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Results tagged with pr.probability
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user 19149
Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
3
votes
0
answers
269
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Conditioning on the current value of a stochastic process
I want to condition a stochastic process $X$ on the current value of another process $Y$ in a continuous-time setting. So I am looking for a process $Z$ such that for every fixed $t$,
$$Z_t = E\big(X …
- 103
1
vote
Law of large numbers for stochastically chosen samples
There is a continuous time version of this problem that sheds some more light on this. The discrete time result follows by choosing piecewise constant processes $k$.
It follows from [1, theorem 5.1] …
- 103
4
votes
3
answers
467
views
Law of large numbers for stochastically chosen samples
Let $X_t$ be a sequence of i.i.d. random variables with mean $\mu$. Then the law of large numbers states that
$$\lim_{T \to \infty} \frac1T \sum_{t=1}^T X_t = \mu \quad a.s.$$
Now suppose that (in a …
- 103
2
votes
surprisingly difficult filtration problem
The result is proven in Peskir&Shiryaev, Section 1.2, Theorem 6 under the following assumption on $\Omega$: for each $t\geq 0$ and each $\omega \in \Omega$ there is $\omega'\in\Omega$ such that $X_s(\ …
- 103