论文标题
杀死率的调节扩散过程
Conditioning diffusion processes with killing rates
论文作者
论文摘要
当无条件的过程是提交给空间依赖的杀戮率$ k（\ vec x）$的扩散时，可以在有限的时间范围内$ t $ t $实施各种条件约束。当人们在时间$ t $上施加尚存的分销和中间时间$ t \ in [0，t] $中的杀戮分布时，我们首先分析条件过程。当调节约束比这些完整分布的限制较少时，我们通过在存在条件约束的情况下优化在2.5级的动态大偏差来构建适当的条件过程。最后，我们描述了无限视野$ t \ to +\ infty $的各种条件过程。 This general construction is then applied to two illustrative examples in order to generate stochastic trajectories satisfying various types of conditioning constraints : the first example concerns the pure diffusion in dimension $d$ with the quadratic killing rate $k(\vec x)= γ\vec x^2$, while the second example is the Brownian motion with uniform drift submitted to the delta killing rate $k(x)=k δ(x)$本地化在原点$ x = 0 $。
When the unconditioned process is a diffusion submitted to a space-dependent killing rate $k(\vec x)$, various conditioning constraints can be imposed for a finite time horizon $T$. We first analyze the conditioned process when one imposes both the surviving distribution at time $T$ and the killing-distribution for the intermediate times $t \in [0,T]$. When the conditioning constraints are less-detailed than these full distributions, we construct the appropriate conditioned processes via the optimization of the dynamical large deviations at Level 2.5 in the presence of the conditioning constraints that one wishes to impose. Finally, we describe various conditioned processes for the infinite horizon $T \to +\infty$. This general construction is then applied to two illustrative examples in order to generate stochastic trajectories satisfying various types of conditioning constraints : the first example concerns the pure diffusion in dimension $d$ with the quadratic killing rate $k(\vec x)= γ\vec x^2$, while the second example is the Brownian motion with uniform drift submitted to the delta killing rate $k(x)=k δ(x)$ localized at the origin $x=0$.
