Stochastic Analysis and Applications最新文献

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Asymptotic of the running maximum distribution of a Gaussian Bridge 高斯桥的运行最大值分布的渐近性

IF 1.3 4区数学 Q3 MATHEMATICS, APPLIED

Stochastic Analysis and Applications

Pub Date : 2022-09-19 DOI: 10.1080/07362994.2022.2123344

M. Abundo

Abstract We study the tail behavior of the distribution of the running maximum of a zero mean Gaussian Bridge obtained from a continuous Gaussian process X(t) with by conditioning X(t) to have the value zero at time T. Some explicit examples are shown.

引用次数: 0

Interventional Imaging Roadmap to Successful Balloon Pulmonary Angioplasty for Chronic Thromboembolic Pulmonary Hypertension. 成功进行慢性血栓栓塞性肺动脉高压球囊肺血管成形术的介入成像路线图。

IF 2.1 4区数学 Q3 MATHEMATICS, APPLIED

Stochastic Analysis and Applications

Pub Date : 2022-08-12 eCollection Date: 2022-11-01 DOI: 10.1016/j.jscai.2022.100429

Nimai Patel, Syed N Hyder, Erinleigh Michaud, Victor Moles, Prachi P Agarwal, Kenneth Rosenfield, Kohtaro Abe, Jonathan Haft, Scott H Visovatti, Thomas M Cascino, William R Auger, Vallerie V Mclaughlin, Vikas Aggarwal

Balloon pulmonary angioplasty (BPA) is an evolving treatment modality for patients with chronic thromboembolic pulmonary hypertension (CTEPH) who are not candidates for pulmonary endarterectomy. Although several imaging modalities currently exist for evaluating CTEPH, their individual use, specifically in the clinical practice of BPA, has not been well described. In this article, we provide a preprocedural, intraprocedural, and postprocedural interventional imaging roadmap for safe and effective BPA performance in routine clinical practice. Preprocedural assessment includes transthoracic echocardiography for right ventricular assessment, ventilation/perfusion scan to identify pulmonary segments with the highest degree of hypoperfusion, cross-sectional chest imaging excluding alternative causes of mismatched defects and providing anatomic and perfusion imaging concurrently, and nonselective invasive pulmonary angiography for risk stratification of individual lesion subtypes. Intraprocedural assessment includes subselective segmental angiography (SSA) for delineating segmental and subsegmental branch anatomy, lesion identification, and vessel sizing. Intravascular ultrasound and optical coherence tomography serve as adjunctive intraprocedural tools for more accurate vessel sizing and lesion characterization when SSA alone is insufficient. Postprocedural considerations include chest radiography to monitor for immediate postprocedure complications and echocardiography for the interval assessment of the right ventricle on longer-term follow-up.

对于不适合进行肺动脉内膜切除术的慢性血栓栓塞性肺动脉高压（CTEPH）患者来说，球囊肺血管成形术（BPA）是一种不断发展的治疗方式。虽然目前有多种成像模式可用于评估 CTEPH，但它们各自的用途，特别是在 BPA 临床实践中的用途，还没有得到很好的描述。在本文中，我们为常规临床实践中安全有效地实施 BPA 提供了一个术前、术中和术后介入成像路线图。术前评估包括用于评估右心室的经胸超声心动图、通气/灌注扫描以确定灌注不足程度最高的肺段、横断面胸部成像以排除造成不匹配缺损的其他原因并同时提供解剖和灌注成像，以及用于对个别病变亚型进行风险分层的非选择性有创肺动脉造影。术中评估包括亚选择性节段血管造影术（SSA），用于划分节段和亚节段分支解剖结构、病变识别和血管大小。血管内超声和光学相干断层扫描可作为术中的辅助工具，在单靠亚选择节段血管造影不足以确定血管大小和病变特征时，可用于更准确地确定血管大小和病变特征。术后注意事项包括胸片检查，以监测术后即刻出现的并发症，以及超声心动图检查，以便在长期随访中对右心室进行间隔评估。

