We derive the existence of infinite level GREM-like K-processes by taking the limit of a sequence of finite level versions of such processes as the number of levels diverges. The main step in the derivation is obtaining the convergence of the sequence of underlying finite level clock processes. This is accomplished by perturbing these processes so as to turn them into martingales, and resorting to martingale convergence to obtain convergence for the perturbed clock processes; nontriviality of the limit requires a specific choice of parameters of the original process; we conclude the step by showing that the perturbation washes away in the limit. The perturbation is done by inserting suitable factors into the expression of the clocks, as well as rescaling the resulting expression suitably; the existence of such factors is itself established through martingale convergence.

我们通过采用有限数量的这种过程的有限级版本序列的限制来推导无限级类GREM样K过程的存在，这是由于级数不同所致。推导的主要步骤是获得底层有限级时钟处理序列的收敛性。这是通过扰动这些过程以使其成为into而实现的，并借助mar的收敛来获得扰动的时钟过程的收敛；极限的琐碎性要求对原始过程的参数进行特定选择；我们通过显示扰动在极限范围内冲刷来结束该步骤。通过在时钟的表达式中插入合适的因子，并适当地调整结果的表达式，来完成扰动。