Stochastic and Multiple Wiener Integrals for Gaussian Processes
نویسندگان
چکیده
منابع مشابه
Gaussian limits for vector-valued multiple stochastic integrals
We establish necessary and sufficient conditions for a sequence of d-dimensional vectors of multiple stochastic integrals Fd = ` F k 1 , ..., F k d ́ , k ≥ 1, to converge in distribution to a d-dimensional Gaussian vector Nd = (N1, ..., Nd). In particular, we show that if the covariance structure of F k d converges to that of Nd, then componentwise convergence implies joint convergence. These re...
متن کاملConditionally Gaussian stochastic integrals
We derive conditional Gaussian type identities of the form E [ exp ( i ∫ T 0 utdBt ) ∣∣∣∣ ∫ T 0 |ut|dt ] = exp ( − 2 ∫ T 0 |ut|dt ) , for Brownian stochastic integrals, under conditions on the process (ut)t∈[0,T ] specified using the Malliavin calculus. This applies in particular to the quadratic Brownian integral ∫ t 0 ABsdBs under the matrix condition A †A2 = 0, using a characterization of Yo...
متن کاملStochastic Integrals and Abelian Processes
We study triangulation schemes for the joint kernel of a diffusion process with uniformly continuous coefficients and an adapted, non-resonant Abelian process. The prototypical example of Abelian process to which our methods apply is given by stochastic integrals with uniformly continuous coefficients. The range of applicability includes also a broader class of processes of practical relevance,...
متن کاملStable convergence of multiple Wiener-Itô integrals
We prove sufficient conditions, ensuring that a sequence of multiple Wiener-Itô integrals (with respect to a general Gaussian process) converges stably to a mixture of normal distributions. Our key tool is an asymptotic decomposition of contraction kernels, realized by means of increasing families of projection operators. We also use an infinite-dimensional Clark-Ocone formula, as well as a ver...
متن کاملCumulant operators for Lie-Wiener-Itô-Poisson stochastic integrals
The classical combinatorial relations between moments and cumulants of random variables are generalized into covariance-moment identities for stochastic integrals and divergence operators. This approach is based on cumulant operators defined by the Malliavin calculus in a general framework that includes Itô-Wiener and Poisson stochastic integrals as well as the Lie-Wiener path space. In particu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1978
ISSN: 0091-1798
DOI: 10.1214/aop/1176995480