends on non-semigroup case some results obtained earlier for semigroups.
These are lecture notes on the subject defined in the title. As such, they do not pretend to be really new, probably except for the only section about Poisson equations with potentials. Yet, the hope of the author is that they may serve as a bridge to the important area of Poisson equations "in the whole space" and with a parameter, the latter theme not being presented here. Why this area is so important was explained in many papers and books (see the references [12, 34, 35]): it provides one of the main tools in diffusion approximation in the area stochastic averaging. Hence, the aim of these…
A localized coupling approach to interacting continuous-state branching processes
本文提出一种包含移民、捕食和竞争的连续状态分支过程模型，通过局部马尔可夫耦合方法研究其均匀ergodic性条件。
In this note, we study a large class of stochastic wave equations with spatial dimension less than or equal to $3$. Via a soft application of Malliavin calculus, we establish that their random field solutions are spatially ergodic.
On Central Limit Theorems for Additive Functionals of Reversible Ergodic Markov Processes
本文证明了Bhattacharya的一般定理在时间可逆情况下的推论，推导了Kipnis-Varadhan功能中心极限定理的核心方法与主要贡献。
In this note we identify the distributional limits of non-negative, ergodic stationary processes, showing that all are possible. Consequences for infinite ergodic theory are also explored and new examples of distributionally stable- and $α$-rationally ergodic tranformations are presented.
Some remarks on the ergodic theorem for $U$-statistics
本文研究二阶平稳遍历$U$-统计量的收敛性，给出几乎必然和$L^1$收敛的充分条件，通过反例说明需中心化及上确界有界的条件。
In this note we prove some sufficient conditions for ergodicity of a Levy-type process, such that on the test functions the generator of the respective semigroup is of the form $$ Lf(x) = a(x)f'(x) + \int_{\mathbb{R}}{ \left( f(x+u)-f(x)- \nabla f(x)\cdot u \mathbb{I}_{|u|\leq 1} \right) ν(x,du)}, \quad f\in C_{\infty}^{2}(\mathbb{R}). $$ Here $ν(x,du)$ is a Levy-type kernel and $a(\cdot): \mathbb{R}\to \mathbb{R}$. We consider the case when the tails are of polynomial decay as well as the case when the decay is (sub)-exponential. For the proof the Foster-Lyapunov approach is used.
We show that elements of control theory, together with an application of Harris' ergodic theorem, provide an alternate method for showing exponential convergence to a unique stationary measure for certain classes of networks of quasi-harmonic classical oscillators coupled to heat baths. With the system of oscillators expressed in the form $\mathrm{d} X_t = A X_t \,\mathrm{d} t + F(X_t) \,\mathrm{d} t + B \,\mathrm{d} W_t$ in $\mathbf{R}^d$, where $A$ encodes the harmonic part of the force and $-F$ corresponds to the gradient of the anharmonic part of the potential, the hypotheses under which w…
This brief pedagogical note re-proves a simple theorem on the convergence, in $L_2$ and in probability, of time averages of non-stationary time series to the mean of expectation values. The basic condition is that the sum of covariances grows sub-quadratically with the length of the time series. I make no claim to originality; the result is widely, but unevenly, spread bit of folklore among users of applied probability. The goal of this note is merely to even out that distribution.
On ergodic properties of stochastic PDEs
本文综述随机偏微分方程展现遍历性质的多种情况，涵盖基本耗散条件、带反射的奇异情形、退化设置（含2006年退化噪声Navier-Stokes方程结果）及退化系数情形（含d≥3维抛物型Anderson模型相变新结果）。
This is lecture notes on the course "Stochastic Processes". In this format, the course was taught in the spring semesters 2017 and 2018 for third-year bachelor students of the Department of Control and Applied Mathematics, School of Applied Mathematics and Informatics at Moscow Institute of Physics and Technology. The base of this course was formed and taught for decades by professors from the Department of Mathematical Foundations of Control A.A. Natan, S.A. Guz, and O.G. Gorbachev. Besides standard chapters of stochastic processes theory (correlation theory, Markov processes) in this book (a…
These expository notes address certain stationary and ergodic properties of the equations of fluid dynamics subject to a spatially degenerate (i.e. frequency localized), white in time gaussian forcing. In order to provide an accessible treatment of some recent progress in this subject we will develop ideas in detail for a class of finite dimensional models.
In this note we consider autonomous SDEs admitting smooth invariant measures. We present a method in finding (almost everywhere) good bounds for $\sup \{\|X_t\|: t \in [0, T]\}$ for strong solutions $X_{\cdot}$ to such SDEs, which in many cases are optimal bounds. In some situation (especially in one-dimensional SDEs' cases), the discarded measure-zero set can be chosen to be a measure-zero set of the underlying Brownian motion uniform for all initial points $X_0=x$.
In this note we introduce a sequence of bilinear operators that unify ergodic averages and backward martingales in a nontrivial way. We establish its convergence in a range of $L^p$-norms and leave its a.s. convergence as an open problem. This problem shares some similarities with a well-known unresolved conjecture on a.s. convergence of double ergodic averages with respect to two commuting transformations.
Generalized uniform laws for tied-down occupation times of infinite ergodic transformations
本文利用算子更新理论建立无限遍历变换在轨道终点返回有限测度集条件下停留时间的条件极限定理，所得广义均匀极限定律适用于含多个中性不动点的间歇性映射。
Motivated from option and derivative pricing, this note develops Edgeworth expansions both in the Kolmogorov and Wasserstein metric for many different types of discrete time volatility models and their possible transformations. This includes, among others, Hölder-type functions of (augmented) Garch processes of any order, iterated random functions or Volterra-processes.
A note on diffusive/random-walk behaviour in Metropolis--Hastings algorithms
该研究探讨了Metropolis-Hastings算法中扩散与随机游走行为的收敛特性，指出在特定条件下，随机游走算法的收敛速率与目标分布的尾部性质相关。
The objective of this note is to present the results from the two recent papers. We study the Navier--Stokes equation on the two--dimensional torus when forced by a finite dimensional white Gaussian noise. We give conditions under which both the law of the solution at any time t>0, projected on a finite dimensional subspace, has a smooth density with respect to Lebesgue measure and the solution itself is ergodic. In particular, our results hold for specific choices of four dimensional white Gaussian noise. Under additional assumptions, we show that the preceding density is everywhere strictly …
In this note not intended for publication, it is observed that a wellnigh trivial application of the ergodic theorem of Karlsson-Ledrappier yields a strong LLN for arbitrary concave moments.
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。