Convergence to Stochastic Integrals with Non-linear Integrands
نویسندگان
چکیده
In this paper we present a general result concerning the convergence to stochastic integrals with non-linear integrands. The key finding represents a generalization of Chan and Wei’s (1988) Theorem 2.4. and that of Ibragimov and Phillips’ (2004) Theorem 8.2. This result is necessary for analysing the asymptotic properties of mis-specification tests, when applied to a unit root process, for which Wooldridge (1999) mentioned that the exiting results in the literature were not sufficient.
منابع مشابه
Error Distributions for Random Grid Approximations of Multidimensional Stochastic Integrals
This paper proves joint convergence of the approximation error for several stochastic integrals with respect to local Brownian semimartingales, for non-equidistant and random grids. The conditions needed for convergence are that the Lebesgue integrals of the integrands tend uniformly to zero and that the squared variation and covariation processes converge. The paper also provides tools which s...
متن کاملItô Formula for Free Stochastic Integrals
The subject of this paper is stochastic integration in the context of free probability. Noncommutative stochastic processes with freely independent increments, especially the free Brownian motion, have been investigated in a number of sources, see [BS98], [Ans00] and their references. In the latter paper, we started the analysis of such processes, which we also call free stochastic measures, us...
متن کاملCombinatorics of Poisson stochastic integrals with random integrands
We present a self-contained account of recent results on moment identities for Poisson stochastic integrals with random integrands, based on the use of functional transforms on the Poisson space. This presentation relies on elementary combinatorics based on the Faà di Bruno formula, partitions and polynomials, which are used together with multiple stochastic integrals, finite difference operato...
متن کاملFrom Random Processes to Generalized Fields: a Unified Approach to Stochastic Integration
The paper studies stochastic integration with respect to Gaussian processes and fields. It is more convenient to work with a field than a process: by definition, a field is a collection of stochastic integrals for a class of deterministic integrands. The problem is then to extend the definition to random integrands. An orthogonal decomposition of chaos space of the random field leads to two suc...
متن کاملOn quantitative approximation of stochastic integrals with respect to the geometric Brownian motion
Papers published in this report series are preliminary versions of journal articles and not for quotations. Abstract. For the geometric Brownian motion St = exp(Wt?t=2), t 2 0; T ], and a Borel{measurable function f : (0; 1) ! 0; 1) such that f (S T) 2 L 2 we approximate f (S T) ? IEf(S T) in L 2 by expressions of type P n i=1 v i?1 (St i ? St i?1), where 0 = t 0 < < tn = T are deterministic bu...
متن کامل