New answers tagged stochastic-analysis
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Proving Levy Process Characteristic Function is a Martingale
$$\mathbb{E}[M_{0,t} \vert \mathcal{F}_s] =\frac{\mathbb{E}[e^{i
\langle \theta, X_t-X_s \rangle} e^{i \langle \theta, X_s-X_0 \rangle} \vert F_s ]}{\mathbb{E}[e^{i \langle \theta, X_t-X_s \rangle}e^{...
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Proving $X_t = 1 + \int_0^t X_s \, dN_s$ is a supermartingale
First, note that these are all about the case where $X$ is an exponential martingale, so $N$ is a local martingale. This also implies $X$ is a local martingale.
For 1), let $(\tau_n) \rightarrow \...
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Help me understand this proof of "the covariance of a Gaussian measure is trace-class"
This is not an answer, but comment.
In case you stuck, there is a detailed proof of Prokhorov-Sazonov theorem re. measures on Hilbert spaces in Bourbaki's "Integration II", chapter IX "...
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Local Lipschitz continuity and explosion time in SDE.
He shows that the events
$$A_{n}:=\{\zeta_n < e, Q_{\zeta_n} - Q_{\eta_n} \leq (Cn)^{-1}\}$$
are summable $\sum P(A_{n})\leq \sum r_{n}$ for $r_{n} = \frac{2n}{\pi} \int_0^{1/2} e^{-nu^2/2} \, du \...
- 1,140
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Is there a measure theoretic interpretation of rough path integrals?
To be clear there is no universal measure $\Lambda$ that can represent any given rough path.
A better analogy is with Riemann-Stieltjes integrals or even better Young integrals $\int f dg$ with $f\in ...
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