标题： 随机微分方程驱动的乘性随机波动率线性倍增器的非参数估计 显示英文标题

标题： Nonparametric estimation of linear multiplier for stochastic differential equations driven by multiplicative stochastic volatility

摘要： 我们研究了非参数估计线性乘子函数$\theta(t)$的问题，针对满足随机微分方程类型的随机过程$$dX_t= \theta(t)X_t dt+ \epsilon\; \sigma_1(t,X_t)\sigma_2(t,Y_t)dW_t, X_0=x_0, 0 \leq t \leq T$$，其中$\{W_t, t\geq 0\}$是标准布朗运动，$\{Y_t, t\geq 0\}$是适应于由布朗运动生成的滤子的过程。 我们研究了基于观测过程$\{X_t,0\leq t \leq T\}.$来估计未知函数$\theta(.)$作为$\epsilon \rightarrow 0$的问题。 显示英文摘要

摘要： We study the problem of nonparametric estimation of the linear multiplier function $\theta(t)$ for processes satisfying stochastic differential equations of the type $$dX_t= \theta(t)X_t dt+ \epsilon\; \sigma_1(t,X_t)\sigma_2(t,Y_t)dW_t, X_0=x_0, 0 \leq t \leq T$$ where $\{W_t, t\geq 0\}$ is a standard Brownian motion, $\{Y_t, t\geq 0\}$ is a process adapted to the filtration generated by the Brownian motion. We study the problem of estimation of the unknown function $\theta(.)$ as $\epsilon \rightarrow 0$ based on the observation of the process $\{X_t,0\leq t \leq T\}.$