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A Direct Reduction from Stochastic Parity Games to Simple Stochastic Games
Rapha\"el Berthon, Joost-Pieter Katoen, Zihan Zhou
https://arxiv.org/abs/2506.06223

A Direct Reduction from Stochastic Parity Games to Simple Stochastic Games
Significant progress has been recently achieved in developing efficient solutions for simple stochastic games (SSGs), focusing on reachability objectives. While reductions from stochastic parity games (SPGs) to SSGs have been presented in the literature through the use of multiple intermediate game models, a direct and simple reduction has been notably absent. This paper introduces a novel and direct polynomial-time reduction from quantitative SPGs to quantitative SSGs. By leveraging a gadget-b…

Amid Trump's order, California tries to not play into his hands (Los Angeles Times)
https://www.latimes.com/california/story/2025-06-08/california-political-stakes
http://www.memeorandum.com/250609/p14#a250609p14

Invariant measures for stochastic Burgers equation on unbounded domains
Zhenxin Liu, Zhiyuan Shi
https://arxiv.org/abs/2506.07119 https://

Invariant measures for stochastic Burgers equation on unbounded domains
In this paper, we investigate the stochastic damped Burgers equation with multiplicative noise defined on the entire real line. We demonstrate the existence and uniqueness of a mild solution to the stochastic damped Burgers equation and establish that the solution is uniformly bounded in time. Furthermore, by employing the uniform estimates on the tails of the solution, we obtain the tightness of a family of probability distributions of the solution. Subsequently, by applying the Krylov-Bogolio…

The Raiders' Many Unknowns Make Them Exciting Heading into 2025 https://www.si.com/nfl/raiders/chip-kelly-las-vegas-eric-stokes-isaiah-pola-mao

Stochastic maximum principle for optimal control problem of non exchangeable mean field systems
Idris Kharroubi, Samy Mekkaoui, Huy\^en Pham
https://arxiv.org/abs/2506.05595

Stochastic maximum principle for optimal control problem of non exchangeable mean field systems
We study the Pontryagin maximum principle by deriving necessary and sufficient conditions for a class of optimal control problems arising in non exchangeable mean field systems, where agents interact through heterogeneous and asymmetric couplings. Our analysis leads to a collection of forward-backward stochastic differential equations (FBSDE) of non exchangeable mean field type. Under suitable assumptions, we establish the solvability of this system. As an illustration, we consider the linear-q…

Cisco unveils updated networking and security products, including a new generation of switches with 10x performance, to boost AI networks and cut bottlenecks (Dina Bass/Bloomberg)
https://www.bloomberg.com/news/articles/20

Tensor Stochastic Regression for High-dimensional Time Series via CP Decomposition
Shibo Li, Yao Zheng
https://arxiv.org/abs/2506.06919 https://

Tensor Stochastic Regression for High-dimensional Time Series via CP Decomposition
As tensor-valued data become increasingly common in time series analysis, there is a growing need for flexible and interpretable models that can handle high-dimensional predictors and responses across multiple modes. We propose a unified framework for high-dimensional tensor stochastic regression based on CANDECOMP/PARAFAC (CP) decomposition, which encompasses vector, matrix, and tensor responses and predictors as special cases. Tensor autoregression naturally arises as a special case within th…

Operators of stochastic adding machines and Julia sets
Danilo Caprio, Ali Messaoudi, Ioannis Tsokanos, Glauco Valle
https://arxiv.org/abs/2506.05703 https:…

Operators of stochastic adding machines and Julia sets
A stochastic adding machine is a Markov chain on the set of non-negative integers $\mathbb{Z}_{+}$ that models the process of adding one by successively updating the digits of a number's expansion in a given numeration system. At each step, random failures may occur, interrupting the procedure and preventing it from continuing beyond a certain point. The first model of such a stochastic adding machine, constructed for the binary base, was introduced by Killeen and Taylor. Their work was motiv…

Value-Set Iteration: Computing Optimal Correlated Equilibria in Infinite-Horizon Multi-Player Stochastic Games
Jiarui Gan, Rupak Majumdar
https://arxiv.org/abs/2506.07186

Value-Set Iteration: Computing Optimal Correlated Equilibria in Infinite-Horizon Multi-Player Stochastic Games
We study the problem of computing optimal correlated equilibria (CEs) in infinite-horizon multi-player stochastic games, where correlation signals are provided over time. In this setting, optimal CEs require history-dependent policies; this poses new representational and algorithmic challenges as the number of possible histories grows exponentially with the number of time steps. We focus on computing $(ε, δ)$-optimal CEs -- solutions that achieve a value within $ε$ of an optimal CE, while al…

Alibaba, Tencent, and other Chinese AI companies temporarily disabled chatbot functions like image recognition during China's annual college entrance exams (Luz Ding/Bloomberg)
https://www.bloomberg.com/news/articles/20