If instead of a regular Wiener process $W_t$, we had a process of the form $X_t=g(t)W_{at}$ where $g$ is continuous and deterministic and $a$ is a deterministic scalar, then what is the autocorrelation function $R_{X}(t,s)$?
Autocorrelation of scaled Wiener process?
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probability
stochastic-processes
brownian-motion