KeyNote Speaker Committee
  • Prof. Wanyang Dai
  • Prof. Wanyang Dai
  • Nanjing University, China
  • Title: A Unified B-SPDE with Levy Jumps: Well-Posedness, Algorithm with Numerics, and Applications
  • Abstract: We study the adapted strong solution and design an algorithm with numerics for a unified backward stochastic partial differential equation (B-SPDE) with Levy jumps. The B-SPDE is vector-valued, whose drift, diffusion, and jump coefficients may involve nonlinear and high-order partial differential operators. Under certain generalized local Lipschitz and linear growth conditions, the well-posedness (existence and uniqueness) of an adapted strong solution to the B-SPDE is proved over suitably constructed functional topological space. The algorithm is based on completely discrete schemes with respect to both time and space. The analysis about the error estimation or the rate of convergence of the algorithm is conducted. The key used in the numerics is to develop new theory for random field Malliavin calculus to prove the well-posedness of adapted strong solutions to the first-order and second-order Malliavin derivative based B-SPDEs under random environments over related Sobolev spaces. We also study the applications of our unified B-SPDE in several areas: optimal control and stochastic differential game problems with jumps and general number of q players (e.g., stochastic Hamilton-Jacobi-Bellman equations with jumps related to a non-Markovian system of coupled forward-backward SDEs); system synchronization and tracking problem; finance engineering (e.g., optimal portfolio decision-making and hedging with external random risk factors); cloud computing, service, and communication systems (e.g., reflecting diffusion processes associated with queueing networks); statistical physics and quantum mechanics (e.g., backward stochastic Schrodinger equation associated with quantum Hall and Anomalous Hall effects); boundary-value problem (e.g., stochastic Dirichlet-Poisson problem); nonlinear filtering (e.g., backward Zakai and Kushner equations); system biology (e.g., genealogy).
  • Biography: Wanyang Dai received his Ph.D degree in applied mathematics jointly with industrial engineering and systems engineering from Georgia Institute of Technology, Atlanta, GA, 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 some 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 finite element algorithm designed and implemented in the thesis to compute the stationary distributions of reflecting Brownian motions living in general-dimensional state space is also well-known to the related fields.
    He was a MTS (permanent) in End-to-End Network Architecture Department of AT&T Bell Labs and then (Alcatel-)Lucent Bell Labs/Network Systems, Atlanta, GA and Warren, NJ, U.S.A., from 1996-1999, where he was a principal investigator and developer of several projects in telecommunication network architecture and design, network performance and financial engineering, operating system and database development, etc. with some won "Technology Transfer".
    He is a full professor since 2004 in Nanjing University, where his research includes stochastic processes related optimization and optimal control, admission/scheduling/routing protocols and performance analysis/optimization for cloud computing and the next generation of wireless and wireline communication systems, forward/backward stochastic (ordinary/partial) differential equations and their applications to queueing systems, communication networks, financial engineering, etc. His achievements are published in "big name" journals: Operations Research, Queueing Systems, etc.
    He is an Editor-in-Chief of International Journal of Information Engineering, an editor or a member of editorial board of over 30 international journals, General Chairs and TPC members of over 20 IEEE and other International conferences, Vice Presidents and standing directors of several probability, statistics, and operations research societies.
    He was a visiting scholar in Academy of Mathematics and Systems Science of China,Beijing, China, in 2001, a Long Term Participant of IMA Annual Program of Probability and Statistics in Complex Systems: Financial Engineering, Communication Networks and Genomics in Institute of Mathematics and Its Applications (IMA), Minneapolis, U.S.A., in 2004, a visiting professor in Department of Systems Engineering and Engineering Management in Chinese University of Hong Kong, Hong Kong, China, in 2007.

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April 14-16, 2015
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December 11, 2014  >> February 16, 2015
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