# Convergence of a stochastic integral [duplicate]

Let $(B_t)$ the standard Brownian Motion and $(H_t)$ be an adapted continuous process. Show that $$\frac{1}{B_t}\int _0^tH_sdB_s$$ converge in probability.
I guess that the limit is $H_0$ but I don't know how to prove this statement. How can we show that $$\mathbb{P}(|\frac{1}{B_t}\int _0^tH_s-H_0dB_s|>\epsilon )\to 0$$ when $t\to 0$ ?
I have tried to use Markov inequality then Cauchy Schartz inequality in order to make appear $\mathbb{E}((\int H_s-H_0dB_s)^2)$ but this didn't work because of the term $\frac{1}{B_t}$.