Suppose $B_t$ is a one dimensional Brownian motion. If I know that $X_t$ is positive and $$ X_t \geq x + \int^t_0 b X_s ds + \int^t_0 \sigma X_s d B_s,$$ can I obtain that $$ X_t \geq x \exp\left( (b-\sigma^2/2)t +\sigma B_t \right) ?$$
2026-04-01 02:00:04.1775008804
Some Grownwall type inequality for stochastic integral equation
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