Abstract: | Let Wt be a one-dimensional Brownian motion on the probability space (Ω,F,P), and let dxt = a(xt)dt + b(xt)dwt, b2(x) > 0, be a one-dimensional Ito stochastic differential equation. For a(x) = a0 + a1x + … + anxn on a bounded interval we obtain a lower bound for p(t,x,y), the transition density function of the homogeneous Markov process xt, depending directly on the coefficients a0,a1, …, an, and b(x). |