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Large deviation limits of invariant measures 不变测度的大偏差极限
4区 数学 Q3 STATISTICS & PROBABILITY Pub Date : 2023-10-06 DOI: 10.1142/s0219493723500521
Anatolii A. Puhalskii
This paper is concerned with the general theme of relating the Large Deviation Principle (LDP) for the invariant measures of stochastic processes to the associated sample path LDP. It is shown that if the sample path deviation function possesses certain structure and the invariant measures are exponentially tight, then the LDP for the invariant measures is implied by the sample path LDP, no other properties of the stochastic processes in question being material. As an application, we obtain an LDP for the stationary distributions of jump diffusions. Methods of large deviation convergence and idempotent probability play an integral part.
本文讨论了随机过程不变测度的大偏差原理与相关样本路径的大偏差原理之间的关系。结果表明,如果样本路径偏差函数具有一定的结构,且不变测度是指数紧的,则不变测度的LDP由样本路径LDP隐含,而随机过程的其他性质无关紧要。作为应用,我们得到了跳跃扩散平稳分布的LDP。大偏差收敛和幂等概率的方法是其中不可或缺的一部分。
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引用次数: 4
Data-driven method to extract mean exit time and escape probability for dynamical systems driven by Levy noises 基于数据驱动的列维噪声驱动动力系统平均退出时间和逃逸概率提取方法
4区 数学 Q3 STATISTICS & PROBABILITY Pub Date : 2023-10-06 DOI: 10.1142/s0219493723400075
Linghongzhi Lu, Yang Li, Xianbin Liu
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引用次数: 0
Uniform large deviations of fractional stochastic equations with polynomial drift on unbounded domains 无界域上具有多项式漂移的分数阶随机方程的一致大偏差
IF 1.1 4区 数学 Q3 STATISTICS & PROBABILITY Pub Date : 2023-09-01 DOI: 10.1142/s0219493723500491
Bixiang Wang
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引用次数: 0
GAUSSIAN STRUCTURE IN COALESCING STOCHASTIC FLOWS 聚并随机流中的高斯结构
IF 1.1 4区 数学 Q3 STATISTICS & PROBABILITY Pub Date : 2023-09-01 DOI: 10.1142/s021949372350048x
A. Dorogovtsev, K.V. Hlyniana
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引用次数: 0
Results on approximate controllability results for fractional stochastic delay differential systems of order r ∈ (1,2) 阶r∈(1,2)的分数阶随机时滞微分系统的近似可控性结果
IF 1.1 4区 数学 Q3 STATISTICS & PROBABILITY Pub Date : 2023-09-01 DOI: 10.1142/s0219493723500478
C. Dineshkumar, V. Vijayakumar, R. Udhayakumar, K. Nisar, A. Shukla
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引用次数: 0
Central Exponents of Linear Stochastic Differential Algebraic Equations of Index 1 指数为1的线性随机微分代数方程的中心指数
IF 1.1 4区 数学 Q3 STATISTICS & PROBABILITY Pub Date : 2023-08-10 DOI: 10.1142/s0219493723500454
Nguyen Thi The
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引用次数: 0
Quadratic BSDEs with mean reflection driven by G-Brownian motion 由g -布朗运动驱动的平均反射二次BSDEs
IF 1.1 4区 数学 Q3 STATISTICS & PROBABILITY Pub Date : 2023-07-14 DOI: 10.1142/s0219493723500442
Zihao Gu, Yiqing Lin, Kun Xu
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引用次数: 0
Stochastic newton equations in the strong potential limit for the multi-dimensional case 多维情况下强势极限下的随机牛顿方程
IF 1.1 4区 数学 Q3 STATISTICS & PROBABILITY Pub Date : 2023-07-14 DOI: 10.1142/s0219493723500430
Song Liang
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引用次数: 0
The asymptotic behaviour of solutions for stochastic evolution equations with pantograph delay 具有受电弓延迟的随机演化方程解的渐近性态
IF 1.1 4区 数学 Q3 STATISTICS & PROBABILITY Pub Date : 2023-07-14 DOI: 10.1142/s0219493723500429
