| 个人简介 | |
|---|---|
 Prof. Wanyang Dai Nanjing University, China |
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| 标题： AI Based Simulation and Analysis by Malliavin Calculus for Backward Stochastic Partial Differential Equations | |
| 摘要： We develop a generic convolution neural network (CNN) based scheme to simulate the 2-tuple adapted strong solution in a classical sense to a generalized Cauchy (or called terminal-value) problem, i.e., to a unified system of stochastic partial differential equations (B-SPDEs including infinite-dimensional B-SDEs) driven by Brownian motions. The scheme consists of two convolution parts: W layers of backward networks and L layers of reinforcement iterations. More importantly, it is a completely discrete and iterative algorithm in terms of both time and space with mean-square convergence supported by both theoretical proof and numerical examples. In doing so, the system is assumed to be high-dimensional and vector-valued, whose drift and diffusion coefficients may involve nonlinear and high-order partial differential operators. Under general local Lipschitz and linear growth conditions, the unique existence of the 2-tuple adapted strong solution to the system is proved by constructing a suitable Banach space to handle the difficulty that the partial differential orders on both sides of these equations are different. During the proof, we also develop new techniques of random field Malliavin calculus to show the unique existence of 2-tuple adapted strong solutions to two embedded systems of the first-order and second-order Malliavin derivative based B-SPDEs under random environments. | |
| 简介： Wanyang Dai is a Distinguished Professor in Mathematics Department of Nanjing University, a Special Guest Expert in Jiangsu FinTech Research Center, President of Jiangsu Probability & Statistics Society, and Editor-in-Chief of Journal of Advances in Applied Mathematics, where 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". He is also 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 20 IEEE and international conferences, member/group leader of judge committee in mathematics for National Natural Science Awards of China. He was a visiting scholar in Academy of Mathematics and Systems Science of China, a Long Term Participant of IMA Annual Program of Probability and Statistics in Complex Systems: Financial Engineering, Communication Networks and Genomics in (U.S. based) Institute of Mathematics and Its Applications (IMA), a visiting professor in Department of Systems Engineering and Engineering Management in Chinese University of Hong Kong. | |
