Weak convergence to the fractional Brownian sheet in Besov spaces
نویسندگان
چکیده
In this paper we study the problem of the approximation in law of the fractional Brownian sheet in the topology of the anisotropic Besov spaces. We prove the convergence in law of two families of processes to the fractional Brownian sheet: the first family is constructed from a Poisson procces in the plane and the second family is defined by the partial sums of two sequences of real independent fractional brownian motions.
منابع مشابه
A Variation Embedding Theorem and Applications
Fractional Sobolev spaces, also known as Besov or Slobodetzki spaces, arise in many areas of analysis, stochastic analysis in particular. We prove an embedding into certain q-variation spaces and discuss a few applications. First we show q-variation regularity of Cameron-Martin paths associated to fractional Brownian motion and other Volterra processes. This is useful, for instance, to establis...
متن کاملA Decomposition and Weak Approximation of the Sub - Fbm
We present a decomposition of the sub-fractional Brownian motion into the sum of a fractional Brownian motion plus a stochastic process with absolutely continuous trajectories. The first application we show of this decomposition is the relation between the spaces of integrable functions with respect each one of these three processes. A general result of weak convergence to integrals of L(R) fun...
متن کاملRegularity Properties of Some Stochastic Volterra Integrals with Singular Kernel
We prove the Hölder continuity of some stochastic Volterra integrals, with singular kernels, under integrability assumptions on the integrand. Some applications to processes arising in the analysis of the fractional Brownian motion are given. The main tool is the embedding of some Besov spaces into some sets of Hölder continuous functions.
متن کاملChapter 5: Asymptotic Methods and Functional Central Limit Theorems
This chapter sketches the fundamentals of asymptotic distribution theory, and applies these speci cally to questions relating to weak convergence on function spaces. These results have important applications in the analysis of nonstationary time series models. A simple case of the functional central limit theorem for processes with independent increments is stated and proved, after detailing th...
متن کاملRegularity Properties of Some Stochastic Volterra Integrals with Degenerate Kernel
We derive sampleepaths continuity results for some sto-chastic Volterra integrals with degenerate kernel under integrability assumptions on the integrand. Some applications to processes arising in the analysis of the fractional Brownian motion are given. Embeddings of Besov spaces into sets of HHlder continuous functions are the key elements. RRSUMM. Nous montrons la continuitt trajectorielle d...
متن کامل