Yarong Liu, Yejuan Wang, T. Caraballo
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引用次数: 0
Theoretical analysis and numerical approximation for the stochastic thermal quasi-geostrophic model 随机热准地转模式的理论分析与数值逼近
IF 1.1 4区 数学 Q3 STATISTICS & PROBABILITY Pub Date : 2023-07-05 DOI: 10.1142/s0219493723500399
Dan Crisan, Darryl D. Holm, Oana Lang, Prince Romeo Mensah, Wei Pan

This paper investigates the mathematical properties of a stochastic version of the balanced 2D thermal quasigeostrophic (TQG) model of potential vorticity dynamics. This stochastic TQG model is intended as a basis for parametrization of the dynamical creation of unresolved degrees of freedom in computational simulations of upper ocean dynamics when horizontal buoyancy gradients and bathymetry affect the dynamics, particularly at the submesoscale (250m–10km). Specifically, we have chosen the Stochastic Advection by Lie Transport (SALT) algorithm introduced in [D. D. Holm, Variational principles for stochastic fluid dynamics, Proc. Roy. Soc. A: Math. Phys. Eng. Sci.471 (2015) 20140963, http://dx.doi.org/10.1098/rspa.2014.0963] and applied in [C. Cotter, D. Crisan, D. Holm, W. Pan and I. Shevchenko, Modelling uncertainty using stochastic transport noise in a 2-layer quasi-geostrophic model, Found. Data Sci.2 (2020) 173, https://doi.org/10.3934/fods.2020010; Numerically modeling stochastic lie transport in fluid dynamics, SIAM Multiscale Model. Simul.17 (2019) 192–232, https://doi.org/10.1137/18M1167929] as our modeling approach. The SALT approach preserves the Kelvin circulation theorem and an infinite family of integral conservation laws for TQG. The goal of the SALT algorithm is to quantify the uncertainty in the process of up-scaling, or coarse-graining of either observed or synthetic data at fine scales, for use in computational simulations at coarser scales. The present work provides a rigorous mathematical analysis of the solution properties of the thermal quasigeostrophic (TQG) equations with SALT [D. D. Holm and E. Luesink, Stochastic wave-current interaction in thermal shallow water dynamics, J. Nonlinear Sci.31 (2021), https://doi.org/10.1007/s00332-021-09682-9; D. D. Holm, E. Luesink and W. Pan, Stochastic mesoscale circulation dynamics in the thermal ocean, Phys. Fluids33 (2021) 046603, https://doi.org/10.1063/5.0040026].

本文研究了位涡动力学平衡二维热准地转(TQG)随机模型的数学性质。当水平浮力梯度和水深测量影响上层海洋动力学时,特别是在亚中尺度(250m-10km),该随机TQG模型旨在作为上层海洋动力学计算模拟中未解决自由度动力学参数化的基础。具体而言,我们选择了[D]中介绍的随机平流by Lie Transport (SALT)算法。D. Holm,随机流体动力学的变分原理,罗伊出版社。Soc。答:数学。理论物理。Eng。Sci.471 (2015) 20140963, http://dx.doi.org/10.1098/rspa.2014.0963],并应用于[C]。Cotter, D. Crisan, D. Holm, W. Pan和I. Shevchenko,在2层准地转模型中使用随机输运噪声建模不确定性,发现。数据科学2 (2020)173,https://doi.org/10.3934/fods.2020010;流体动力学中随机lie输运的数值模拟,SIAM多尺度模型。Simul.17 (2019) 192-232, https://doi.org/10.1137/18M1167929]作为我们的建模方法。SALT方法保留了开尔文循环定理和TQG的无穷一族积分守恒定律。SALT算法的目标是量化放大过程中的不确定性,或者在精细尺度上对观测数据或合成数据进行粗粒度处理,以便在更大尺度上进行计算模拟。本文对含SALT的热准地转(TQG)方程的解性质进行了严格的数学分析[D]。D. Holm和E. Luesink,热浅水动力学随机波流相互作用[j] .非线性科学31 (2021),https://doi.org/10.1007/s00332-021-09682-9;黄晓明,黄晓明,黄晓明,热海洋随机中尺度环流动力学,物理学报。流体学报,33 (2021)046603,https://doi.org/10.1063/5.0040026]。
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引用次数: 0
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