Piecewise-Deterministic Markov Processes: A General Class of Non-Diffusion Stochastic Models
本文引入一类非扩散随机模型，用于研究排队系统、库存理论和资源分配中的优化问题，并发展了随机微积分，给出了扩展生成元的完整刻画。
SUMMARY A general class of non-diffusion stochastic models is introduced with a view to providing a framework for studying optimization problems arising in queueing systems, inventory theory, resource allocation and other areas. The corresponding stochastic processes are Markov processes consisting of a mixture of deterministic motion and random jumps. Stochastic calculus for these processes is developed and a complete characterization of the extended generator is given; this is the main technical result of the paper. The relevance of the extended generator concept in applied problems is discussed and some recent results on optimal control of piecewise-deterministic processes are described.