Stochastic Processes and their Applications最新文献

英文中文

Optimal prediction of the last r-excursion time of Brownian motion models 布朗运动模型最后r偏移时间的最优预测

IF 1.2 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications

Pub Date : 2026-04-01 Epub Date: 2025-12-13 DOI: 10.1016/j.spa.2025.104852

B. Li , M.A. Lkabous , J.M. Pedraza

This paper investigates the optimal prediction of the last r-excursion time for a Brownian motion model. The last r-excursion time, denoted by l_r, refers to the right endpoint of the last negative excursion lasting longer than a constant r > 0. It reduces to the standard last passage time when r↓0. For a Brownian motion with drift μ > 0 and volatility σ > 0, our goal is to identify an optimal stopping time that minimizes the (L₁) distance from the last r-excursion time l_r. We find that the optimal stopping barrier exhibits two distinct structures: a constant barrier (characterized as a solution of a non-linear equation) or a moving barrier (characterized by the unique solution to an integral equation) depending on the ratio

R = \frac{μ \sqrt{r}}{σ}

which integrates a firm’s financial profitability, volatility, and risk tolerance to financial distress. To obtain the optimal stopping time, we examine the smooth fit condition, Lipschitz continuity of the barrier, and probability regularity of the boundary points. As an application in risk management, we develop a decision rule that informs the timing of business expansion and contraction.

本文研究了布朗运动模型最后r偏移时间的最优预测。最后的r偏移时间，用lr表示，指的是最后一个负偏移的右端点，持续时间超过一个常数r >； 0。当r↓0时，它缩减为标准的最后通过时间。对于漂移μ >； 0和波动率σ >； 0的布朗运动，我们的目标是确定一个最优停止时间，使（L1）距离上次r-偏移时间lr最小。我们发现，最优停止障碍表现出两种不同的结构：一个恒定的障碍（表征为非线性方程的解）或一个移动的障碍（表征为积分方程的唯一解），这取决于比值R=μrσ，该比值集成了公司的财务盈利能力、波动性和对财务困境的风险承受能力。为了获得最优停止时间，我们考察了光滑拟合条件、障壁的Lipschitz连续性和边界点的概率规则性。作为风险管理中的一个应用，我们开发了一个决策规则，通知业务扩张和收缩的时机。

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引用次数: 0

Scaling methods for stochastic chemical reaction networks 随机化学反应网络的标度方法

IF 1.2 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications

Pub Date : 2026-04-01 Epub Date: 2025-12-27 DOI: 10.1016/j.spa.2025.104855

Lucie Laurence , Philippe Robert

The asymptotic properties of some Markov processes associated to stochastic chemical reaction networks (CRNs) driven by the kinetics of the law of mass action are analyzed. The scaling regime introduced in the paper assumes that the norm of the initial state is converging to infinity. The reaction rate constants are kept fixed. The purpose of the paper is of showing, with simple examples, a scaling analysis in this context. The main difference with the scalings of the literature is that it does not change the graph structure of the CRN or its reaction rates. Several CRNs are investigated to illustrate the insight that can be gained on the qualitative properties of these networks. A detailed scaling analysis of a CRN with several interesting asymptotic properties, with a bi-modal behavior in particular, is worked out in the last section. Additionally, with several examples, we also show that a stability criterion due to Filonov for positive recurrence of Markov processes may simplify significantly the stability analysis of these networks.

分析了由质量作用定律驱动的随机化学反应网络马尔可夫过程的渐近性质。本文引入的标度域假设初始态范数收敛到无穷远。反应速率常数保持不变。本文的目的是用简单的例子来展示在这种情况下的标度分析。与文献标度的主要区别在于它不会改变CRN的图结构或其反应速率。研究了几个crn，以说明可以从这些网络的定性性质中获得的见解。最后一节对具有几个有趣的渐近性质的CRN进行了详细的标度分析，特别是双峰行为。此外，通过几个例子，我们还证明了由于Filonov的稳定性准则对于马尔可夫过程的正递归可以显著地简化这些网络的稳定性分析。

引用次数: 0

Continuous time reinforcement learning: A random measure approach 连续时间强化学习：随机测量方法

IF 1.2 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications

Pub Date : 2026-04-01 Epub Date: 2025-12-11 DOI: 10.1016/j.spa.2025.104848

Christian Bender , Nguyen Tran Thuan

We present a random measure approach for modeling exploration, i.e., the execution of measure-valued controls, in continuous-time reinforcement learning with controlled diffusion and jumps. We begin with the case when sampling the randomized control in continuous time takes place on a discrete-time grid and reformulate the resulting SDE as an equation driven by suitable random measures. Our main result is a limit theorem for these random measures as the mesh-size of the sampling grid goes to zero. The resulting limit SDE can be applied for the theoretical analysis of exploratory control problems and for the derivation of learning algorithms.

