论文标题
带有罗宾型边界的SPDE，用于在正半线上弹性杀死的扩散系统
An SPDE with Robin-type boundary for a system of elastically killed diffusions on the positive half-line
论文作者
论文摘要
我们考虑了一个经历了与半线相关扩散与弹性边界条件相关的颗粒系统。通过占据较大的粒子极限，我们确定了限制幸存颗粒的经验测量值的独特性。该过程可以看作是粒子密度满足嘈杂的罗宾边界条件的SPDE的弱形式。我们在此密度过程的$ l^2 $ regormultity属性上建立了结果，表明它在域的内部表现很好，但可能在一系列密集的时间在边界上表现出奇异性。在非线性情况下，我们还显示了经验度量的限制点的存在，粒子具有量度依赖性漂移。我们将线性问题与相应的吸收和反射SPDE进行连接，因为弹性参数采用其极端值。
We consider a system of particles undergoing correlated diffusion with elastic boundary conditions on the half-line. By taking the large particle limit we establish existence and uniqueness for the limiting empirical measure valued process for the surviving particles. This process can be viewed as the weak form for an SPDE with a noisy Robin boundary condition satisfied by the particle density. We establish results on the $L^2$-regularity properties of this density process, showing that it is well behaved in the interior of the domain but may exhibit singularities on the boundary at a dense set of times. We also show existence of limit points for the empirical measure in the non-linear case where the particles have a measure dependent drift. We make connections for our linear problem to the corresponding absorbing and reflecting SPDEs, as the elastic parameter takes its extreme values.
