Stochastic Processes and their Applications最新文献

英文中文

On the distribution of the telegraph meander and its properties 论电报弯曲的分布及其性质

IF 1.2 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications

Pub Date : 2026-01-14 DOI: 10.1016/j.spa.2026.104887

A. Pedicone, E. Orsingher

In this paper we study the telegraph meander, a random function obtained by conditioning the telegraph process to stay above the zero level. The finite dimensional distribution of the telegraph meander is derived by applying the reflection principle for the telegraph process and the Markovianity of the telegraph process with the velocity process. We show that the law of the telegraph meander at the end time is a solution to a hyperbolic equation, and we find the characteristic function and moments of any order. Finally, we prove that Brownian meander is the weak limit of the telegraph meander.

本文研究了电报迂回，这是一种通过使电报过程保持在零水平以上而得到的随机函数。利用电报过程的反射原理和电报过程与速度过程的马尔可夫性，导出了电报曲流的有限维分布。我们证明了终端时间的电报弯曲定律是一个双曲方程的解，并找到了任意阶的特征函数和矩。最后，我们证明了布朗弯曲是电报弯曲的弱极限。

引用次数: 0

An injective martingale coupling 一个内射鞅耦合

IF 1.2 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications

Pub Date : 2026-01-12 DOI: 10.1016/j.spa.2026.104883

David Hobson , Dominykas Norgilas

<div><div>We give an injective martingale coupling; in particular, given measures μ and ν in convex order on <math><mi>R</mi></math> such that ν is continuous, we construct a martingale transport such that for each y in the support of the target law ν there is a unique x in a support of the initial law μ such that (some of) the mass at x is transported to y. Then π has disintegration <math><mrow><mi>π</mi><mrow><mo>(</mo><mi>d</mi><mi>x</mi><mo>,</mo><mi>d</mi><mi>y</mi><mo>)</mo></mrow><mo>=</mo><mi>ν</mi><mrow><mo>(</mo><mi>d</mi><mi>y</mi><mo>)</mo></mrow><msub><mi>δ</mi><mrow><mi>θ</mi><mo>(</mo><mi>y</mi><mo>)</mo></mrow></msub><mrow><mo>(</mo><mi>d</mi><mi>x</mi><mo>)</mo></mrow></mrow></math> for some function θ.</div><div>More precisely we construct a martingale coupling π of the measures μ and ν such that there is a set Γμ such that <math><mrow><mi>μ</mi><mo>(</mo><msub><mstyle><mi>Γ</mi></mstyle><mi>μ</mi></msub><mo>)</mo><mo>=</mo><mn>1</mn></mrow></math> and a disintegration <math><msub><mrow><mo>(</mo><msub><mi>π</mi><mi>x</mi></msub><mo>)</mo></mrow><mrow><mi>x</mi><mo>∈</mo><msub><mstyle><mi>Γ</mi></mstyle><mi>μ</mi></msub></mrow></msub></math> of π of the form <math><mrow><mi>π</mi><mrow><mo>(</mo><mi>d</mi><mi>x</mi><mo>,</mo><mi>d</mi><mi>y</mi><mo>)</mo></mrow><mo>=</mo><msub><mi>π</mi><mi>x</mi></msub><mrow><mo>(</mo><mi>d</mi><mi>y</mi><mo>)</mo></mrow><mi>μ</mi><mrow><mo>(</mo><mi>d</mi><mi>x</mi><mo>)</mo></mrow></mrow></math> such that, with <math><msub><mstyle><mi>Γ</mi></mstyle><msub><mi>π</mi><mi>x</mi></msub></msub></math> a support of πx, we have <math><mrow><mo>#</mo><mrow><mo>{</mo><mi>x</mi><mo>∈</mo><msub><mstyle><mi>Γ</mi></mstyle><mi>μ</mi></msub><mo>:</mo><mi>y</mi><mo>∈</mo><msub><mstyle><mi>Γ</mi></mstyle><msub><mi>π</mi><mi>x</mi></msub></msub><mo>}</mo></mrow><mo>∈</mo><mrow><mo>{</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>}</mo></mrow></mrow></math> for all y and <math><mrow><mrow><mo>{</mo><mi>y</mi><mo>:</mo><mo>#</mo><mrow><mo>{</mo><mi>x</mi><mo>∈</mo><msub><mstyle><mi>Γ</mi></mstyle><mi>μ</mi></msub><mo>:</mo><mi>y</mi><mo>∈</mo><msub><mstyle><mi>Γ</mi></mstyle><msub><mi>π</mi><mi>x</mi></msub></msub><mo>}</mo></mrow><mo>=</mo><mn>1</mn><mo>}</mo></mrow><mo>=</mo><mtext>supp</mtext><mrow><mo>(</mo><mi>ν</mi><mo>)</mo></mrow></mrow></math>. Moreover, if μ is continuous we may take <math><mrow><msub><mstyle><mi>Γ</mi></mstyle><msub><mi>π</mi><mi>x</mi></msub></msub><mo>=</mo><mtext>supp</mtext><mrow><mo>(</mo><msub><mi>π</mi><mi>x</mi></msub><mo>)</mo></mrow></mrow></math> for each x. However, we cannot also insist that <math><mrow><msub><mstyle><mi>Γ</mi></mstyle><mi>μ</mi></msub><mo>=</m