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引用次数: 0

On the Ayed-Kuo stochastic integration for anticipating integrands 关于预测被积函数的Ayed Kuo随机积分

IF 1.3 4区数学 Q3 MATHEMATICS, APPLIED

Stochastic Analysis and Applications

Pub Date : 2022-08-07 DOI: 10.1080/07362994.2022.2104730

M. Jornet

Abstract In this article, we prove new results for the anticipating stochastic integral introduced by Ayed and Kuo. We present an existence criterion for the integral, a Fubini’s theorem, a Leibniz integral rule, and an alternative definition for a class of integrands.

摘要本文证明了Ayed和Kuo提出的预测随机积分的新结果。我们给出了积分的存在性准则，Fubini定理，Leibniz积分规则，以及一类被积函数的另一个定义。

引用次数: 1

Backward doubly stochastic differential equations with discontinuous and stochastic linear growth generator 具有不连续随机线性增长发生器的倒向双随机微分方程

IF 1.3 4区数学 Q3 MATHEMATICS, APPLIED

Stochastic Analysis and Applications

Pub Date : 2022-08-05 DOI: 10.1080/07362994.2022.2104314

J. Owo

Abstract In this paper, we investigate an existence of minimal (resp. maximal) solutions for backward doubly stochastic differential equations (BDSDEs, in short) when the coefficient with respect to the forward integral is left (resp. right)-continuous in y and continuous in z with stochastic linear growth in (y, z). Also, the associated comparison theorem is obtained.

摘要本文研究了一类极小值的存在性。最大)解的后向双随机微分方程(BDSDEs，简而言之)，当相对于前向积分的系数是左(参见。(右)在y上连续，在z上连续，在(y, z)上随机线性增长，并得到了相关的比较定理。

引用次数: 0

Mathematical modeling of smoking habits in the society 社会吸烟习惯的数学建模

IF 1.3 4区数学 Q3 MATHEMATICS, APPLIED

Stochastic Analysis and Applications

Pub Date : 2022-07-09 DOI: 10.1080/07362994.2022.2093223

I. R. Sofia, M. Ghosh

Abstract In this study, we formulate and analyze a non-linear mathematical model to study the dynamics of smoking and its impact on society. This is a compartment model which has four compartments, namely, potential smoker, occasional smoker, smoker and quitters. As per WHO, each year there is a significant number of smoking-related deaths. Keeping this in view, we have incorporated smoking-related death in our proposed model. Further, we investigate the model for possible equilibria, compute the basic reproduction number and investigate the stability of obtained equilibria. Later we extend this model to stochastic model and perform numerical simulation for both the deterministic and the stochastic model. The results of stochastic model are almost similar to the results obtained for deterministic model. We have also explored the impact of the parameters related to quitting smoking habits on the equilibrium level of occasional smokers. We also perform sensitivity analysis to find the key parameters which make significant change in the reproduction numbers.

摘要在本研究中，我们建立并分析了一个非线性数学模型，以研究吸烟的动力学及其对社会的影响。这是一个有四个隔间的模型，即潜在吸烟者、偶尔吸烟者、吸烟者和戒烟者。根据世界卫生组织的数据，每年都有大量与吸烟有关的死亡。考虑到这一点，我们将吸烟相关死亡纳入了我们提出的模型中。此外，我们研究了可能平衡的模型，计算了基本繁殖数，并研究了所获得平衡的稳定性。随后，我们将该模型扩展到随机模型，并对确定性和随机性模型进行了数值模拟。随机模型的结果与确定性模型的结果几乎相似。我们还探讨了与戒烟习惯相关的参数对偶尔吸烟者平衡水平的影响。我们还进行了灵敏度分析，以找到使繁殖数量发生重大变化的关键参数。

引用次数: 2

Modeling social media addiction with case detection and treatment 用病例检测和治疗建模社交媒体成瘾

