论文标题
布朗连续树随机树条件很大
Brownian continuum random tree conditioned to be large
论文作者
论文摘要
我们考虑了我们在{zt = at}上条件的情况，我们考虑了坠落的扩散（zs，s $ \ ge $ 0）（具有扩散系数$ \ sqrt $ 2 $β$和drift $θ$ $ \ in $ r），在{zt = at}中，我们是确定性的功能，我们研究条件流程的限制和属于属的$ +$ $ +$ +$ +$ +。当AT不快速增加时，我们会恢复标准尺寸偏见的过程（以及Kesten树给出的相关家谱树）。当$θ$ = 0或$α$ e 2 $ e 2 $β$ | $β$ | $θ$ | t的行为为$α$β$ 2 t 2当$θ$ = 0时，我们获得了一个新的过程，该过程由吉尔萨诺夫（Girsanov）转换描述，并与poissonian移民的SDE相等。它相关的家谱树由一个无限的离散骨骼（不满足分支特性）描述，该骨骼用泊松点测量给出的布朗连续树随机树装饰。作为这项研究的副产品，我们介绍了几种具有gromovtype距离的树木，这些树木具有独立感兴趣，并且在这里允许以正式和可衡量的方式定义带有连续性随机树的骨架的装饰。
We consider a Feller diffusion (Zs, s $\ge$ 0) (with diffusion coefficient $\sqrt$ 2$β$ and drift $θ$ $\in$ R) that we condition on {Zt = at}, where at is a deterministic function, and we study the limit in distribution of the conditioned process and of its genealogical tree as t $\rightarrow$ +$\infty$. When at does not increase too rapidly, we recover the standard size-biased process (and the associated genealogical tree given by the Kesten's tree). When at behaves as $α$$β$ 2 t 2 when $θ$ = 0 or as $α$ e 2$β$|$θ$|t when $θ$ = 0, we obtain a new process whose distribution is described by a Girsanov transformation and equivalently by a SDE with a Poissonian immigration. Its associated genealogical tree is described by an infinite discrete skeleton (which does not satisfy the branching property) decorated with Brownian continuum random trees given by a Poisson point measure. As a by-product of this study, we introduce several sets of trees endowed with a Gromovtype distance which are of independent interest and which allow here to define in a formal and measurable way the decoration of a backbone with a family of continuum random trees.
