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Some additive functionals concerning the Cauchy's principal value or the Hadamard's finite past are investigatd. A decomposition of additive functionals is proposed by using the Hilbert transform t...
The representations of Wiener process by uniformly convergent series of onedimensional Gaussian random processes in a separable Banach space are given (Section I). The Ito stochastic integral of an...
We show that for a von Neumann algebra in standard form with cyclic and separating tracial vector, and some classes of noncommutative processes on it, stopping and integrals of these processes can ...
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...
In this note, we are interested in the regularity in the sense of total variation of the joint laws of multiple stable stochastic integrals. Namely, we show that the convergence L 􀀀 Id1 ...
The paper is devoted to sharp inequalities between moments of nonnegative supermartingales and their strong subordinates. Analogous estimates hold true for stochastic integrals with respect to a non...
We show that the general stable convergence results proved in Peccati and Taqqu(2007)for generalized adapted stochastic integrals can be used to obtain limit theorems for multiple stochastic integrals...
Two families of improper stochastic integrals with respect to Lévy processes.
Equivalent upper and lower bounds for the L1 norm of Hilbert space valued infinitely divisible random variables are obtained and used to find bounds for different types of stochastic integrals.
Let $X=(X_t)_{tgeq 0}$ be a martingale and $H=(H_t)_{tgeq 0}$ be a predictable process taking values in $[-1,1]$. Let $Y$ denote the stochastic integral of $H$ with respect to $X$. We show that $$ ||s...
Let $X=(X_t)_{tgeq 0}$ be a martingale and $H=(H_t)_{tgeq 0}$ be a predictable process taking values in $[-1,1]$. Let $Y$ denote the stochastic integral of $H$ with respect to $X$. We show that $$ ||s...

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