近似弹性边界处的扩散反射
Approximating diffusion reflections at elastic boundaries
摘要：
我们展示了一个概率函数的限制结果，反映在弹性边界的反射当地时间的函数的一维扩散过程。这样的过程被构造为一个序列的扩散，这是离散的弹性边界处的小跳跃反映的限制，反射当地时间近似由$\varepsilon$ -步骤过程。该构造产生反射的逆当地时间的拉普拉斯变换。这种类型的过程和近似在奇异随机控制的有限燃料问题中起作用。
英文摘要：
We show a probabilistic functional limit result for one-dimensional diffusion processes that are reflected at an elastic boundary which is a function of the reflection local time. Such processes are constructed as limits of a sequence of diffusions which are discretely reflected by small jumps at an elastic boundary, with reflection local times being approximated by $\varepsilon$-step processes. The construction yields the Laplace transform of the inverse local time for reflection. Processes and approximations of this type play a role in finite fuel problems of singular stochastic control.
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