University of Melbourne
Stochastic Processes Seminar
Time: Wednesdays during Semester, 1pm-2pm
Location: New Seminar Room 162, Peter Hall Building
Upcoming seminars
1 May 2024
Speaker: Philip Yam (The Chinese University of Hong Kong)
Title: Mean Field Games, their FBSDEs and Master Equations
Abstract: Modeling collective behaviors of individuals in account of their mutual interactions arisen in various physical or sociological dynamical systems have been one of the major problems in the history of mankind. To resolve this matter, a completely different macroscopic approach inspired from statistical physics had been gradually developed in the last decade, which eventually leads to the primitive notion of mean field game theory. In this talk, we shall introduce a theory of global-in-time well-posedness fora general class of mean field game problems, which include as an example setting with quasi-convex payoff functions as long as the mean field sensitivity is not too large. Through the stochastic maximum principle, we adopt the forward backward stochastic differential equation (FBSDE) approach to investigate the unique existence of the corresponding equilibrium strategies. This FBSDE is first solved locally in time, then by controlling the sensitivity with respect to the initial condition of the solution to the backward equation via studying its Jacobian flow, the global-in-time solution is warranted. Further analysis of the Jacobian flow of the solution to the FBSDE will be discussed so as to establish the regularities of the value function, including its linear functional differentiability, that also leads to the classical well-posedness of the complicated one-directional master equations on R^n. In contrast to the recent approach with an emphasis on the well-posedness of the master equations, we solve the whole problem by tackling the mean field game equilibrium problems directly; indeed, we extend the well-posedness result in [P. Caradaliaguet, F. Delarue, J.-M. Lasry, and P.-L. Lions. The master equation and the convergence problem in mean field games:(ams-201).], which founds their theory on a torus in a Holder space, to the whole unbounded domain R^n via the Sobolev space language.
8 May 2024
Speaker: Aram Perez (Monash University)
Title: TBC
15 May 2024
Speaker: Kazutoshi Yamakazi (University of Queensland)
Title: TBC
22 May 2024
Speaker: Mario Kieburg (University of Melbourne)
Title: TBC
29 May 2024
Speaker: Simon Harris (University of Auckland)
Title: TBC
12 June 2024
Speaker: Allan Sly (Princeton University)
Title: TBC
Past seminars
24 April 2024 -- Greg Markowsky (Monash University) -- Ways in which the geometry of plane domains is reflected in the distribution of Brownian motion exit times
17 April 2024 -- Kostya Borovkov (University of Melbourne) -- Large deviation probabilities for random walks: Light vs heavy tails
10 April 2024 -- Nadia Sidorova (University College London) -- Edge-reinforced branching random walk on the triangle
27 March 2024 -- Vincent Liang (University of Melbourne) -- On boundary crossing probabilities of diffusion processes
20 March 2024 -- Emma Horton (University of Warwick) -- Genealogies of branching Markov processes
13 March 2024 -- Renjie Feng (University of Sydney) -- Determinantal point processes on spheres: Multivariate linear statistics
6 March 2024 -- Yuzuru Inahama (Kyushu University) -- Wong-Zakai approximation of density functions
Organisers
Xi Geng, Stephen Muirhead
To subscribe to our mailing list contact one of the organisers or subscribe directly (University of Melbourne login required):