On asymptotic behavior of the modified Arratia flow

Sticky flows on the circle

The purpose of this note is to give an example of stochastic flows of kernels, which naturally interpolates between the Arratia coalescing flow associated with systems of coalescing independent Brownian particles on the circle and the deterministic diffusion flow (actually, the results are given in the slightly more general framework of symmetric Levy processes for which points are not polar). The construction is performed using Dirichlet form theory and the extension of De Finetti's theorem given in the previous work by the authors. The sticky flows of kernels are associated with systems of s…

Hermite过程修正二次变差的渐近正态性

Asymptotic normality for a modified quadratic variation of the Hermite process

本文利用Hermite过程特殊增量构造修正二次变差，证明其中心极限定理并给出Wasserstein距离收敛速度，进而首次得到Hurst参数的强一致渐近正态估计量。

Flux fluctuations in the one dimensional nearest neighbors symmetric simple exclusion process

Let $J(t)$ be the the integrated flux of particles in the symmetric simple exclusion process starting with the product invariant measure $ν_ρ$ with density $ρ$. We compute its rescaled asymptotic variance: \[ \lim_{t\to\infty} t^{-1/2} \V J(t) = \sqrt{2/π} (1-ρ)ρ\] Furthermore we show that $t^{-1/4}J(t)$ converges weakly to a centered normal random variable with this variance. From these results we compute the asymptotic variance of a tagged particle in the nearest neighbor case and show the corresponding central limit theorem, results previously proven by Arratia.

修正EM方案对非耗散随机微分方程的非渐近收敛界

Non-asymptotic convergence bounds of modified EM schemes for non-dissipative SDEs

本文提出修正欧拉方案用于非耗散SDEs，建立了非渐近收敛界，并探讨了其在瓦瑟斯坦距离下的收敛速率。

Asymptotic behavior for a modified Maki-Thompson model with directed inter-group interactions

In this work we propose a new extension for the Maki-Thompson rumor model which incorporates inter-group directed contacts. The model is defined on an homogeneously mixing population where the existence of two differentiated groups of individuals is assumed. While individuals of one group have an active role in the spreading process, individuals of the other group only contribute in stifling the rumor provided they would contacted. For this model we measure the impact of dissemination by studying the remaining proportion of ignorants of both groups at the end of the process. In addition we dis…

Large deviations of a modified Jackson network: stability and rough asymptotics

Consider a modified, stable, two node Jackson network where server 2 helps server 1 when server 2 is idle. The probability of a large deviation of the number of customers at node one can be calculated using the flat boundary theory of Schwartz and Weiss [Large Deviations Performance Analysis (1994), Chapman and Hall, New York]. Surprisingly, however, these calculations show that the proportion of time spent on the boundary, where server 2 is idle, may be zero. This is in sharp contrast to the unmodified Jackson network which spends a nonzero proportion of time on this boundary.

极值过程的最后 progeny 修改分支随机游走

Extremal Process of Last Progeny Modified Branching Random Walks

研究最后 progeny 修改分支随机游走的极值过程，通过分析随机变量Y的尾部渐进行为，揭示模型在n趋于无穷时的渐进行为。

改进的破产概率：由复合混合泊松过程驱动的Cramér-Lundberg模型

Modified ruin probability for a Cramér-Lundberg model driven by a compound mixed Poisson process

研究改进的破产概率，探讨在重尾和轻尾情况下，改进与经典破产概率的等价性及端点原子结果和密度渐近性。

Ruin probabilities in the Cramér-Lundberg model with temporarily negative capital

We study the asymptotics of the ruin probability in the Cramér-Lundberg model with a modified notion of ruin. The modification is as follows. If the portfolio becomes negative, the asset is not immediately declared ruined but may survive due to certain mechanisms. Under a rather general assumption on the mechanism - satisfied by most such modified models from the literature - we study the relation of the asymptotics of the modified ruin probability to the classical ruin probability. This is done under the Cramér condition as well as for subexponential integrated claim sizes.

Asymptotic replication with modified volatility under small transaction costs

Dynamic hedging of an European option under a general local volatility model with small linear transaction costs is studied. A continuous control version of Leland's strategy that asymptotically replicates the payoff is constructed. An associated central limit theorem of hedging error is proved. The asymptotic error variance is minimized by an explicit trading strategy.

On the asymptotic distribution of block-modified random matrices

We study random matrices acting on tensor product spaces which have been transformed by a linear block operation. Using operator-valued free probability theory, under some mild assumptions on the linear map acting on the blocks, we compute the asymptotic eigenvalue distribution of the modified matrices in terms of the initial asymptotic distribution. Moreover, using recent results on operator-valued subordination, we present an algorithm that computes, numerically but in full generality, the limiting eigenvalue distribution of the modified matrices. Our analytical results cover many cases of i…

随机吸引子的存在性及其渐近自抗扰性研究：三维随机全局修正纳维-斯托克斯方程在无界领域中的应用

Existence and asymptotic autonomous robustness of random attractors for three-dimensional stochastic globally modified Navier-Stokes equations on unbounded domains

本文研究了三维随机全局修正纳维-斯托克斯方程在无界领域中随机吸引子的存在性及渐近自抗扰性，通过证明解的回溯均匀性质，首次实现了该领域的相关理论突破。