Conic martingales from stochastic integrals
定义了锥形鞅（在给定边界内演化的鞅），提供了构造方法，并重点研究了[0,1]区间内的鞅，发现其中一种具有可分离扩散系数且可通过高斯扩散的时齐映射得到，最后用单变量和双变量随机条件生存概率建模示例。
Abstract In this paper, we introduce the concept of conic martingales . This class refers to stochastic processes that have the martingale property but that evolve within given (possibly time‐dependent) boundaries. We first review some results about the martingale property of solution to driftless stochastic differential equations. We then provide a simple way to construct and handle such processes. Specific attention is paid to martingales in [0, 1]. One of these martingales proves to be analytically tractable. It is shown that up to shifting and rescaling constants, it is the only martingale (with the trivial constant, Brownian motion, and geometric Brownian motion) having a separable diffusion coefficient and that can be obtained via a time‐homogeneous mapping of Gaussian diffusions . The approach is exemplified by modeling stochastic conditional survival probabilities in the univariate and bivariate cases.