Stochastic Processes and their Applications最新文献

英文中文

Tube formula for spherically contoured random fields with subexponential marginals 具有次指数边缘的球形随机场的管式公式

IF 1.2 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications

Pub Date : 2025-12-25 DOI: 10.1016/j.spa.2025.104858

Satoshi Kuriki , Evgeny Spodarev

It is widely known that the tube method, or equivalently the Euler characteristic heuristic, provides a very accurate approximation for the tail probability that the supremum of a smooth Gaussian random field exceeds a threshold value c. The relative approximation error Δ(c) is exponentially small as a function of c when c tends to infinity. On the other hand, little is known about non-Gaussian random fields.

In this paper, we obtain the approximation error of the tube method applied to the canonical isotropic random fields on a unit sphere defined by u↦⟨u, ξ⟩,

u \in M \subset S^{n - 1}

, where ξ is a spherically contoured random vector. These random fields have statistical applications in multiple testing and simultaneous regression inference when the unknown variance is estimated. The decay rate of the relative error Δ(c) depends on the tail of the distribution of ‖ξ‖² and the critical radius of the index set M. If this distribution is subexponential but not regularly varying, Δ(c) → 0 as c → ∞. However, in the regularly varying case, Δ(c) does not vanish and hence is not negligible. To address this limitation, we provide simple upper and lower bounds for Δ(c) and for the tube formula itself. Numerical studies are conducted to assess the accuracy of the asymptotic approximation.

众所周知，管法，或等效的欧拉特征启发式，为光滑高斯随机场的极值超过阈值c的尾部概率提供了非常精确的近似。当c趋于无穷时，相对近似误差Δ(c)作为c的函数呈指数小。另一方面，人们对非高斯随机场知之甚少。在本文中，我们得到了管法应用于单位球上的正则各向同性随机场的近似误差，该随机场由u∈⟨u， ξ⟩，u∈M∧Sn−1定义，其中ξ是一个球面轮廓随机向量。当估计未知方差时，这些随机场在多重检验和同时回归推理中具有统计应用。相对误差Δ(c)的衰减率取决于‖ξ‖2分布的尾部和指标集m的临界半径。如果该分布是次指数的，但没有规则变化，则Δ(c) → 0为c → ∞。然而，在规律变化的情况下，Δ(c)不会消失，因此不可忽略。为了解决这个限制，我们为Δ(c)和管式公式本身提供了简单的上限和下限。通过数值研究来评估渐近逼近的准确性。

{"title":"Tube formula for spherically contoured random fields with subexponential marginals","authors":"Satoshi Kuriki , Evgeny Spodarev","doi":"10.1016/j.spa.2025.104858","DOIUrl":"10.1016/j.spa.2025.104858","url":null,"abstract":"<div><div>It is widely known that the tube method, or equivalently the Euler characteristic heuristic, provides a very accurate approximation for the tail probability that the supremum of a smooth Gaussian random field exceeds a threshold value <em>c</em>. The relative approximation error Δ(<em>c</em>) is exponentially small as a function of <em>c</em> when <em>c</em> tends to infinity. On the other hand, little is known about non-Gaussian random fields.</div><div>In this paper, we obtain the approximation error of the tube method applied to the canonical isotropic random fields on a unit sphere defined by <em>u</em>↦⟨<em>u, ξ</em>⟩, <span><math><mrow><mi>u</mi><mo>∈</mo><mi>M</mi><mo>⊂</mo><msup><mi>S</mi><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup></mrow></math></span>, where <em>ξ</em> is a spherically contoured random vector. These random fields have statistical applications in multiple testing and simultaneous regression inference when the unknown variance is estimated. The decay rate of the relative error Δ(<em>c</em>) depends on the tail of the distribution of ‖<em>ξ</em>‖<sup>2</sup> and the critical radius of the index set <em>M</em>. If this distribution is subexponential but not regularly varying, Δ(<em>c</em>) → 0 as <em>c</em> → ∞. However, in the regularly varying case, Δ(<em>c</em>) does not vanish and hence is not negligible. To address this limitation, we provide simple upper and lower bounds for Δ(<em>c</em>) and for the tube formula itself. Numerical studies are conducted to assess the accuracy of the asymptotic approximation.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"195 ","pages":"Article 104858"},"PeriodicalIF":1.2,"publicationDate":"2025-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145886100","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Fractional interacting particle system: Drift parameter estimation via Malliavin calculus 分数阶相互作用粒子系统：用Malliavin演算估计漂移参数

IF 1.2 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications

Pub Date : 2025-12-24 DOI: 10.1016/j.spa.2025.104857

Chiara Amorino , Ivan Nourdin , Radomyra Shevchenko

We address the problem of estimating the drift parameter in a system of N interacting particles driven by additive fractional Brownian motion of Hurst index H ≥ 1/2. Considering continuous observation of the interacting particles over a fixed interval [0, T], we examine the asymptotic regime as N → ∞. Our main tool is a random variable reminiscent of the least squares estimator but unobservable due to its reliance on the Skorohod integral. We demonstrate that this object is consistent and asymptotically normal by establishing a quantitative propagation of chaos for Malliavin derivatives, which holds for any H ∈ (0, 1). Leveraging a connection between the divergence integral and the Young integral, we construct computable estimators of the drift parameter. These estimators are shown to be consistent and asymptotically Gaussian. Finally, a numerical study highlights the strong performance of the proposed estimators.