IF 1.3 4区数学 Q3 MATHEMATICS, APPLIED

Stochastic Analysis and Applications

Pub Date : 2022-06-26 DOI: 10.1080/07362994.2022.2087677

G. Kumar, M. Mullai

Abstract Introduction This paper discusses the problem of social media addiction that pose a major threat to the human population especially children and teenagers. It is well known that Cognitive Behavioral Therapy (CBT) is an effective treatment to treat the addict individuals and delay in the treatment leads the patient to worst stage even to death. Therefore, it is important to identify the individuals who has addiction symptoms at early stage and to provide proper counseling. Method We propose and analyze a nonlinear mathematical model for social media addiction problem using case detection strategy to reduce the addiction. The basic reproduction number and equilibria of the model are computed. Further, the deterministic model is extended to delay differential equation model by incorporating transmission delay and treatment delay in the system. The local stability of different equilibria is discussed in detail. Additionally, the model is converted to stochastic model and numerical simulation is carried out to compare the results of both deterministic and stochastic model. Results Numerical result shows that the introduction of time delays can destabilize the model system and Hopf bifurcation occurs due to periodic oscillations when certain equilibrium point crosses the delay threshold limit. Our results of stochastic model show a smaller number of social media users and addict population when compared with deterministic model. Also, our results reveal that detection and counseling parameters play a vital role in reducing addiction population. Discussion Presented results clearly suggest that there is a need to use effective detection strategy and suitable counseling program to reduce the social media addiction level.

摘要引言本文讨论了社交媒体成瘾问题，社交媒体成瘾对人类尤其是儿童和青少年构成了重大威胁。众所周知，认知行为疗法（CBT）是治疗成瘾个体的有效方法，延迟治疗会导致患者进入最糟糕的阶段甚至死亡。因此，在早期识别有成瘾症状的人并提供适当的咨询是很重要的。方法我们提出并分析了社交媒体成瘾问题的非线性数学模型，使用案例检测策略来减少成瘾。计算了模型的基本繁殖数和平衡点。此外，通过在系统中引入传输延迟和处理延迟，将确定性模型扩展为延迟微分方程模型。详细讨论了不同平衡点的局部稳定性。此外，将模型转换为随机模型，并进行了数值模拟，以比较确定性和随机性模型的结果。结果数值结果表明，时滞的引入会使模型系统不稳定，当某一平衡点超过时滞阈值极限时，由于周期性振荡会产生Hopf分岔。我们的随机模型结果显示，与确定性模型相比，社交媒体用户和成瘾人群的数量更少。此外，我们的研究结果表明，检测和咨询参数在减少成瘾人群方面发挥着至关重要的作用。讨论提出的结果清楚地表明，有必要使用有效的检测策略和适当的咨询程序来降低社交媒体成瘾水平。

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引用次数: 1

Existence and uniqueness of solutions of nonlinear fractional stochastic differential systems with nonlocal functional boundary conditions 具有非局部泛函边界条件的非线性分数随机微分系统解的存在唯一性

IF 1.3 4区数学 Q3 MATHEMATICS, APPLIED

Stochastic Analysis and Applications

Pub Date : 2022-06-07 DOI: 10.1080/07362994.2022.2078839

Ouaddah Abdelhamid, J. Graef, A. Ouahab

Abstract The authors study the existence and uniqueness of solutions to nonlinear first-order fractional stochastic differential systems driven by Brownian motion and with nonlocal functional boundary conditions. The technique of proof involves Perov’s fixed point theorem with matrices that converge to zero and the Leray–Schauder theorem.

