Stochastic comparisons of Itô processes
Stochastic comparisons are results in terms of the stochastic ordering \(\leq_{st}\), where, for random variables \(X_ 1\) and \(X_ 2\) taking values in a partially ordered measurable space, \(X_ 1\leq_{st}X_ 2\) if \(Eg(X_ 1)\leq Eg(X_ 2)\) for every increasing positive measurable function \(g\) on that space. Here the authors consider general Itô processes (i.e. solutions of stochastic differential equations of jump type). The laws of such processes are given essentially by three deterministic functions governing the drift, diffusion and jumps. This representation is particularly useful for stochastic comparisons, ``because it loads all the randomness onto the standard processes (Brownian and Poisson)''. Here stochastic comparisons for Itô processes are provided in terms of these deterministic functions. Results on semi- martingale Hunt processes are also supplied, and the detrimental effect of time changes on such comparisons is displayed.
scientific article; zbMATH DE number 167142
scientific article