human: Given a hyperedge-centered hypergraph: <hypergraph>, where the center hyperedge is induced by one source paper and its member nodes are the cited papers.

Details of the hypergraph:
Center hyperedge (induced by source paper "ergodic theory for controlled markov chains with stationary inputs"):
  Abstract: Consider a stochastic process X on a finite state space X = {1,. .. , d}. It is conditionally Markov, given a real-valued 'input process' ζ. This is assumed to be small, which is modeled through the scaling, ζ t = eζ 1 t , 0 ≤ e ≤ 1 , where ζ 1 is a bounded stationary process. The following conclusions are obtained, subject to smoothness assumptions on the controlled transition matrix and a mixing condition on ζ: (i) A stationary version of the process is constructed, that is coupled with a stationary version of the Markov chain X • obtained with ζ ≡ 0. The triple (X, X • , ζ) is a jointly stationary process satisfying P{X(t) = X • (t)} = O(e) Moreover, a second-order Taylor-series approximation is obtained: P{X(t) = i} = P{X • (t) = i} + e 2 π (2) (i) + o(e 2), 1 ≤ i ≤ d, with an explicit formula for the vector π (2) ∈ R d. (ii) For any m ≥ 1 and any function f : {1,. .. , d} × R → R m , the stationary stochastic process Y (t) = f (X(t), ζ(t)) has a power spectral density S f that admits a second order Taylor series expansion: A function S (2) f : [−π, π] → C m×m is constructed such that S f (θ) = S • f (θ) + e 2 S (2) f (θ) + o(e 2), θ ∈ [−π, π] in which the first term is the power spectral density obtained with e = 0. An explicit formula for the function S (2) f is obtained, based in part on the bounds in (i). The results are illustrated with two general examples: mean field games, and a version of the timing channel of Anantharam and Verdu.

Includes members:
  Member "state estimation for the individual and the population in mean field control with application to demand dispatch":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "estimation and control of quality of service in demand dispatch")
  Member "estimation and control of quality of service in demand dispatch":
    also connected through other hyperedges:
      (none)

Question: Please tell me which class the source paper belongs to. The 40 classes are: cs.NA(Numerical Analysis), cs.MM(Multimedia), cs.LO(Logic in Computer Science), cs.CY(Computers and Society), cs.CR(Cryptography and Security), cs.DC(Distributed, Parallel, and Cluster Computing), cs.HC(Human-Computer Interaction), cs.CE(Computational Engineering, Finance, and Science), cs.NI(Networking and Internet Architecture), cs.CC(Computational Complexity), cs.AI(Artificial Intelligence), cs.MA(Multiagent Systems), cs.GL(General Literature), cs.NE(Neural and Evolutionary Computing), cs.SC(Symbolic Computation), cs.AR(Hardware Architecture), cs.CV(Computer Vision and Pattern Recognition), cs.GR(Graphics), cs.ET(Emerging Technologies), cs.SY(Systems and Control), cs.CG(Computational Geometry), cs.OH(Other Computer Science), cs.PL(Programming Languages), cs.SE(Software Engineering), cs.LG(Machine Learning), cs.SD(Sound), cs.SI(Social and Information Networks), cs.RO(Robotics), cs.IT(Information Theory), cs.PF(Performance), cs.CL(Computation and Language), cs.IR(Information Retrieval), cs.MS(Mathematical Software), cs.FL(Formal Languages and Automata Theory), cs.DS(Data Structures and Algorithms), cs.OS(Operating Systems), cs.GT(Computer Science and Game Theory), cs.DB(Databases), cs.DL(Digital Libraries), cs.DM(Discrete Mathematics). Directly output the class name.

gpt: cs.PF(Performance)