论文标题
几何布朗运动的无限麦迪
Infinite ergodicity for geometric Brownian motion
论文作者
论文摘要
几何布朗运动是一种典型的随机过程，遵守乘法噪声，在几个领域中广泛应用，例如在金融，物理和生物学领域。 The definition of the process depends crucially on the interpretation of the stochastic integrals which involves the discretization parameter $α$ with $0 \leq α\leq 1$ , giving rise to the well-known special cases $α=0$ (Itô), $α=1/2$ (Fisk-Stratonovich) and $α=1$ (Hänggi-Klimontovich or anti-Itô).在本文中，我们研究了几何布朗运动的概率分布函数（PDFS）的渐近限制和一些相关的概括。我们确定存在可正常化的渐近分布的条件，具体取决于离散参数$α$。使用无限的登山方法，最近将E. barkai和合作者带到具有乘法噪声的随机过程中，我们展示了如何以透明的方式制定有意义的渐近结果。
Geometric Brownian motion is an exemplary stochastic processes obeying multiplicative noise, with widespread applications in several fields, e.g. in finance, in physics and biology. The definition of the process depends crucially on the interpretation of the stochastic integrals which involves the discretization parameter $α$ with $0 \leq α\leq 1$ , giving rise to the well-known special cases $α=0$ (Itô), $α=1/2$ (Fisk-Stratonovich) and $α=1$ (Hänggi-Klimontovich or anti-Itô). In this paper we study the asymptotic limits of the probability distribution functions (PDFs) of geometric Brownian motion and some related generalizations. We establish the conditions for the existence of normalizable asymptotic distributions depending on the discretization parameter $α$. Using the infinite ergodicity approach, recently applied to stochastic processes with multiplicative noise by E. Barkai and collaborators, we show how meaningful asymptotic results can be formulated in a transparent way.
