Probability Question (Expectation Value Limit)
Show that for any $\phi \in C_0(\mathbb{R^n})$ (a continuous function on $\mathbb{R^n}$ which tends to 0 at $\infty$), if we set
$\phi_\epsilon(x) = \mathbb{E}\phi(x + \epsilon Z)$
for any random variable $Z$ on $\mathbb{R^n}$, then $\phi_\epsilon(x)$ → $\phi(x)$ as $\epsilon$ → 0.
L Ellis
369
Answer
Answers can be viewed only if
- The questioner was satisfied and accepted the answer, or
- The answer was disputed, but the judge evaluated it as 100% correct.
1 Attachment
Cmartman
42
The answer is accepted.
Join Matchmaticians Affiliate Marketing
Program to earn up to 50% commission on every question your affiliated users ask or answer.
- answered
- 380 views
- $10.00
Related Questions
- Need help with integrals (Urgent!)
- Calculating the Probability of a Varied Selection in Pet Shop Purchases
- Joint PDF evaluated over a curve $P_{U,V}$
- Compute the cumulative density function of X
- Calculating P values from data.
- How to adjust for an additional variable.
- Compound Interest with monthly added capital
- Trying to figure out probability problem for a series
Should we interpret x as being real valued and deterministic?