Unbiased Approximation of the Ergodic Measure for Piecewise α-Stable Ornstein-Uhlenbeck Processes Arising in Queueing Networks Using an Euler-Maruyama Scheme with Decreasing Step Sizes
This research paper presents a novel Euler-Maruyama (EM) scheme with decreasing step sizes to approximate the ergodic measures of piecewise α-stable Ornstein-Uhlenbeck processes, which are commonly used to model queueing networks.
A Multi-level Monte Carlo Simulation for Approximating the Invariant Distribution of a Class of Stochastic Differential Equations
This paper presents a novel numerical method for approximating the invariant distribution of Markovian switching Lévy-driven stochastic differential equations (SDEs) with super-linearly growth coefficients, combining a tamed-adaptive Euler-Maruyama scheme with a Multi-level Monte Carlo method.
経路依存型マッキーン・ブラソフ確率微分方程式の指数収縮性に関するカップリング手法とその応用
本稿では、分布依存の拡散係数を持つ経路依存型マッキーン・ブラソフ確率微分方程式（SDE）に対して、カップリング手法を用いて指数収縮性を解析する。具体的には、条件付き確率測度の変更によるカップリングを用いて対数ハルナック不等式を確立し、一様散逸条件下での相対エントロピーにおける指数収縮性を導出する。さらに、係数が部分的にのみ散逸的な場合に、漸近反射カップリングを用いて、分布に依存しない場合でも新しい結果となる、L1-ワッサーシュタイン距離における指数収縮性を導出する。
Exponential Contractivity of Path Dependent McKean-Vlasov SDEs: Coupling Methods and Applications
This paper presents new findings on the exponential contractivity of path-dependent McKean-Vlasov stochastic differential equations (SDEs) using coupling methods, establishing log-Harnack inequalities and exploring contractivity under both uniformly and partially dissipative conditions.
고확산 SDE에 대한 수정된 오일러 기법의 L2-바서슈타인 수축 및 응용: 투영 및 길들인 오일러 기법의 개선된 수렴률 분석
본 논문에서는 높은 확산성을 가진 확률 미분 방정식(SDE)에 대한 수정된 오일러 기법의 L2-바서슈타인 수축 특성을 분석하고, 이를 바탕으로 수치적 불변 확률 측도와 정확한 불변 확률 측도 사이의 비점근적 L2-바서슈타인 오차 경계를 유도하여 기존 연구보다 개선된 수렴률을 보입니다.
L2-Wasserstein Contraction of Modified Euler Schemes for SDEs: Theory and Applications to Non-Asymptotic Bounds and Strong Law of Large Numbers
This paper proves the weak L2-Wasserstein contraction of a modified Euler scheme for stochastic differential equations (SDEs) with super-linear and locally dissipative drifts under the condition of high diffusivity.
잡음 하의 강: 확률 미분 방정식에서의 점근적 동역학
이 논문은 잡음이 있는 환경에서 비자율적 미분 방정식의 해의 장기적인 동작, 특히 '강' 현상의 지속성을 탐구합니다.
Stochastic Analysis of River Phenomena in Non-Autonomous Differential Equations
This research paper investigates the persistence of "river" phenomena, observed in deterministic non-autonomous differential equations, when stochastic noise is introduced.
Large Deviation Principle for a Specific Class of Slow-Fast Systems Driven by Infinite-Dimensional Mixed Fractional Brownian Motion
This research paper presents a mathematical proof of the large deviation principle for a specific class of slow-fast systems perturbed by infinite-dimensional mixed fractional Brownian motion, providing a framework for understanding the probability of rare events in these systems.
隨機微分方程強逼近格式的弱誤差分析 II：有限矩與高階格式
本文放寬了隨機微分方程數值解的矩限制，並分析了有限矩對高階顯式格式弱收斂性的影響。
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