给出了一个内射鞅耦合；特别地，给定R上凸阶的μ和ν，使得ν是连续的，我们构造了一个鞅输运，使得对于支持目标定律ν的每一个y，在初始定律μ的支持下，有一个唯一的x，使得x处的（一些）质量被传输到y。然后π对某些函数θ有分解π(dx,dy)=ν(dy)δθ(y)（dx）。更精确地说，我们构造了测度μ和ν的鞅耦合π，使得π有一个集合Γμ使得μ（Γμ）=1， π的分解（πx）x∈Γμ的形式为π(dx,dy)=πx(dy)μ(dx)，使得在Γπx πx的支持下，我们有#{x∈Γμ:y∈Γπx}∈{0,1}对于所有y和{y:#{x∈Γμ:y∈Γπx}=1}=supp（ν）。此外，如果μ是连续的，我们可以对每个x取Γπx=supp(πx)，但是，我们也不能坚持Γμ=supp（μ）。

引用次数: 0

The multi-level friendship paradox for sparse random graphs 稀疏随机图的多级友谊悖论

IF 1.2 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications

Pub Date : 2026-01-09 DOI: 10.1016/j.spa.2026.104873

Rajat Subhra Hazra, Frank den Hollander, Azadeh Parvaneh

In [1] we analysed the friendship paradox for sparse random graphs. For four classes of random graphs we characterised the empirical distribution of the friendship biases between vertices and their neighbours at distance 1, proving convergence as n → ∞ to a limiting distribution, with n the number of vertices, and identifying moments and tail exponents of the limiting distribution. In the present paper we look at the multi-level friendship bias between vertices and their neighbours at distance

k \in N

obtained via a k-step exploration according to a backtracking or a non-backtracking random walk. We identify the limit of the empirical distribution of the multi-level friendship biases as n → ∞ and/or k → ∞. We show that for non-backtracking exploration the two limits commute for a large class of sparse random graphs, including those that locally converge to a rooted Galton-Watson tree. In particular, we show that the same limit arises when k depends on n, i.e.,

k = k_{n}

, provided

\lim_{n \to \infty} k_{n} = \infty

under some mild conditions. We exhibit cases where the two limits do not commute and show the relevance of the mixing time of the exploration.

在b[1]中，我们分析了稀疏随机图的友谊悖论。对于四类随机图，我们描述了距离为1的顶点与其邻居之间的友谊偏差的经验分布，证明了收敛为n → ∞到具有n个顶点的极限分布，并识别了极限分布的矩和尾指数。在本文中，我们通过k步探索，根据回溯或非回溯随机漫步，研究距离k∈N的顶点与其邻居之间的多级友谊偏差。我们确定了多级友谊偏差的经验分布的极限为n → ∞和/或k → ∞。我们证明了对于非回溯探索的两个极限可交换的一大类稀疏随机图，包括那些局部收敛到有根的高尔顿-沃森树。特别地，我们证明了当k依赖于n时，即k=kn，在一些温和的条件下，假设limn→∞kn=∞，也会出现相同的极限。我们展示了两种极限不相适应的情况，并展示了勘探混合时间的相关性。

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引用次数: 0

Numerical approximation of ergodic BSDEs using non linear Feynman-Kac formulas 非线性Feynman-Kac公式的遍历BSDEs数值逼近

IF 1.2 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications

Pub Date : 2026-01-07 DOI: 10.1016/j.spa.2026.104871

Emmanuel Gobet , Adrien Richou , Lukasz Szpruch

In this work we study the numerical approximation of a class of ergodic Backward Stochastic Differential Equations. These equations are formulated in an infinite horizon framework and provide a probabilistic representation for elliptic Partial Differential Equations of ergodic type. In order to build our numerical scheme, we put forward a new representation of the PDE solution by using a classical probabilistic representation of the gradient. Then, based on this representation, we propose a fully implementable numerical scheme using a Picard iteration procedure, a grid space discretization and a Monte-Carlo approximation. Up to a limiting technical condition that guarantees the contraction of the Picard procedure, we obtain an upper bound for the numerical error. We also provide some numerical experiments that show the efficiency of this approach for small dimensions.