我们提出了一种用于建模探索的随机测量方法，即在具有控制扩散和跳跃的连续时间强化学习中执行测量值控制。我们从连续时间的随机控制采样发生在离散时间网格上的情况开始，并将结果SDE重新表述为由合适的随机度量驱动的方程。我们的主要结果是当采样网格的网格大小趋于零时，这些随机度量的极限定理。所得的极限SDE可以应用于探索性控制问题的理论分析和学习算法的推导。

引用次数: 0

Frog model on Z with random survival parameter 具有随机生存参数的Z上的青蛙模型

IF 1.2 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications

Pub Date : 2026-04-01 Epub Date: 2025-12-23 DOI: 10.1016/j.spa.2025.104856

Gustavo O. De Carvalho, Fábio P. Machado

We study the frog model on

Z

with geometric lifetimes, introducing a random survival parameter. Active and inactive particles are placed at the vertices of

Z

. The lifetime of each active particle follows a geometric random variable with parameter

1 - p

, where p is randomly sampled from a distribution π. Each active particle performs a simple random walk on

Z

until it dies, activating any inactive particles it encounters along its path. In contrast to the usual case where p is fixed, we show that there exist non-trivial distributions π for which the model survives with positive probability. More specifically, for π ∼ Beta(α, β), we establish the existence of a critical value

β = 0.5

, that separates almost sure extinction from survival with positive probability. Furthermore, we show that the model is recurrent whenever it survives with positive probability.

我们研究了Z上具有几何寿命的青蛙模型，引入了一个随机生存参数。每个活跃粒子的寿命遵循一个参数为1 - p的几何随机变量，其中p是从分布π中随机抽样的。每个活跃粒子在Z上执行简单的随机漫步，直到它死亡，激活它在路径上遇到的任何不活跃粒子。与p固定的通常情况相反，我们证明存在非平凡分布π，模型以正概率存活。更具体地说，对于π ~ β (α, β)，我们建立了临界值β=0.5的存在性，该临界值将几乎确定的灭绝与具有正概率的生存区分开来。此外，我们证明，只要模型以正概率存活，它就是循环的。

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引用次数: 0

Strong large deviation principles for pair empirical measures of random walks in the Mukherjee-Varadhan topology Mukherjee-Varadhan拓扑中随机游走对经验测度的强大偏差原则

IF 1.2 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications

Pub Date : 2026-04-01 Epub Date: 2025-12-20 DOI: 10.1016/j.spa.2025.104853

Dirk Erhard , Julien Poisat

In this paper we introduce a topology under which the pair empirical measure of a large class of random walks satisfies a strong Large Deviation principle. The definition of the topology is inspired by the recent article by Mukherjee and Varadhan [1]. This topology is natural for translation-invariant problems such as the downward deviations of the volume of a Wiener sausage or simple random walk, known as the Swiss cheese model [2]. We also adapt our result to some rescaled random walks and provide a contraction principle to the single empirical measure despite a lack of continuity from the projection map, using the notion of diagonal tightness.

本文介绍了一类随机漫步的对经验测度满足强大偏差原理的拓扑结构。拓扑的定义受到Mukherjee和Varadhan[1]最近的文章的启发。这种拓扑结构对于平移不变量问题是很自然的，比如腊肠体积的向下偏离，或者简单的随机漫步，也就是瑞士奶酪模型[2]。我们还使用对角紧度的概念，将我们的结果适应于一些重新缩放的随机漫步，并为单个经验测量提供了一个收缩原理，尽管缺乏投影图的连续性。

引用次数: 0

Comparison theorems for mean-field BSDEs whose generators depend on the law of the solution (Y,Z) 产生子依赖于解（Y，Z）律的平均场BSDEs的比较定理

