Stochastic Processes and their Applications最新文献

英文中文

Limit theorems for stochastic integrals with long memory processes 长记忆过程随机积分的极限定理

IF 1.2 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications

Pub Date : 2026-05-01 Epub Date: 2026-01-17 DOI: 10.1016/j.spa.2026.104888

Zhishui Hu , Hanying Liang , Qiying Wang

On the convergence to stochastic integrals, semi-martingale structure is imposed in most of previous literature. This semi-martingale structure is restrictive in many statistical and econometric applications, particularly in the field of cointegration. In this paper, we investigate the convergence to stochastic integrals beyond the semi-martingale structure. In particular, we consider the convergence of stochastic integrals with general linear process innovations, allowing for long memory, short memory and antipersistence processes in a unified framework.

在收敛到随机积分的问题上，以往的文献大多采用半鞅结构。这种半鞅结构在许多统计和计量经济学应用中是限制性的，特别是在协整领域。本文研究了随机积分在半鞅结构以外的收敛性。特别地，我们考虑随机积分与一般线性过程创新的收敛性，在统一的框架中允许长记忆，短记忆和反持久性过程。

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 : 2026-05-01 Epub 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

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 : 2026-05-01 Epub 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

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 : 2026-05-01 Epub 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

Yet another notion of irregularity through small ball estimates 这是另一个通过小球估算得出的不规则概念

IF 1.2 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications

Pub Date : 2026-05-01 Epub Date: 2026-01-28 DOI: 10.1016/j.spa.2026.104895

Marco Romito , Leonardo Tolomeo

We introduce a new notion of irregularity of paths, in terms of control of growth of the size of small balls by means of the occupation measure of the path. This notion ensures Besov regularity of the occupation measure and thus extends the analysis of Catellier and Gubinelli [1] to general Besov spaces. On stochastic processes this notion is granted by suitable properties of local non-determinism.

我们引入了路径不规则性的新概念，通过路径的占用度量来控制小球的大小增长。这一概念保证了占用测度的Besov正则性，从而将Catellier和Gubinelli[1]的分析推广到一般的Besov空间。在随机过程中，这一概念是由局部不确定性的适当性质赋予的。

引用次数: 0

Small-time central limit theorems for stochastic Volterra integral equations and their Markovian lifts 随机Volterra积分方程的小时中心极限定理及其马尔可夫提升

IF 1.2 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications

Pub Date : 2026-05-01 Epub Date: 2026-01-22 DOI: 10.1016/j.spa.2026.104892

Martin Friesen , Stefan Gerhold , Kristof Wiedermann

We study small-time central limit theorems for stochastic Volterra integral equations with Hölder continuous coefficients and general locally square integrable Volterra kernels. We prove the convergence of the finite-dimensional distributions, a functional CLT, and limit theorems for smooth transformations of the process, covering a large class of Volterra kernels including rough models based on Riemann-Liouville kernels with short- or long-range dependencies. To illustrate our results, we derive asymptotic pricing formulae for digital calls on the realized variance in three different regimes. The latter provides a robust and largely model-independent pricing method for small maturities in rough volatility models. Finally, for the case of completely monotone kernels, we introduce a flexible framework of Hilbert space-valued Markovian lifts and derive analogous limit theorems for such lifts. The latter provides new small-time limit theorems for stochastic Volterra processes obtained by transformation of the underlying Volterra kernels.

研究了具有Hölder连续系数和一般局部平方可积Volterra核的随机Volterra积分方程的小时中心极限定理。我们证明了有限维分布的收敛性，一个泛函CLT，以及过程平滑变换的极限定理，涵盖了大量的Volterra核，包括基于Riemann-Liouville核的具有短期或长期依赖关系的粗糙模型。为了说明我们的结果，我们在三种不同的制度下推导了数字呼叫对实现方差的渐近定价公式。后者为粗糙波动率模型中的小到期日提供了一种鲁棒且在很大程度上与模型无关的定价方法。最后，在完全单调核的情况下，我们引入了Hilbert空间值马尔可夫提升的柔性框架，并推导了类似的极限定理。后者为随机Volterra过程提供了新的小时极限定理，该定理是由底层Volterra核的变换得到的。

