Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userLinear Stochastic Fluid Networks: Rare-Event Simulation and Markov Modulation
105
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We consider a linear stochastic fluid network under Markov modulation, with a focus on the probability that the joint storage level attains a value in a rare set at a given point in time. The main objective is to develop efficient importance sampling algorithms with provable performance guarantees. For linear stochastic fluid networks without modulation, we prove that the number of runs needed (so as to obtain an estimate with a given precision) increases polynomially (whereas the probability under consideration decays essentially exponentially); for networks operating in the slow modulation regime, our algorithm is asymptotically efficient. Our techniques are in the tradition of the rare-event simulation procedures that were developed for the sample-mean of i.i.d. one-dimensional light-tailed random variables, and intensively use the idea of exponential twisting. In passing, we also point out how to set up a recursion to evaluate the (transient and stationary) moments of the joint storage level in Markov-modulated linear stochastic fluid networks.
rate research
Read More
In this paper we use splitting technique to estimate the probability of hitting a rare but critical set by the continuous component of a switching diffusion. Instead of following classical approach we use Wonham filter to achieve multiple goals including reduction of asymptotic variance and exemption from sampling the discrete components.
We study linear-quadratic stochastic differential games on directed chains inspired by the directed chain stochastic differential equations introduced by Detering, Fouque, and Ichiba. We solve explicitly for Nash equilibria with a finite number of players and we study more general finite-player games with a mixture of both directed chain interaction and mean field interaction. We investigate and compare the corresponding games in the limit when the number of players tends to infinity. The limit is characterized by Catalan functions and the dynamics under equilibrium is an infinite-dimensional Gaussian process described by a Catalan Markov chain, with or without the presence of mean field interaction.
The study of linear-quadratic stochastic differential games on directed networks was initiated in Feng, Fouque & Ichiba cite{fengFouqueIchiba2020linearquadratic}. In that work, the game on a directed chain with finite or infinite players was defined as well as the game on a deterministic directed tree, and their Nash equilibria were computed. The current work continues the analysis by first developing a random directed chain structure by assuming the interaction between every two neighbors is random. We solve explicitly for an open-loop Nash equilibrium for the system and we find that the dynamics under equilibrium is an infinite-dimensional Gaussian process described by a Catalan Markov chain introduced in cite{fengFouqueIchiba2020linearquadratic}. The discussion about stochastic differential games is extended to a random two-sided directed chain and a random directed tree structure.
In this paper we address the problem of rare-event simulation for heavy-tailed Levy processes with infinite activities. We propose a strongly efficient importance sampling algorithm that builds upon the sample path large deviations for heavy-tailed Levy processes, stick-breaking approximation of extrema of Levy processes, and the randomized debiasing Monte Carlo scheme. The proposed importance sampling algorithm can be applied to a broad class of Levy processes and exhibits significant improvements in efficiency when compared to crude Monte-Carlo method in our numerical experiments.
The Cross Entropy method is a well-known adaptive importance sampling method for rare-event probability estimation, which requires estimating an optimal importance sampling density within a parametric class. In this article we estimate an optimal importance sampling density within a wider semiparametric class of distributions. We show that this semiparametric version of the Cross Entropy method frequently yields efficient estimators. We illustrate the excellent practical performance of the method with numerical experiments and show that for the problems we consider it typically outperforms alternative schemes by orders of magnitude.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
