Ergodic Markov processes and Poisson equations (lecture notes)

By Alexander Yur'evich Veretennikov. 2016

12 citations recorded by the source corpus.

These are lecture notes on the subject defined in the title. As such, they do not pretend to be really new, probably except for the only section about Poisson equations with potentials. Yet, the hope of the author is that they may serve as a bridge to the important area of Poisson equations "in the whole space" and with a parameter, the latter theme not being presented here. Why this area is so important was explained in many papers and books (see the references [12, 34, 35]): it provides one of the main tools in diffusion approximation in the area stochastic averaging. Hence, the aim of these lectures is to prepare the reader to "real" Poisson equations -- i.e., for differential operators instead of difference operators -- and, indeed, to diffusion approximation. Among other presented topics we mention coupling method.

Subfields: Finance, Statistical and Nonlinear Physics, Statistics and Probability

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Citations in the corpus

• RUDDER: Return Decomposition for Delayed Rewards (2018, background): “quation or Poisson equation. For the Poisson equation see Equation 33 to Equation 37 for the undiscounted case and Equation 34 and Equation 43 for the discounted case in Alexander Veretennikov, 2016, [137]. This form of the Poisson equation describes the Dirichlet boundary value problem. The Bellman”