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Some properties of exponential integrals of Levy processes and examples
properties exponential integrals Levy processes examples
2009/4/3
The improper stochastic integral $Z=int_0^{infty-}exp(-X_{s-})dY_s$ is studied, where ${ (X_t ,Y_t) , t ges 0 }$ is a L'evy process on $R ^{1+d}$ with ${X_t }$ and ${Y_t }$ being $R$-valued and $R ^d$...
On the rate of growth of Levy processes with no positive jumps conditioned to stay positive
asymptotic behaviour Levy process related process
2009/3/20
In this note, we study the asymptotic behaviour of Lévy processes with no positive jumps conditioned to stay positive and some related processes. In particular, we establish an integral test for the l...
For real Lévy processes $(X_t)_{t geq 0}$ having no Brownian component with Blumenthal-Getoor index $beta$, the estimate $E sup_{s leq t} |X_s - a_p s|^p leq C_p t$ for every $t in [0,1]$ and suitable...