Modelling continuous measurements

In the attachment from a set of notes, a brief description of how we describe a continuous measurement is described. I have a few basic questions regarding this, any assistance would be appreciated:


  • I think the motivation for defining \(
    \Delta\)\(W_n\) is to define it as the error per measurement \(n\) such that the variance (3.5) does not change with increased \( N\). Is this correct and how is this achieved by introducing \(
    \Delta\)\(W\) (and \(
    \Delta\)\(W_n\)) and endowing it with variance \(

  • Why is (3.8) defined in this form?

  • How is (3.9) the best estimate of \(x\)?