我们研究了由Hurst指数H ≥ 1/2的加性分数布朗运动驱动的N个相互作用粒子系统的漂移参数估计问题。考虑在固定区间[0，T]上对相互作用粒子的连续观测，我们研究了N → ∞的渐近区域。我们的主要工具是一个随机变量，让人想起最小二乘估计量，但由于它依赖于Skorohod积分而不可观测。通过对任意H ∈ （0,1）建立混沌的定量传播，证明了该目标是一致且渐近正态的。利用散度积分和Young积分之间的联系，我们构造了漂移参数的可计算估计量。这些估计量被证明是一致的和渐近高斯的。最后，数值研究表明了所提估计器的良好性能。

引用次数: 0

Stretched non-local Pearson diffusions 拉伸非局部皮尔逊扩散

IF 1.2 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications

Pub Date : 2025-12-23 DOI: 10.1016/j.spa.2025.104854

Luisa Beghin , Nikolai Leonenko , Ivan Papić , Jayme Vaz

We define a novel class of time-changed Pearson diffusions, termed stretched non-local Pearson diffusions, where the stochastic time-change model has the Kilbas-Saigo function as its Laplace transform. Moreover, we introduce a stretched variant of the Caputo fractional derivative and prove that its eigenfunction is, in fact, the Kilbas-Saigo function. Furthermore, we solve fractional Cauchy problems involving the generator of the Pearson diffusion and the Fokker-Planck operator, providing both analytic and stochastic solutions, which connect the newly defined process and fractional operator with the Kilbas-Saigo function. We also prove that stretched non-local Pearson diffusions share the same limiting distributions as their standard counterparts. Finally, we investigate fractional hyperbolic Cauchy problems for Pearson diffusions, which resemble time-fractional telegraph equations, and provide both analytical and stochastic solutions. As a byproduct of our analysis, we derive a novel representation and an asymptotic formula for the Kilbas-Saigo function with complex arguments, which, to the best of our knowledge, are not currently available in the existing literature.

我们定义了一类新的时变皮尔逊扩散，称为拉伸非局部皮尔逊扩散，其中随机时变模型的拉普拉斯变换为Kilbas-Saigo函数。此外，我们引入了Caputo分数阶导数的一个拉伸变体，并证明了它的特征函数实际上是Kilbas-Saigo函数。此外，我们还解决了包含Pearson扩散和Fokker-Planck算子的分数阶Cauchy问题，提供了解析解和随机解，将新定义的过程和分数阶算子与kilass - saigo函数联系起来。我们还证明了拉伸的非局部皮尔逊扩散与它们的标准对应物具有相同的极限分布。最后，我们研究了类似于时间分数阶电报方程的Pearson扩散的分数阶双曲柯西问题，并给出了解析解和随机解。作为我们分析的副产品，我们推导出了具有复杂参数的Kilbas-Saigo函数的新颖表示和渐近公式，据我们所知，这在现有文献中目前是不可用的。

{"title":"Stretched non-local Pearson diffusions","authors":"Luisa Beghin , Nikolai Leonenko , Ivan Papić , Jayme Vaz","doi":"10.1016/j.spa.2025.104854","DOIUrl":"10.1016/j.spa.2025.104854","url":null,"abstract":"<div><div>We define a novel class of time-changed Pearson diffusions, termed stretched non-local Pearson diffusions, where the stochastic time-change model has the Kilbas-Saigo function as its Laplace transform. Moreover, we introduce a stretched variant of the Caputo fractional derivative and prove that its eigenfunction is, in fact, the Kilbas-Saigo function. Furthermore, we solve fractional Cauchy problems involving the generator of the Pearson diffusion and the Fokker-Planck operator, providing both analytic and stochastic solutions, which connect the newly defined process and fractional operator with the Kilbas-Saigo function. We also prove that stretched non-local Pearson diffusions share the same limiting distributions as their standard counterparts. Finally, we investigate fractional hyperbolic Cauchy problems for Pearson diffusions, which resemble time-fractional telegraph equations, and provide both analytical and stochastic solutions. As a byproduct of our analysis, we derive a novel representation and an asymptotic formula for the Kilbas-Saigo function with complex arguments, which, to the best of our knowledge, are not currently available in the existing literature.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"195 ","pages":"Article 104854"},"PeriodicalIF":1.2,"publicationDate":"2025-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145847611","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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 : 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。