引用次数: 0

On k-clusters of high-intensity random geometric graphs 关于高强度随机几何图的k-簇

IF 1.2 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications

Pub Date : 2026-05-01 Epub Date: 2026-01-11 DOI: 10.1016/j.spa.2026.104882

Mathew D. Penrose , Xiaochuan Yang

Let k, d be positive integers. We determine a sequence of constants that are asymptotic to the probability that the cluster at the origin in a d-dimensional Poisson Boolean model with balls of fixed radius is of order k, as the intensity becomes large. Using this, we determine the asymptotics of the mean of the number of components of order k, denoted S_n,k in a random geometric graph on n uniformly distributed vertices in a smoothly bounded compact region of d-dimensional Euclidean space, with distance parameter r(n) chosen so that the expected degree grows slowly as n becomes large (the so-called mildly dense limiting regime). We also show that the variance of S_n,k is asymptotic to its mean, and prove Poisson and normal approximation results for S_n,k in this limiting regime. We provide analogous results for the corresponding Poisson process (i.e. with a Poisson number of points).

We also give similar results in the so-called mildly sparse limiting regime where r(n) is chosen so the expected degree decays slowly to zero as n becomes large.

设k d是正整数。当强度变大时，我们确定了一个常数序列，该序列趋近于具有固定半径球的d维泊松布尔模型中原点处簇为k阶的概率。利用这一方法，我们确定了在d维欧几里德空间光滑有界紧致区域的n个均匀分布顶点上的随机几何图中k阶分量（表示为Sn，k）的平均值的渐近性，选择距离参数r(n)，使得期望度随着n变大而缓慢增长（所谓的温和密集极限区）。我们还证明了Sn，k的方差是渐近于均值的，并证明了Sn，k在这个极限域中的泊松近似和正态近似结果。我们对相应的泊松过程（即具有泊松点数）提供了类似的结果。我们也给出了类似的结果，在所谓的轻度稀疏的限制条件下，选择r(n)，当n变大时，期望度缓慢地衰减到零。

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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 : 2026-05-01 Epub 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

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 : 2026-05-01 Epub 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

Occupied processes: Going with the flow 已占用进程：随波逐流

IF 1.2 2区数学 Q3 STATISTICS & PROBABILITY

Stochastic Processes and their Applications

Pub Date : 2026-05-01 Epub Date: 2026-01-29 DOI: 10.1016/j.spa.2026.104890

Valentin Tissot-Daguette

A stochastic process X becomes occupied when it is enlarged with its occupation flow

O

that tracks the time spent by the path at each level. When X is Markov, the occupied process

(O, X)

enjoys a Markov structure as well. We develop an Itô calculus for occupied processes that lies midway between Dupire’s functional Itô calculus and the classical version. We derive Itô formulae and, through Feynman-Kac, unveil a broad class of path-dependent PDEs where

O

plays the role of time. The space variable, given by the current value of X, remains finite-dimensional, thereby paving the way for standard elliptic PDE techniques and numerical methods.

The framework’s benefits are illustrated via an optimal stopping problem involving local times, followed by financial applications. For the latter, we show how occupation flows provide unified Markovian lifts for exotic options and variance instruments, allowing financial institutions to price derivatives books with a single numerical solver. We finally explore an extension of forward variance models so as to leverage the entire forward occupation surface.

当一个随机过程X被它的占用流O放大时，它就被占用了，这个占用流O跟踪每一层路径所花费的时间。当X是马尔可夫时，被占用进程（O，X）也具有马尔可夫结构。我们为占用进程开发了一个Itô演算，它介于Dupire的函数式Itô演算和经典版本之间。我们推导出Itô公式，并通过费曼-卡茨揭示了一类广泛的路径相关偏微分方程，其中O扮演时间的角色。由X的当前值给出的空间变量仍然是有限维的，从而为标准椭圆PDE技术和数值方法铺平了道路。该框架的好处是通过一个涉及当地时间的最优停车问题来说明的，其次是金融应用。对于后者，我们展示了职业流如何为外来期权和方差工具提供统一的马尔可夫升降机，允许金融机构使用单个数值求解器对衍生品进行定价。最后，我们探索了前向方差模型的扩展，以利用整个前向占用面。

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