I need to evaluate $$ \int_0^t B(\min \{{1,s}\})dB(s), $$ where $B$ is the Brownian motion.
I am starting solving this problem by using the stochastic integration. Any suggestions.
2026-03-29 10:26:42.1774780002
Evaluate stochastic integration
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HINT Assuming $t > 1$, $$ \int_0^t B_{\min\{1,s\}} dB_s = \int_0^1 B_{\min\{1,s\}} dB_s + \int_1^t B_{\min\{1,s\}} dB_s $$ Now $\min\{1,s\}$ can be explicitly computed over each interval of integration. Can you now finish?