Suppose $\{X_i, i=1,2,\cdots\}$ are random variables are i.i.d. from standard exponential distribution.
Define the random walk as: $$S_0=0,$$ $$S_{i+1}=\max\{0,S_i+X_i-k\},$$ where $k>1$.
Then how can we calculate the average hitting time of this process? In other words, how to calculate $$E[T(h)]=E[\inf_i{X_i\ge h}].$$
In addition, how to calculate the expected hitting time of a random process bounded below but has increments with a negative expectation.
Thank you.