This article is cited in 6 papers

Short Communications

Semimartingale functions of a class of diffusion processes

M. G. Mania^a, R. N. Tevzadze<sup>b

a</sup> A. Razmadze Mathematical Institute, Georgian Academy of Sciences
^b Institute of Cybernetics

Abstract: This paper obtains the necessary and sufficient conditions on the function $f=(f(t,x), t\ge0, x\in \mathbf{R})$ for which the transformed process $f=f(t,\xi_t)$ will be a semimartingale (or the Ito process) for any diffusion process $\xi$ with measurable bounded coefficients and uniformly nondegenerate Hölder diffusion.

Keywords: semimartingale functions, diffusion process, generalized derivatives.

Received: 06.04.1998

DOI: 10.4213/tvp470

 English version: Theory of Probability and its Applications, 2001, 45:2, 337–343

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