On a stochastic version of Prouse model in fluid dynamics

On the excursions of reflected local time processes and stochastic fluid queues

This paper extends previous work by the authors. We consider the local time process of a strong Markov process, add negative drift, and reflect it à la Skorokhod. The resulting process is used to model a fluid queue. We derive an expression for the joint law of the duration of an excursion, the maximum value of the process on it, and the time distance between successive excursions. We work with a properly constructed stationary version of the process. Examples are also given in the paper.

The geometry of big queues

We use Hamilton equations to find optimal paths to big queues in Jackson networks. They are shown to be given by fluid trajectories of the dual network. The fluid equations are shown to be dual to the Hamilton equations. Thus, a version of the extended Onzager-Machlup principle is proved: a fluctuation trajectory is the time reversal of a relaxation trajectory of the dual dynamic. The case of a two-node network is given a geometric treatment.

Analysis of stochastic fluid queues driven by local time processes

We consider a stochastic fluid queue served by a constant rate server and driven by a process which is the local time of a certain Markov process. Such a stochastic system can be used as a model in a priority service system, especially when the time scales involved are fast. The input (local time) in our model is always singular with respect to the Lebesgue measure which in many applications is ``close'' to reality. We first discuss how to rigorously construct the (necessarily) unique stationary version of the system under some natural stability conditions. We then consider the distribution of…

最优传输与施罗德inger桥的关系：一个随机控制的观点

On the relation between optimal transport and Schrödinger bridges: A stochastic control viewpoint

从随机控制视角重新审视最优传输与施罗德inger桥的关系，揭示其更丰富的联系，提出新的流体动力学版本并探讨其与最优传输的连接。

Bounds on the heat transfer rate via passive advection

In heat exchangers, an incompressible fluid is heated initially and cooled at the boundary. The goal is to transfer the heat to the boundary as efficiently as possible. In this paper we study a related steady version of this problem where a steadily stirred fluid is uniformly heated in the interior and cooled on the boundary. For a given large Péclet number, how should one stir to minimize some norm of the temperature? This version of the problem was previously studied by Marcotte, Doering et\ al.\ (SIAM Appl.\ Math '18) in a disk, where the authors used matched asymptotics to show that when t…

带Navier边界条件的随机三阶流体方程的局部强解

Local strong solutions to the stochastic third grade fluid equations with Navier boundary conditions

本文研究二维和三维有界域上受非线性乘性Wiener噪声驱动的三阶非牛顿流体，结合截断逼近、随机紧性论证与Yamada-Watanabe定理，证明了取值于H^3的局部强路径解的存在唯一性。