Definition 4.9 Quantitative Methods · الفصل 4 — Stochastic Differential Equations The infinitesimal generator of a time-homogeneous diffusion dX=μ(X) dt+σ(X) dWdX = \mu(X)\,dt + \sigma(X)\,dWdX=μ(X)dt+σ(X)dW is the operator Lf(x)=limt↓0(Ex[f(Xt)]−f(x))/t=μ(x)f′(x)+12σ2(x)f′′(x)\mathcal Lf(x) = \lim_{t\downarrow 0} (\E_x[f(X_t)] - f(x))/t = \mu(x)f'(x) + \tfrac12\sigma^2(x)f^{\prime\prime}(x)Lf(x)=limt↓0(Ex[f(Xt)]−f(x))/t=μ(x)f′(x)+21σ2(x)f′′(x) on C2C^2C2 functions. اقرأ في الفصل →