基于optimization的保平均变差过程
Average preserving variation processes in view of optimization
摘要：
在本文中，我们研究了特定的最小作用原理的法律的随机过程的框架内，它站在过滤保持变化。我们得到的相关Euler-Lagrange条件，除了正则鞅项外，在动力学中表现出一个确定性过程。特别是，采取特定的行动泛函，极值过程就这些变化包括特定的法律连续半鞅的漂移特性是可积的独立增量。然后，我们涉及的极值过程的经典费用函数，特别是特定的熵函数，一类向前向后系统的Mckean-Vlasov随机微分方程。
英文摘要：
In this paper, we investigate specific least action principles for laws of stochastic processes within a framework which stands on filtrations preserving variations. The associated Euler-Lagrange conditions, which we obtain, exhibit a deterministic process in the dynamics aside the canonical martingale term. In particular, taking specific action functionals, extremal processes with respect to those variations encompass specific laws of continuous semi-martingales whose drift characteristic is integrable with independent increments. Then, we relate extremal processes of classical cost functions, in particular of specific entropy functions, to a class of forward-backward systems of Mckean-Vlasov stochastic differential equations.
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