论文标题
一类新的随机流程，具有巨大潜力用于有趣的应用
A new class of stochastic processes with great potential for interesting applications
论文作者
论文摘要
本文有助于研究一个新的，杰出的随机过程家族，我们将其称为$σ^{r}（h）$。该类可能很有趣，因为它统一了两个已知类别的研究：类$（σ）$和$ \ Mathcal {m}（h）$。换句话说，我们认为将随机过程$ x $分解为$ x = m+v+a $，其中$ m $是本地的martingale，$ v $和$ a $是有限的变化过程，因此$ da $由$ \ \ \ {t \ geq0：x__ {x_ {t} = 0 \} $ of $ h MERT $ hers $ hers $ h，$ hers $ hers， $ D $。首先，我们引入了一个通用框架。因此，我们提供了一些新类元素的示例，并提供了一些属性。其次，我们提供一系列表征结果。之后，我们得出了一些表示结果，这些结果允许从其最终值和诚实的时间$ g = \ sup \ {t \ geq0：x_ {t} = 0 \} $和$γ= = \ sup {h} $中恢复$σ^{r}（h）$的过程。在最后，我们研究了一个有趣的应用程序，并使用目前研究的过程进行了研究。更确切地说，我们使用类$σ^{r}（h）$的随机过程构建偏斜运动方程的解决方案。
This paper contributes to the study of a new and remarkable family of stochastic processes that we will term class $Σ^{r}(H)$. This class is potentially interesting because it unifies the study of two known classes: the class $(Σ)$ and the class $\mathcal{M}(H)$. In other words, we consider the stochastic processes $X$ which decompose as $X=m+v+A$, where $m$ is a local martingale, $v$ and $A$ are finite variation processes such that $dA$ is carried by $\{t\geq0:X_{t}=0\}$ and the support of $dv$ is $H$, the set of zeros of some continuous martingale $D$. First, we introduce a general framework. Thus, we provide some examples of elements of the new class and present some properties. Second, we provide a series of characterization results. Afterwards, we derive some representation results which permit to recover a process of the class $Σ^{r}(H)$ from its final value and of the honest times $g=\sup\{t\geq0:X_{t}=0\}$ and $γ=\sup{H}$. In final, we investigate an interesting application with processes presently studied. More precisely, we construct solutions for skew Brownian motion equations using stochastic processes of the class $Σ^{r}(H)$.
