Linear transformations of Wiener process that born Wiener process, Brownian bridge or Ornstein-Uhlenbeck process
نویسنده
چکیده
Investigation of asymptotic properties of a statistical estimator or of a testing statistic often leads to a linear transformation of a Wiener process that born a Wiener process or a Brownian bridge. Let us recall some typical examples of such transformations. Provided a Wiener process (W(t) , £ > 0) the processes (^W(a • t) ,t > 0), a T-: 0 and (tW(\) , £ > 0) are Wiener processes and (W(t) tW(\) ,t G [0,1]) and (tW(^) ,* G (0,1)) are Brownian bridges. In the paper a more general schema is treated. We consider a collection of stochastic integrals of non-random real functions w.r.t. Wiener process, i. e.
منابع مشابه
Gaussian Processes: the Wiener Isometry and the Kolmogorov-chentsov Theorem
We will be most interested in Gaussian processes indexed by an interval J ⇢ R, usually J = [0,1) or J = [0, T ] for some 0 < T < 1. Under weak hypotheses there will always exist centered Gaussian processes with specified covariance functions, but it is not generally the case that such processes will have versions with continuous sample paths. Our primary objective in this chapter will be to dev...
متن کامل1 Fe b 20 11 General α - Wiener bridges
An α-Wiener bridge is a one-parameter generalization of the usual Wiener bridge, where the parameter α > 0 represents a mean reversion force to zero. We generalize the notion of α-Wiener bridges to continuous functions α : [0, T ) → R. We show that if the limit limt↑T α(t) exists and is positive, then a general α-Wiener bridge is in fact a bridge in the sense that it converges to 0 at time T wi...
متن کاملA Piecewise-Deterministic Model for Brownian Motion
In the present paper, the classical Brownian motion of a particle suspended in an homogeneous liquid is modeled as a piecewise–deterministic Markov process with state space inculding position as well as velocity of the particle in motion. This model is less idealized than the classical Wiener or Ornstein–Uhlenbeck processes. It leads to more complex expressions for the transition densities, but...
متن کاملStein’s method on Wiener chaos
We combine Malliavin calculus with Stein’s method, in order to derive explicit bounds in the Gaussian and Gamma approximations of random variables in a fixed Wiener chaos of a general Gaussian process. Our approach generalizes, refines and unifies the central and non-central limit theorems for multiple Wiener-Itô integrals recently proved (in several papers, from 2005 to 2007) by Nourdin, Nuala...
متن کاملOrnstein - Uhlenbeck Process
Also, a process {Yt : t ≥ 0} is said to have independent increments if, for all t0 < t1 < . . . < tn, the n random variables Yt1 − Yt0 , Yt2 − Yt1 , ..., Ytn − Ytn−1 are independent. This condition implies that {Yt : t ≥ 0} is Markovian, but not conversely. The increments are further said to be stationary if, for any t > s and h > 0, the distribution of Yt+h− Ys+h is the same as the distributio...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Kybernetika
دوره 37 شماره
صفحات -
تاریخ انتشار 2001