Tagged Questions
7
votes
1answer
124 views
generating set of predictable sigma algebra
I am solving an exercise in Rogers and Williams and want to ask if my solution is correct. Let me first introduce the notation. The space $b\mathcal{E}$ is the space of processes of the form
...
2
votes
1answer
52 views
Some preliminaries for the canonical construction of a Brownian Motion, help needed.
I have a lecture in stochastic analysis and I was given some facts, which are completely new to me and I do not really understand hot to understand/proof them. I would very happy if somebody could ...
1
vote
3answers
205 views
Exchange integral and conditional expectation
I know that if we have $E[\int_0^1 |X_t|dt] < \infty$ we may apply Fubini's theorem and compute $E[\int_0^1 X_tdt] = \int_0^1 E[X_t]dt$. Is there a similar version that allows the exchange of ...
2
votes
1answer
59 views
Laplace functional of a Poisson random measure with stochastic intensity
This is one of the problems from Cinlar's 2011 book - "Probability and Stochastics" (Chapter VI, page 262, exercise 2.36) : Let $N$ be a Poisson random measure on $R^{+}$, defined by
$N(\omega, B) = ...
8
votes
0answers
172 views
Generated sigma algebra from Brownian Motion
Suppose that we have a Brownian motion and we define the P-augmented filtration by
$$\mathcal{F}^W_t:=\sigma(\mathcal{F}^0_t \cup \mathcal{N})$$
where $\mathcal{F}_t^0:=\sigma(W_s;s\le t)$ and ...
