# Modelling continuous measurements

#### Jickro

##### New Member
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:

Questions:

• 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 $$\Delta$$$$t$$?

• Why is (3.8) defined in this form?

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