Stochastic Approximation Procedures for Lévy-Driven SDEs
研究了由一般Lévy过程驱动的随机微分方程的连续时间Robbins-Monro型随机逼近过程，利用Lyapunov函数给出了收敛的充分条件，并展示了通过适当选择噪声系数可在比扩散情形更弱的条件下实现收敛。
Abstract We consider a continuous-time Robbins–Monro-type stochastic approximation procedure for a system described by a (multidimensional) stochastic differential equation driven by a general Lévy process, and we find sufficient conditions for its convergence in terms of Lyapunov functions. While the jump part of the noise may spoil convergence to the root of the drift in some cases, we show that by a suitable choice of noise coefficients we obtain convergence under hypotheses on the drift weaker than those used in the diffusion case or convergence to a selected root in the case of multiple roots of the drift.