Uniqueness of Solutions of Stochastic Differential Equations
Uniqueness of Solutions of Stochastic Differential Equations
We consider the stochastic differential equation dx(t) = dW(t) + f(t, x(t))dt, x(0) = x0 for t ≥ 0, where x(t) ∈ ℝd, W is a standard d-dimensional Brownian motion, and f is a bounded Borel function from [0, ∞) × ℝd to ℝd. We show that, for almost all …