16 мар. 2018 г. · Suppose now that Y is also a random variable (Ω,F). Then intuitively the expectation should be computed as ˜E[1AY]=E[1AYX],.

27 сент. 2013 г. · Now, the trick is to use F-measurability of Eν(X∣F) to write Eν(X∣F)⋅Eμ(dνdμ⋅∣F)=Eμ(Eν(X∣F)⋅dνdμ⋅∣F),. then integrate over F with respect to μ.

15 сент. 2016 г. · Calculations which are difficult under one measure can often become very simple if we change to a suitably modified measure.

14 мар. 2018 г. · It really just comes down to the formal definition of the expectation of a random variable, and the transformation ("change of measure") theorem ...

10 февр. 2019 г. · Let μ be defined on S by μ(E)=P(X−1(E)). Then ∫X−1(E)g(X)dP=∫Egdμ. If A is not of the form X−1(E) for some measurabke set E in S we cannot ...

12 апр. 2020 г. · When we look at the change of measure in probability theory, are the R-N derivative always computed on the level of probability density (defined ...

4 сент. 2011 г. · Suppose I have a probability measure P([a,b])=∫baxdx and I want to find the expectation of the random variable X=w2, which is by definition: E(X) ...

23 дек. 2018 г. · Suppose that Z≜dQdP,X∈L2P(Ω;F) and G is a sub-σ-algebra of F. How can I prove that: EP[ZX|G]=EQ[X|G]EP[Z|G], only using L2P(Ω;F) arguments?

10 июн. 2022 г. · Change of measure in expectation of a discrete random variable w.r.t a continuous random variable. · Do you want to find EQ[α|X]? – Snoop.

14 мар. 2018 г. · The answer is to use the measure-theoretic definition of expectation for measurable functions. Since the proof of the change of variable formula is actually to ...