WEAK CONVERGENCE FOR MULTIPLE STOCHASTIC INTEGRALS IN SKOROHOD SPACE

김윤태

doi:http://dx.doi.org/10.11568/kjm.2014.22.1.71

논문KCI 등재

WEAK CONVERGENCE FOR MULTIPLE STOCHASTIC INTEGRALS IN SKOROHOD SPACE

1

조회

0

다운로드

0

인용

0

참고문헌

키워드

fractional Brownian motion Central limit theorem Gaussian process Malliavin calculus Multiple stochastic integrals Skorohod space

주제분류수학

초록

By using the multidimensional normal approximation of functionals of Gaussian fields, we prove that functionals of Gaussian fields, as functions of t, converge weakly to a standard Brownian motion. As an application, we consider the convergence of the Stratonovich-type Riemann sums, as a function of t, of fractional Brownian motion with Hurst parameter H=1/4.

Abstract

By using the multidimensional normal approximation of functionals of Gaussian fields, we prove that functionals of Gaussian fields, as functions of t, converge weakly to a standard Brownian motion. As an application, we consider the convergence of the Stratonovich-type Riemann sums, as a function of t, of fractional Brownian motion with Hurst parameter H=1/4.

참고문헌 (7)

Billingsley. P., "Converges of probability measures" (1968), John Wiley & Sons, Inc.
Nourdin, I., "Multivariate normal approximnation using Stein's method and Malliavin calculus", Ann. Inst. Henri Poincare Probab. Stat, 46(1), pp.45~58 (2010)
D. Nualart, "Malliavin calculus and related topics" (2006), Springer
Nualart, D., "Central limit theorems for multiple stochastic integrals and Malliavin calculus", Stochastic Process. Appl, 118, pp.614~628 (2008)
Nualart, D., "Central limit theorems for sequences of multiple stochastic integrals", Ann. Probab, 33(1), pp.173~193 (2005)
Peccati, G., "Seminaire de Probabilites XXXVIII. Lecture Notes in Math", pp.247~262 (2005), Springer
Swanson, J., "Variations of the solution to a stochastic heat equation", Ann. Probab, 35(6), pp.2122~2159 (2007)

이 간행물의 다른 논문 (14건)

THE POSITIVITY OF THE HYPERGEOMETRIC TRANSLATION OPERATORS ASSOCIATED TO THE CHEREDNIK OPERATORS AND THE HECKMAN-OPDAM THEORY ATTACHED TO THE ROOT SYSTEMS OF TYPE B2 AND C2Khalifa Trime`chepp. 1-28 ON THE MARTINGALE EXTENSION OF LIMITING DIFFUSION IN POPULATION GENETICS최원pp. 29-36 σ-COMPLETE BOOLEAN ALGEBRAS AND BASICALLY DISCONNECTED COVERS신창협, 김창일pp. 37-43 A STUDY FOR DEVELOPMENT OF UNIVERSITY MATHEMATICS COURSE BASED ON REAL LIFE CONTEXT AND CLASSROOM DISCUSSION이향주pp. 45-56 PARTS FORMULAS INVOLVING CONDITIONAL INTEGRAL TRANSFORMS ON FUNCTION SPACE김봉진, 김병수pp. 57-69