Path-dependent Poisson random measures and stochastic integrals constructed from general point processes

Abstract

In this paper, we consider an extension of the Poisson random measure for the formulation of continuous-time reinforcement learning, such that both the frequency and the width of the jumps depend on the path. Starting from a general point process, we define a new Poisson random measure as limit of the linear sum of these counting processes, and name it the Mesgaki random measure. We also construct its Stochastic integral and Itô's formula.

It was clearly too playful in the way the words were chosen. arXiv admin note: the author affiliation in the paper is incorrect

References in corpus (1)

• Incremental Reinforcement Learning --- a New Continuous Reinforcement Learning Frame Based on Stochastic Differential Equation methods