双向网格约束随机过程的隐几何
Hidden Geometry of Bi-Directional Grid Constrained Stochastic Processes
摘要：
双向网格约束（BGC）随机过程（BGCSP）是受约束的伊藤扩散，其性质是它们离原点越远，在该方向上运动的阻力就越大。我们调查的基本特征的BGC参数$Ψ(x, t)$通过检查其几何性质。在对各种可能的形式进行广泛的模拟之后，确定了$Ψ$的最合适的凸形式，即抛物柱面。通过将其与更简单的Ornstein-Uhlenbeck过程（OUP）进行比较来确定所得到的隐藏反射屏障的公式。BGCSP的应用出现时，一系列的半渗透障碍，如调节利率和浓度梯度下的化学反应，这引起了两个隐藏的反射障碍。
英文摘要：
Bi-Directional Grid Constrained (BGC) stochastic processes (BGCSP) are constrained Itô diffusions with the property that the further they drift away from the origin, the more resistance to movement in that direction they undergo. We investigate the underlying characteristics of the BGC parameter $Ψ(x, t)$ by examining its geometric properties. The most appropriate convex form for $Ψ$, i.e. the parabolic cylinder is identified after extensive simulation of various possible forms. The formula for the resulting hidden reflective barrier(s) is determined by comparing it with the simpler Ornstein-Uhlenbeck process (OUP). Applications of BGCSP arise when a series of semipermeable barriers are present, such as regulating interest rates and chemical reactions under concentration gradients, which gives rise to two hidden reflective barriers.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
