论文标题
Bessel SDE和SLE的复杂解决方案
Complex Solutions to Bessel SDEs and SLEs
论文作者
论文摘要
我们通过允许溶液的复杂价值来考虑Bessel SDE的一种变体。在研究Schramm-Loewner-Evolutions（SLE）的痕迹时，这种SDE自然而然地出现。当尺寸为负时，我们确定了强大解决方案的强大解决方案的存在和独特性。我们还考虑与此类SDE相关的随机流，并证明它几乎是连续的。我们的证明是基于对Rohde-Schramm \ cite {rs05}的衍生估计值的改进。我们最终显示了这种随机流与$κ<4 $的SLE $_κ$之间的联系。
We consider a variant of Bessel SDE by allowing the solution to be complex valued. Such SDEs appear naturally while studying the trace of Schramm-Loewner-Evolutions (SLE). We establish the existence and uniqueness of the strong solution to such SDEs when the dimension is negative. We also consider the stochastic flow associated to such SDEs and prove that it is almost surely continuous. Our proofs are based on an improvement of the derivative estimate of Rohde-Schramm \cite{RS05}. We finally show the connection between such stochastic flows and SLE$_κ$ for $κ<4$.
