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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
316
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Joint distribution of Ito integral and its quadratic varation
Any idea on solving the joint distribution of
$X_T=\int_0^T \alpha_t dZ_t$ and $Y_T=\int_0^T \alpha_t^2 dt$ ? Here $X_T$ is an Ito integral and $Z_t$ is a standard Brownian process. When $\alpha_t$ an …
2
votes
Accepted
Given a Levy Exponent find the jump-measure and drift
Once you get $\gamma$, you can calculate
$\frac{\phi'(\lambda)-\gamma}{\lambda}=\int_0^\infty e^{-\lambda s}\nu(ds)$
and $\nu$ can be obtained by Laplace inversion.