标题： 广义Feller理论的后果 显示英文标题

标题： Ramifications of generalized Feller theory

摘要： 广义Feller理论为非局部紧状态空间提供了重要的Feller理论类比。 这对于某些随机偏微分方程的解、分数过程的马尔可夫提升或无限维仿射和多项式过程在签名随机微分方程理论中的显著应用非常有用。 我们扩展了与广义Feller过程相关的几个常识性结果，特别是关于它们的构造和路径性质，并以完整细节提供了通常相当复杂的证明。 我们还引入了扩展Feller过程的新概念，并将其与标准和广义的Feller过程进行比较。 一个关键的例子通过特征方法将广义Feller半群与代数同态联系到传输方程和加权空间上的连续半流，即处理加权空间上微分方程的一种显著通用方法。 我们还提供了一个反例，表明广义Feller半群的基本定义中的任何条件都不能被省略。 显示英文摘要

摘要： Generalized Feller theory provides an important analog to Feller theory beyond locally compact state spaces. This is very useful for solutions of certain stochastic partial differential equations, Markovian lifts of fractional processes, or infinite dimensional affine and polynomial processes which appear prominently in the theory of signature stochastic differential equations. We extend several folklore results related to generalized Feller processes, in particular on their construction and path properties, and provide the often quite sophisticated proofs in full detail. We also introduce the new concept of extended Feller processes and compare them with standard and generalized ones. A key example relates generalized Feller semigroups of algebra homomorphisms via the method of characteristics to transport equations and continuous semiflows on weighted spaces, i.e. a remarkably generic way to treat differential equations on weighted spaces. We also provide a counterexample, which shows that no condition of the basic definition of generalized Feller semigroups can be dropped.