機率研討會
主講者: 1.Prof.Daniel Hernandez-Hernandez(Center for Research in Mathematics, Maxico) 2.Prof. Naoyuki Ichihara(Aoyama Gakuin University, Japan)
講題: 1.Singular control problems driven by Levy processes with discretionary stopper 2.Phase transitions for controlled Markov chains on infinite graphs
時間: 2014-08-26 (Tue.)  15:00 - 17:10
地點: 數學所 617 研討室 (台大院區)
Abstract: 1.Since the fundamental work of V.E. Benes et.al. Sochastics (1980) 4, 39-82, where the problem of tracking a standard Brownian motion by a finite variation process was explicitly solved, the problems of singular control have found multiple applications in a number of fields, like queues, networks, insurance and mathematical finance. These applications are multiplied when the previous problem is accompanied by another player, which can collaborate or compete, using a discretionary stopping time. In this talk we shall present some recent results for controlled Levy processes, putting special emphasis in the applications. 2. In this talk, I will present recent results on phase transitions arising in certain stochastic optimal control problems. More precisely, we are concerned with the maximization problem of long-run-average for controlled Markov chains, or Markov decision processes, on infinite graphs. Some phase transition phenomena are observed in terms of the associated optimality equation. The results provide a stochastic control interpretation for the discrete model of homopolymers, as well as the principal eigenvalue of discrete Schrodinger operators on graphs.
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