Electron. J. Probab. 18 (2013), no. 100, DOI: 10.1214/EJP.v18-2945
نویسندگان
چکیده
We prove new upper and lower bounds for Banach space-valued stochastic integrals with respect to a compensated Poisson random measure. Our estimates apply to Banach spaces with non-trivial martingale (co)type and extend various results in the literature. We also develop a Malliavin framework to interpret Poisson stochastic integrals as vector-valued Skorohod integrals, and prove a Clark-Ocone representation formula.
منابع مشابه
Electron. J. Probab. 18 (2013), no. 29, DOI: 10.1214/EJP.v18-2103
Let Xi,j , i, j = 1, ..., n, be independent, not necessarily identically distributed random variables with finite first moments. We show that the norm of the random matrix (Xi,j) n i,j=1 is up to a logarithmic factor of the order of E max i=1,...,n ∥∥(Xi,j)nj=1∥∥2 +E max i=1,...,n ∥∥(Xi,j)nj=1∥∥2 . This extends (and improves in most cases) the previous results of Seginer and Latała.
متن کاملElectron. Commun. Probab. 19 (2014), no. 57, DOI: 10.1214/ECP.v19-3678
We give an explicit bound for the L1-distance between two additive processes of local characteristics (fj(·), σ(·), νj), j = 1, 2. The cases σ = 0 and σ(·) > 0 are both treated. We allow ν1 and ν2 to be time-homogeneous Lévy measures, possibly with infinite variation. Some examples of possible applications are discussed.
متن کاملElectron. Commun. Probab. 19 (2014), no. 72, DOI: 10.1214/ECP.v19-3005
We give a multivariate generalization of Borell’s noise stability theorem for Gaussian vectors. As a consequence we recover two inequalities, also due to Borell, for exit times of the Ornstein-Uhlenbeck process.
متن کاملElectron. Commun. Probab. 19 (2014), no. 84, DOI: 10.1214/ECP.v19-3629
In this note we look into detail at the box-counting dimension of subordinators. Given that X is a non-decreasing Lévy process, which is not a compound Poisson process, we show that in the limit, the minimum number of boxes of size δ that cover the range of (Xs)s≤t is a.s. of order t/U(δ), where U is the potential function of X. This is a more refined result than the lower and upper index of th...
متن کاملElectron. Commun. Probab. 21 (2016), no. 21, DOI: 10.1214/16-ECP4364
We study the propagation of high peaks (intermittency fronts) of the solution to a stochastic heat equation driven by multiplicative centered Gaussian noise in R. The noise is assumed to have a general homogeneous covariance in both time and space, and the solution is interpreted in the senses of the Wick product. We give some estimates for the upper and lower bounds of the propagation speed, b...
متن کامل