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A question about convergence of stochastic processes converging to a random walk
Consider the following random walk $(y_t)_{t \in \mathbb Z_+}$:
$$y_t = y_{t-1} + u_t,\quad (u_t)_{t \in \mathbb Z_+} \overset{iid}{\sim} N(0,1), \quad (t \in \mathbb Z_+)$$
where $y_0, u_1, u_2,...$ ...
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1
vote
2
answers
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Asymptotic properties of weighted random walks / infinite convolutions of random variables
Let $(X_n)_{n\in\mathbb{N}}$ be a sequence of i.i.d. real-random variables. Let further $0<c<1$. I'm interested in the asymptotic properties of
$$
\sum_{k=1}^n c^k X_k.
$$
I can prove that this ...
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