本文研究了一类遍历倒向随机微分方程的数值逼近。这些方程是在无限视界框架下建立的，并给出了遍历型椭圆型偏微分方程的概率表示。为了构造我们的数值格式，我们利用梯度的经典概率表示提出了PDE解的一种新的表示。然后，在此基础上，我们提出了一个完全可实现的数值格式，使用皮卡德迭代过程，网格空间离散化和蒙特卡罗近似。在保证Picard过程收缩的极限技术条件下，得到了数值误差的上界。我们还提供了一些数值实验，证明了该方法在小尺寸情况下的有效性。

引用次数: 0

Global maximum principle for partially observed risk-sensitive progressive optimal control of FBSDE with Poisson jumps 带泊松跳的FBSDE部分可观测风险敏感渐进最优控制的全局极大原理

IF 1.2 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications

Pub Date : 2026-01-07 DOI: 10.1016/j.spa.2026.104870

Jingtao Lin, Jingtao Shi

This paper is concerned with one kind of partially observed progressive optimal control problems of coupled forward-backward stochastic systems driven by both Brownian motion and Poisson random measure with risk-sensitive criteria. The control domain is not necessarily convex, and the control variable can enters into all the coefficients. The observation equation also has correlated noises with the state equation. Under the Poisson jump setting, the original problem is equivalent to a stochastic recursive optimal control problem of a forward-backward system with quadratic-exponential generator. In order to establish the first- and second-order variations, some new techniques are introduced to overcome difficulties caused by the quadratic-exponential feature. A new global stochastic maximum principle is deduced. As an application, a risk-sensitive optimal investment problem with factor model is studied. Moreover, the risk-sensitive stochastic filtering problem is studied, which involves both Brownian and Poissonian correlated noises. A modified Zakai equation is obtained.

研究一类由布朗运动和泊松随机测度驱动的具有风险敏感准则的正-后向耦合随机系统的部分观测渐进最优控制问题。控制域不一定是凸的，控制变量可以进入所有的系数。观测方程还存在与状态方程相关的噪声。在泊松跳设下，原问题等价于一个具有二次指数生成器的正反向系统的随机递推最优控制问题。为了建立一阶和二阶变分，引入了一些新技术来克服二次指数特征带来的困难。导出了一个新的全局随机极大值原理。作为应用，研究了一个具有因子模型的风险敏感最优投资问题。此外，还研究了布朗相关噪声和泊松相关噪声的风险敏感随机滤波问题。得到了修正的Zakai方程。

引用次数: 0

Littlewood-Offord problems for Ising models 伊辛模型的Littlewood-Offord问题

IF 1.2 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications

Pub Date : 2026-01-06 DOI: 10.1016/j.spa.2026.104872

Yinshan Chang

We consider the one-dimensional Littlewood-Offord problem for general Ising models. More precisely, we consider the concentration function

\begin{matrix} Q_{n} (x, v) = P (\sum_{i = 1}^{n} ε_{i} v_{i} \in (x - 1, x + 1)), \end{matrix}

where

x \in R

v_{1}, v_{2}, \dots, v_{n}

are real numbers such that

| v_{1} | \geq 1, | v_{2} | \geq 1, \dots, | v_{n} | \geq 1

, and

{(ε_{i})}_{i = 1, 2, \dots, n} \in {- 1, 1}^{n}

are random spins of some Ising model. Let

Q_{n} = \sup_{x, v} Q_{n} (x, v)

. Under natural assumptions, we show that there exists a universal constant C such that for all n ≥ 1,

\begin{matrix} (\frac{n}{[n / 2]}) 2^{- n} \leq Q_{n} \leq C n^{- \frac{1}{2}} . \end{matrix}

As an application of the method, under the same assumption, we give a lower bound on the smallest eigenvalue of the truncated correlation matrix of the Ising model.

