Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
권호 표지

An Approximation Theorem for Two-Parameter Wiener Process

  • Kim, Yoon-Tae (Topology and Geometry Research Center, Kyungpook National University, Taegu 702-701)
  • Published : 1997.03.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, a two-parameter version of Ikeda-Watanabe's mollifiers approximation of the Brownian motion is considered, and an approximation theorem corresponding to the one parameter case is proved. Using this approximation, we formulate Wong-Zakai type theorem is a Stochastic Differential Equation (SDE) driven by a two-parameter Wiener process.

Keywords

References

  1. The Annals of Probability v.10 Stochastic equations of hyperbolic and a two-parameter Stratonovich calculus B. Hajek
  2. Stochastic Differential Equations and Diffusion Processes N.Ikeda;S. Watanabe
  3. ACTA Mathematica v.134 Stochastic integrals in the plane R. Cairoli;J.B. Walsh
  4. SIAM Journal on Control and Optimization v.4 no.2 A new representation for stochastic integrals and equations R.L. Stratonovich
  5. Annals of Mathematical Statistics v.36 On the convergence of ordinary integrals to stochastic integrals E. Wong;M. Zakai