IF 1.2 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications

Pub Date : 2026-03-01 Epub Date: 2025-11-15 DOI: 10.1016/j.spa.2025.104833

Juan Li , Zhanxin Li , Chuanzhi Xing

For general mean-field backward stochastic differential equations (BSDEs) it is well-known that we usually do not have the comparison theorem if the coefficients depend on the law of

Z

-component of the solution process

(Y, Z)

. A natural question is whether general mean-field BSDEs whose coefficients depend on the law of

Z

have the comparison theorem for some cases. In this paper we establish the comparison theorems for one-dimensional mean-field BSDEs whose coefficients also depend on the joint law of the solution process

(Y, Z)

. With the help of Malliavin calculus and a BMO martingale argument, we obtain two comparison theorems for different cases and a strong comparison result. In particular, in this framework, we compare not only the first component

Y

of the solution

(Y, Z)

for such mean-field BSDEs, but also the second component

Z

. After a discussion of mean-field BSDEs whose terminal condition and the driving coefficient are Malliavin differentiable, the results are extended in a second phase to the case without assumption of Malliavin differentiability.

对于一般的平均场倒向随机微分方程（BSDEs），众所周知，如果系数依赖于解过程（Y，Z）的Z分量规律，我们通常没有比较定理。一个自然的问题是，系数依赖于Z定律的一般平均场BSDEs在某些情况下是否具有比较定理。本文建立了系数依赖于求解过程（Y，Z）联合律的一维平均场BSDEs的比较定理。利用Malliavin演算和BMO鞅论证，得到了两个不同情况下的比较定理和一个较强的比较结果。特别地，在这个框架中，我们不仅比较了这类平均场BSDEs解（Y，Z）的第一分量Y，而且比较了第二分量Z。在讨论了终端条件和驱动系数为Malliavin可微的平均场BSDEs后，在第二阶段将结果推广到不假设Malliavin可微的情况。

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引用次数: 0

On domination for (non-symmetric) dirichlet forms 关于（非对称）狄利克雷形式的支配

IF 1.2 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications

Pub Date : 2026-03-01 Epub Date: 2025-12-03 DOI: 10.1016/j.spa.2025.104846

Liping Li, Jiangang Ying

The primary aim of this article is to investigate the domination relationship between two L²-semigroups using probabilistic methods. According to Ouhabaz’s domination criterion, the domination of semigroups can be transformed into relationships involving the corresponding Dirichlet forms. Our principal result establishes the equivalence between the domination of Dirichlet forms and the killing transformation of the associated Markov processes, which generalizes and completes the results in [1] and [2]. Based on this equivalence, we provide a representation of the dominated Dirichlet form using the bivariate Revuz measure associated with the killing transformation and further characterize the sandwiched Dirichlet form within the broader Dirichlet form framework. In particular, our findings apply to the characterization of operators sandwiched between the Dirichlet Laplacian and the Neumann Laplacian. For the local boundary case, we eliminate all technical conditions identified in the literature [3] and deliver a complete representation of all sandwiched operators governed by a Robin boundary condition determined by a specific quasi-admissible measure. Additionally, our results offer a comprehensive characterization of related operators in the non-local Robin boundary case, specifically resolving an open problem posed in the literature [4].

本文的主要目的是利用概率方法研究两个l2 -半群之间的支配关系。根据Ouhabaz的控制准则，半群的控制可以转化为包含相应狄利克雷形式的关系。我们的主要结果建立了Dirichlet形式的支配与相关马尔可夫过程的消灭变换之间的等价性，推广并完成了[1]和[2]的结果。在此等价的基础上，我们利用与杀伤变换相关的二元Revuz测度给出了占主导地位的狄利克雷形式的表示，并在更广泛的狄利克雷形式框架内进一步表征了夹在中间的狄利克雷形式。特别是，我们的发现适用于夹在狄利克雷拉普拉斯算子和诺伊曼拉普拉斯算子之间的算子特征。对于局部边界情况，我们消除了文献[3]中确定的所有技术条件，并给出了由特定准可接受测度所决定的Robin边界条件所控制的所有夹层算子的完整表示。此外，我们的结果提供了非局部Robin边界情况下相关算子的综合表征，具体解决了文献[4]中提出的一个开放问题。

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引用次数: 0

Higher order fluctuation expansions for nonlinear stochastic heat equations in singular limits 奇异极限下非线性随机热方程的高阶涨落展开

