Abstract

We find new conditions for existence of strong solutions of ordinary differential equations with random right-hand side, stochastic differential equations with measurable random drift, and their trajectory analogs with symmetric integrals. We show that solutions of Itô equations satisfy a parabolic equation along trajectories of a Wiener process.

中文翻译：

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随机微分方程的强解及其轨迹类比

摘要

我们找到了存在右端随机常微分方程、具有可测量随机漂移的随机微分方程及其具有对称积分的轨迹模拟的强解的新条件。我们表明 Itô 方程的解满足沿维纳过程轨迹的抛物线方程。