论文标题
射击噪声，弱收敛和扩散近似
Shot noise, weak convergence and diffusion approximations
论文作者
论文摘要
由于其数学属性及其在几种应用中的相关性，因此对射击噪声过程进行了广泛的研究。在这里，我们考虑了非负射击噪声过程，并证明了它们与莱维驱动的Ornstein-Uhlenbeck（OU）的弱收敛性，其特征依赖于基本的跳跃分布。除其他外，我们将获得OU-Gamma和OU-Inverse Gaussian过程，分别以伽玛和逆高斯过程作为背景莱维过程。然后，我们得出确保加斯OU过程的扩散极限的必要条件，表明它们没有得到满足，除非允许概率为零的负跳跃发生，否则在用OU过程和非高斯OU进程替换射击噪声时会量化错误。结果提供了一类新的模型，而不是通常应用的高斯OU过程，以近似于突触输入电流，膜电压或通过单个神经元建模中的Shot噪声建模的电导率。
Shot noise processes have been extensively studied due to their mathematical properties and their relevance in several applications. Here, we consider nonnegative shot noise processes and prove their weak convergence to Lévy-driven Ornstein-Uhlenbeck (OU), whose features depend on the underlying jump distributions. Among others, we obtain the OU-Gamma and OU-Inverse Gaussian processes, having gamma and inverse gaussian processes as background Lévy processes, respectively. Then, we derive the necessary conditions guaranteeing the diffusion limit to a Gaussian OU process, show that they are not met unless allowing for negative jumps happening with probability going to zero, and quantify the error occurred when replacing the shot noise with the OU process and the non-Gaussian OU processes. The results offer a new class of models to be used instead of the commonly applied Gaussian OU processes to approximate synaptic input currents, membrane voltages or conductances modelled by shot noise in single neuron modelling.