我们考虑一般Ising模型的一维littlewood - offford问题。更精确地说，我们考虑浓度函数qn (x,v)=P(∑i=1nεivi∈(x−1,x+1))，其中x∈R， v1,v2，…，vn是实数，使得|v1|≥1，|v2|≥1，…，|vn|≥1,(εi)i=1,2，…，n∈{−1,1}n是某个Ising模型的随机自旋。让Qn = supx vQn (x, v)。在自然假设下，我们证明了存在一个普适常数C，使得对于所有n ≥ 1，（n[n/2]）2−n≤Qn≤Cn−12。作为该方法的一个应用，在相同的假设下，给出了伊辛模型截断相关矩阵的最小特征值的下界。

引用次数: 0

Sharp Lq-convergence rate in p-Wasserstein distance for empirical measures of diffusion processes 扩散过程经验测度的p-Wasserstein距离的尖锐lq收敛速率

IF 1.2 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications

Pub Date : 2026-01-05 DOI: 10.1016/j.spa.2026.104869

Feng-Yu Wang , Bingyao Wu , Jie-Xiang Zhu

In this paper we study the long time behavior in Wasserstein distance for empirical measures of (non-symmetric) diffusion processes on a length space satisfying the Nash inequality, which in particular include the (reflecting) diffusion processes on a connected compact Riemannian manifold. As a general result, the sharp convergence rate in

L^{q} (P)

for the p-Wasserstein distance is derived uniformly in p ∈ [1, ∞) and q ∈ (0, ∞). A key novelty of our approach, compared to existing works, is the use of a Bernstein-type inequality for diffusion processes.

本文研究了满足Nash不等式的长度空间上（非对称）扩散过程的经验测度在Wasserstein距离上的长时间行为，特别是包括连通紧黎曼流形上的（反射）扩散过程。作为一般结果，在P ∈ [1，∞]和q ∈ （0,∞）中，一致地导出了P - wasserstein距离在Lq(P)中的急剧收敛速率。与现有的工作相比，我们的方法的一个关键新颖之处在于对扩散过程使用了伯恩斯坦型不等式。

引用次数: 0

Asymptotic behaviors of subcritical branching killed Lévy processes 亚临界分支的渐近性

IF 1.2 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications

Pub Date : 2026-01-04 DOI: 10.1016/j.spa.2025.104867

Yan-Xia Ren , Renming Song , Yaping Zhu

In this paper, we investigate the asymptotic behaviors of the survival probability and maximal displacement of a subcritical branching killed Lévy process X in

R

. Let ζ denote the extinction time, M_t be the maximal position of all the particles alive at time t, and

M : = \sup_{t \geq 0} M_{t}

be the all-time maximum. Under the assumption that the offspring distribution satisfies the Llog L condition and some conditions on the spatial motion, we find the decay rate of the survival probability

P_{x} (ζ > t)

and the tail behavior of M_t as t → ∞. As a consequence, we establish a Yaglom-type theorem. We also find the asymptotic behavior of

P_{x} (M > y)

as y → ∞.

本文研究了一类亚临界分支死亡lsamvy过程X在r中的生存概率和最大位移的渐近行为，设ζ为灭绝时间，Mt为时刻t所有存活粒子的最大位置，M:=supt≥0Mt为时间最大值。假设子代分布满足llogl条件和空间运动的一些条件，我们得到生存概率Px（ζ>t）的衰减率和Mt的尾部行为为t → ∞。因此，我们建立了一个yaglomtype定理。我们还发现了Px（M>y）的渐近性为y → ∞。

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引用次数: 0

Sensitivity of functionals of McKean-Vlasov SDEs with respect to the initial distribution McKean-Vlasov SDEs泛函对初始分布的敏感性

IF 1.2 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications

Pub Date : 2026-01-03 DOI: 10.1016/j.spa.2025.104868

Filippo de Feo , Salvatore Federico , Fausto Gozzi , Nizar Touzi

We examine the sensitivity at the origin of the distributional robust optimization problem in the context of a model generated by a mean field stochastic differential equation. We adapt the finite dimensional argument developed by Bartl, Drapeau, Obloj, & Wiesel to our framework involving the infinite dimensional gradient of the solution of the mean field SDE with respect to its initial data. We revisit the derivation of this gradient process as previously introduced by Buckdahn, Li, Peng, & Rainer and we complement the existing properties so as to satisfy the requirement of our main result. We use the theory developed in the context of a mean-field systemic risk model by evaluating the sensitivity with respect to the initial distribution for the variance of the log-monetary reserve of a representative bank.

在平均场随机微分方程生成的模型中，我们研究了分布鲁棒优化问题原点的灵敏度。我们将Bartl， Drapeau, Obloj, &； Wiesel提出的有限维论点适用于我们的框架，该框架涉及平均场SDE的解相对于其初始数据的无限维梯度。我们重新考虑了Buckdahn， Li, Peng， Rainer之前介绍的这个梯度过程的推导，并补充了现有的性质，以满足我们的主要结果的要求。我们使用在平均场系统风险模型的背景下发展的理论，通过评估相对于初始分布的敏感性的对数货币储备的代表性银行的方差。

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 : 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。

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