{"title":"Frog model on Z with random survival parameter","authors":"Gustavo O. De Carvalho, Fábio P. Machado","doi":"10.1016/j.spa.2025.104856","DOIUrl":"10.1016/j.spa.2025.104856","url":null,"abstract":"<div><div>We study the frog model on <span><math><mi>Z</mi></math></span> with geometric lifetimes, introducing a random survival parameter. Active and inactive particles are placed at the vertices of <span><math><mi>Z</mi></math></span>. The lifetime of each active particle follows a geometric random variable with parameter <span><math><mrow><mn>1</mn><mo>−</mo><mi>p</mi></mrow></math></span>, where <em>p</em> is randomly sampled from a distribution <em>π</em>. Each active particle performs a simple random walk on <span><math><mi>Z</mi></math></span> until it dies, activating any inactive particles it encounters along its path. In contrast to the usual case where <em>p</em> is fixed, we show that there exist non-trivial distributions <em>π</em> for which the model survives with positive probability. More specifically, for <em>π</em> ∼ <em>Beta</em>(<em>α, β</em>), we establish the existence of a critical value <span><math><mrow><mi>β</mi><mo>=</mo><mn>0.5</mn></mrow></math></span>, that separates almost sure extinction from survival with positive probability. Furthermore, we show that the model is recurrent whenever it survives with positive probability.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"194 ","pages":"Article 104856"},"PeriodicalIF":1.2,"publicationDate":"2025-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145842462","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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 : 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

Quasi-stationarity of the Dyson Brownian motion with collisions 带碰撞的戴森-布朗运动的准平稳性

IF 1.2 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications

Pub Date : 2025-12-15 DOI: 10.1016/j.spa.2025.104851

Arnaud Guillin , Boris Nectoux , Liming Wu

In this work, we investigate the ergodic behavior of a system of particules, subject to collisions, before it exits a fixed subdomain of its state space. This system is composed of several one-dimensional ordered Brownian particules in interaction with electrostatic repulsions, which is usually referred as the (generalized) Dyson Brownian motion. The starting points of our analysis are the work [E. Cépa and D. Lépingle, 1997 Probab. Theory Relat. Fields] which provides existence and uniqueness of such a system subject to collisions via the theory of multivalued SDEs and a Krein-Rutman type theorem derived in [A. Guillin, B. Nectoux, L. Wu, 2020 J. Eur. Math. Soc.].

在这项工作中，我们研究了一个粒子系统，受到碰撞，在它退出其状态空间的固定子域之前的遍历行为。该系统由若干一维有序布朗粒子与静电斥力相互作用组成，通常称为（广义）戴森布朗运动。我们分析的起点是工作[E]。c.c.a和d.l acimingle, 1997。代数理论。域]，通过多值sde理论和[a]中导出的Krein-Rutman型定理提供了这种受碰撞影响的系统的存在唯一性。吴丽娟，吴丽娟，吴丽娟，2020 。欧元。数学。Soc。]。

引用次数: 0

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 : 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。

{"title":"Optimal prediction of the last r-excursion time of Brownian motion models","authors":"B. Li , M.A. Lkabous , J.M. Pedraza","doi":"10.1016/j.spa.2025.104852","DOIUrl":"10.1016/j.spa.2025.104852","url":null,"abstract":"<div><div>This paper investigates the optimal prediction of the last <em>r</em>-excursion time for a Brownian motion model. The last <em>r</em>-excursion time, denoted by <em>l<sub>r</sub></em>, refers to the right endpoint of the last negative excursion lasting longer than a constant <em>r</em> > 0. It reduces to the standard last passage time when <em>r</em>↓0. For a Brownian motion with drift <em>μ</em> > 0 and volatility <em>σ</em> > 0, our goal is to identify an optimal stopping time that minimizes the (<em>L</em><sub>1</sub>) distance from the last <em>r</em>-excursion time <em>l<sub>r</sub></em>. 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 <span><math><mrow><mi>R</mi><mo>=</mo><mfrac><mrow><mi>μ</mi><msqrt><mi>r</mi></msqrt></mrow><mi>σ</mi></mfrac></mrow></math></span> 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.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"194 ","pages":"Article 104852"},"PeriodicalIF":1.2,"publicationDate":"2025-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145814323","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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 : 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。

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 : 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

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 : 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

首页上一页

下一页尾页

类型

全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

数据库

全部 ACS Publications Elsevier ieeexplore Springer The Royal Society of Chemistry Wiley

期刊

Stochastic Processes and their Applications

全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.

﹀