6 votes

Quadratic Variation Of Mixed Brownian Motion and Poisson Process

Your attempt is correct. The quadratic variation for a Poisson process is: $$[N]_t=\lim_{\sup(t_{i+1}-t_i)\rightarrow0}\sum_{i:t_i\leq t}(N_{t_{i+1}}-N_{t_i})^2\tag{1}$$ for some partition $\Pi(t)=0\...
Daneel Olivaw's user avatar
1 vote

Pure jump process in Duffie, Pan and Singleton's paper

Essentially yes - $Z_t$ is a compound Poisson process, except that the underlying counting process $N_t$ has intensity $\lambda(X_t)$. I.e $$ N_t - N_s \sim Pois\bigg( \int_s^t \lambda(X_u) \mathrm{d}...
Achrbot's user avatar
  • 69

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