Prof. Wanyang Dai
Prof. Wanyang Dai
Nanjing University, China
Title: Stochastic Differential Games and Stochastic Partial Differential Equations with Levy Jumps
We formulate a stochastic differential game (SDG) problem with q players, which is driven by Levy Big Data (i.e., a general-dimensional vector Levy process). Both non-zero-sum and zero-sum games are considered. The well-known AlphaGo and AlphaGo Zero aided Go games are covered. By establishing a vector-form Ito-Ventzell's formula and a 4-tuple vector-field solution to a unified system of stochastic partial differential equations (SPDEs), we get a BestGo policy process to the game, i.e., a Pareto optimal Nash equilibrium policy process or a saddle point policy process to the SDG in a non-zero-sum or a zero-sum sense. The unified SPDE is in a vector-form and forward-backward coupling manner. The partial differential operators in its drift, diffusion, and jump coefficients are in time-variable and position-parameters over a domain (e.g., a hyperbox or a manifold). Since the unified system is a general-dimensional vector-form one with general nonlinearity and general high-order, the popular computation (e.g., integration by parts) based proving method can not be applied. Thus, by constructing a supporting topological space, we develop an approach to prove the unique existence of an adapted 4-tuple strong solution to the system under general local linear growth and Lipschitz conditions.
Finally, examples in quantum physics, queueing game, and Go game are also presented.
Wanyang Dai is a Distinguished Professor in Mathematics Department of Nanjing University, President & CEO of U.S. based (Industrial 6.0) SIR Forum, a Special Guest Expert in Jiangsu FinTech Research Center, President of Jiangsu Probability & Statistics Society, Chairman of Jiangsu Big Data-Blockchain and Smart Information Special Committee, Editor-in-Chief of Journal of Advances in Applied Mathematics, editors of over 20 international journals ranging from pure mathematics to its applications (e.g., Wireless Engineering and Technology, Artificial Intelligence), General Chairs and plenary/keynote speakers of over 30 IEEE and international conferences.  

His research includes stochastic processes related optimization and Pareto optimal control/game, admission/scheduling/routing protocols and performance analysis/optimization for BigData-Blockchain oriented quantum-cloud computing and wireless/wireline communication systems, forward/backward stochastic (ordinary/partial) differential equations and their applications to queueing systems, Internet of Things, energy and power engineering. His "influential" papers are published in "big name" journals, e.g., Operations Research, Communications in Mathematical Sciences, Journal of Computational and Applied Mathematics, Queueing Systems, Mathematical and Computer Modeling of Dynamical Systems. His researches were awarded as outstanding papers by academic societies, e.g., IEEE Top Conference Series.

He received his Ph.D degree in applied mathematics jointly with industrial engineering and systems engineering from Georgia Institute of Technology, U.S.A., in 1996, where he worked on stochastics and applied probability concerning network performance modeling and analysis, algorithm design and implementation via stochastic diffusion approximation. The breakthrough results and methodologies developed in his thesis were cited, used, and claimed as "contemporaneous and independent" achievements by other subsequent breakthrough papers that were presented as "45 minute invited talk in probability and statistics" in International Congress of Mathematicians (ICM) 1998, which is the most privilege honor in the mathematical society. The designed finite element-Galerkin algorithm to compute the stationary distributions of reflecting Brownian motions (weak solutions of general dimensional partial differential equations) is also well-known to the related fields.

He was an MTS (permanent) in End-to-End Network Architecture Department of AT&T Bell Labs (now called Nokia Bell Labs) in U.S.A. from 1996-1999, where he was principal investigators and developers of several projects in telecommunication network architecture and design, network performance and financial engineering, operating system and database development to support various intelligent engines/models for strategy planning and BigData analytics in a "Plug-in and Play" manner, with some (nowadays called cloud computing) project won "Technology Transfer".