Central Limit Theorem and Moderate Deviation Principle for McKean-Vlasov SDEs

Large Population Stochastic Dynamic Games: Closed-loop Mckean-vlasov Systems and the Nash Certainty Equivalence Principle

Abstract. We consider stochastic dynamic games in large population conditions where multiclass agents are weakly coupled via their individual dynamics and costs. We approach this large population game problem by the so-called Nash Certainty Equivalence (NCE) Principle which leads to a decentralized control synthesis. The McKean-Vlasov NCE method presented in this paper has a close connection wi...

Central Limit Theorem in Multitype Branching Random Walk

A discrete time multitype (p-type) branching random walk on the real line R is considered. The positions of the j-type individuals in the n-th generation form a point process. The asymptotic behavior of these point processes, when the generation size tends to infinity, is studied. The central limit theorem is proved.

A Large Deviation Rate and Central Limit Theorem for Horton Ratios

Moderate Deviation Principle for Exponentially Ergodic Markov Chain

For 1 2 < α < 1, we propose the MDP analysis for family

The McKean –Vlasov Equation in Finite Volume

We study the McKean–Vlasov equation on the finite tori of length scale L in d–dimensions. We (re)derive the necessary and sufficient conditions for the existence of a phase transition – first uncovered in [13] and [20]. Therein and in subsequent works, one finds indications pointing to critical transitions at a particular model dependent value, θ of the interaction parameter. We show (there is ...