IF 1.2 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications

Pub Date : 2026-03-01 Epub Date: 2025-12-11 DOI: 10.1016/j.spa.2025.104847

Benjamin Gess , Zhengyan Wu , Rangrang Zhang

Higher order fluctuation expansions for stochastic heat equations (SHE) with nonlinear, non-conservative and conservative noise are obtained. These Edgeworth-type expansions describe the asymptotic behavior of solutions in suitable joint scaling regimes of small noise intensity (ε → 0) and diverging singularity (δ → 0). The results include both the case of the SHE with regular and irregular diffusion coefficients. In particular, this includes the correlated Dawson-Watanabe and Dean-Kawasaki SPDEs, as well as SPDEs corresponding to the Fleming-Viot and symmetric simple exclusion processes.

得到了具有非线性、非保守和保守噪声的随机热方程的高阶涨落展开式。这些edgeworth型展开描述了在小噪声强度（ε → 0）和发散奇点（δ → 0）的合适联合标度域中解的渐近行为。计算结果包括规则扩散系数和不规则扩散系数两种情况。特别地，这包括相关的Dawson-Watanabe和Dean-Kawasaki spde，以及对应于Fleming-Viot和对称简单不相容过程的spde。

引用次数: 0

Non-Leray-Hopf solutions to 3D stochastic hyper-viscous Navier-Stokes equations: Beyond the lions exponent 三维随机超粘性Navier-Stokes方程的非leray - hopf解：超越狮子指数

IF 1.2 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications

Pub Date : 2026-03-01 Epub Date: 2025-12-02 DOI: 10.1016/j.spa.2025.104836

Wenping Cao , Zirong Zeng , Deng Zhang

We consider the 3D stochastic Navier-Stokes equations where the viscosity exponent can be larger than the Lions exponent 5/4. Though it is well-known that the Leray-Hopf solutions are unique in this high viscous regime, we prove that the uniqueness would fail in two scaling-supercritical regimes with respect to the Ladyžhenskaya-Prodi-Serrin criteria. The constructed solutions can be non-Leray-Hopf and very close to the Leray-Hopf solutions. Furthermore, we prove the vanishing noise limit result, which relates together the stochastic solutions and the deterministic convex integration solutions constructed by Buckmaster-Vicol [1] and the recent work [2].

我们考虑三维随机Navier-Stokes方程，其中粘度指数可能大于Lions指数的5/4。虽然大家都知道Leray-Hopf解在这种高粘性状态下是唯一的，但我们证明了根据Ladyžhenskaya-Prodi-Serrin准则，在两个标度超临界状态下，这种唯一性将失效。构造的解可以是非Leray-Hopf解并且非常接近Leray-Hopf解。进一步证明了由Buckmaster-Vicol[1]和最近的工作[2]构造的随机解和确定性凸积分解之间的噪声消失极限结果。

引用次数: 0

Clustering of large deviations events in heavy-tailed moving average processes: The catastrophe principle in the short-memory case 重尾移动平均过程中大偏差事件的聚类：短时记忆情况下的突变原理

IF 1.2 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications

Pub Date : 2026-03-01 Epub Date: 2025-12-13 DOI: 10.1016/j.spa.2025.104850

Jiaqi Wang, Gennady Samorodnitsky

How do large deviation events in a stationary process cluster? The answer depends not only on the type of large deviations, but also on the length of memory in the process. Somewhat unexpectedly, it may also depend on the tails of the process. In this paper we work in the context of large deviations for partial sums in moving average processes with short memory and regularly varying tails. We show that the structure of the large deviation cluster in this case markedly differs from the corresponding structure in the case of exponentially light tails, considered in Chakrabarty and Samorodnitsky (2024). This is due to the difference between the “conspiracy” vs. the “catastrophe” principles underlying the large deviation events in the light tailed case and the heavy tailed case, correspondingly.

平稳过程集群中的大偏差事件是如何发生的？答案不仅取决于大偏差的类型，还取决于记忆过程中的时间长度。出乎意料的是，它还可能取决于流程的尾部。在本文中，我们在具有短记忆和规则变化尾的移动平均过程中的部分和的大偏差的背景下工作。我们表明，在这种情况下，大偏差簇的结构明显不同于Chakrabarty和Samorodnitsky（2024）中考虑的指数轻尾的相应结构。这是由于相应的，在轻尾和重尾情况下，大偏差事件背后的“阴谋”与“灾难”原则存在差异。

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Stochastic Processes and their Applications

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