摘要研究了布朗运动驱动的具有非局部泛函边界条件的非线性一阶分数阶随机微分系统解的存在性和唯一性。证明技术涉及矩阵收敛到零的Perov不动点定理和Leray–Schauder定理。

引用次数: 0

Higher-order robust attractors for stochastic retarded degenerate parabolic equations 随机时滞退化抛物方程的高阶鲁棒吸引子

IF 1.3 4区数学 Q3 MATHEMATICS, APPLIED

Stochastic Analysis and Applications

Pub Date : 2022-06-02 DOI: 10.1080/07362994.2022.2080706

Qiangheng Zhang

Abstract We study the existence, measurability and time-dependent property of pullback random attractors in the higher-order space for stochastic degenerate parabolic equations with variable delay defined on Let X, Z be the square integrable space and the p-times (p > 2) integrable space, respectively. We first prove the existence of a unique pullback -random attractor with and and establish the forward compactness, measurability and long-time stability of the bi-spatial attractor in the higher-order space We then investigate the higher-order delay-free stability of in more precisely, the upper semicontinuity of under the topology of as the memory time tends to zero is established.

摘要研究了变时滞随机退化抛物方程在高阶空间上的拉回随机吸引子的存在性、可测性和随时间变化的性质，该方程分别定义在X, Z为平方可积空间和p倍(p > 2)可积空间上。首先证明了具有和的唯一的回拉随机吸引子的存在性，建立了双空间吸引子在高阶空间上的前向紧致性、可测性和长时间稳定性，然后进一步研究了高阶无延迟稳定性，更准确地说，在拓扑下的上半连续性随着记忆时间趋于零。

引用次数: 1

Irregular barrier reflected BSDEs driven by a Lévy process Lévy过程驱动的不规则屏障反射BSDE

IF 1.3 4区数学 Q3 MATHEMATICS, APPLIED

Stochastic Analysis and Applications

Pub Date : 2022-05-30 DOI: 10.1080/07362994.2022.2079529

M. Marzougue, M. El Otmani

Abstract We consider reflected backward stochastic differential equations driven by Teugels martingales associated with a Lévy process, in which the barrier process is optional with regulated trajectories (i.e., trajectories with left and right finite limits), which is assumed to be right upper semi-continuous. We prove the existence and uniqueness of such equations by using the predictable representations for Lévy processes due to Nualart and Schoutens, and some tools from the general theory of processes such as Mertens decomposition of optional strong supermartingales. We also discuss the case where the barrier is assumed to be completely irregular, and we establish an infinitesimal characterization of the solution in terms of a value process to an extension of the optimal stopping problem.

摘要我们考虑了由Teugels鞅驱动的与Lévy过程相关的反射后向随机微分方程，其中屏障过程是可选的，具有调节的轨迹（即具有左和右有限极限的轨迹），假设其是右上半连续的。我们利用Nualart和Schoutens的Lévy过程的可预测表示，以及过程一般理论中的一些工具，如可选强超鞅的Mertens分解，证明了这类方程的存在性和唯一性。我们还讨论了屏障被假设为完全不规则的情况，并根据最优停止问题的值过程建立了解的无穷小特征。

引用次数: 3

Parameter-dependent filtering of Gaussian processes in Hilbert spaces 希尔伯特空间中高斯过程的参数相关滤波

IF 1.3 4区数学 Q3 MATHEMATICS, APPLIED

Stochastic Analysis and Applications

Pub Date : 2022-05-29 DOI: 10.1080/07362994.2022.2080078

V. Kubelka, B. Maslowski, O. Týbl

Abstract The filtering problem for non-Markovian Gaussian processes on rigged Hilbert spaces is considered. Continuous dependence of the filter and observation error on parameters which may be present both in the signal and observation processes is proved. The general results are applied to signals governed by stochastic heat equations driven by distributed or pointwise fractional noise. The observation process may be a noisy observation of the signal at given points in the domain, the position of which may depend on the parameter.

摘要研究了装配Hilbert空间上非马尔可夫高斯过程的滤波问题。证明了滤波器和观测误差对信号和观测过程中可能存在的参数的连续依赖性。一般结果应用于由分布或逐点分数噪声驱动的随机热方程控制的信号。观测过程可以是在域中的给定点处对信号的有噪声观测，其位置可以取决于参数。

引用次数: 0

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