A Convolution Approach to Multivariate Bessel Proceses

Thu Van Nguyen, S. Ogawa and M. Yamazato
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Thu Van Nguyen: Department of Mathematics, International University, HCM City, Vietnam
S. Ogawa: Department of Mathematical Sciences, Ritsumeikan University, Japan
M. Yamazato: Department of Mathematics, Ryukyu University, Japan

Chapter 14 in Stochastic Processes and Applications to Mathematical Finance, 2007, pp 233-244 from World Scientific Publishing Co. Pte. Ltd.

Abstract: AbstractIn this paper we introduce and study Bessel processes $\{{\bf B}_t^{\bf x}\}$ which take values in a d-dimensional nonnegative cone ${\mathcal R}^{+d}$ of ${\mathcal R}^d$ and are constructed via the multi-dimensional Kingman convolution. We prove that every d-variate Bessel process is a stationary independent increments-type process. Moreover, a stochastic integral with respect to $\{{\bf B}_t^{\bf x}\}$ with the convergence in distribution is defined.

Keywords: Stochastic Calculus; Mathematical Finance; Insider Trading; Stochastic Control; Real Options; Filtering Model of Credit Risks; Stochastic Growth Models (search for similar items in EconPapers)
Date: 2007
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