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We study the relationship between the distribution of the supremum functional M, = sup,,,,,(X(t)-fit) for a process X with stationary, but not necessarily independent increments, and the I limiting...
In this paper, we firstly study the Besov regularity of the local time of symmetric stable processes and of its fractional derivative. Secondly, we establish Limit theorems for occupation times of ...
The main theme of Urbanik's work was infinite divisibility and its r d c a t i o n s . The aim of this memorial article is to trace the application of this theme in mathematical fmanoe, one of the m...
We review infinite divisibility and LBvy processes in Banach spaces and discuss the relationship with notions of type and i cotype. The LBvy-It6 decomposition is described. Strong, weak and Pettis-s...
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 $R ^d$...
A different but very short proof of a recent result of Khoshnevisan.
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 $R ^d$...
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 vy 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...
Let X(t) t  0 ,X(0) = 0, be a L´evy process with spectral evy measure . Assuming that ((−1, 0)) < 1 and the right tail of  is light, we show that in the presence of Brownian co...
The notion that natural disasters can be controlled is, of course, farcical; history is permeated with examples of countless failed attempts at this pointless task; it is synonymous with trying to bui...
An explicit formula for the chaotic representation of the powers of increments, (Xt+t0 − Xt0)n ,of a L´evy process is presented. There are two different chaos expansions of a square integr...

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