|
This article is cited in 2 scientific papers (total in 2 papers)
On decomposition of continuous submartingales
K. È. Dambis Moscow
Abstract:
Doob (see [2], p. 267) proved that every discrete parameter submartingale $X=(x_n,\mathfrak F_n)$, $1\le n<\infty$, may be decomposed as a sum $X=\Psi+\Gamma$ where $\Psi=(\psi_n,\mathfrak F_n)$ is a non-decreasing process and $\Gamma=(\gamma_n,\mathfrak F_n)$ is a martingale. Meyer (see [4], p. 199) found necessary and sufficient conditions for a right continuous submartingale $X=(x_t,\mathfrak F_t)$, $0\le t<\infty$ to have Doob's decomposition. In the present paper a generalisation of Doob's decomposition is obtained which is applicable to every continuous submartingale. The second main result of this paper consist in the fact that every continuous martingale $X=(x_t,\mathfrak F_t)$, $0\le t<\infty$, with $X_0=0$ has an equivalent one $X'=(x'_t,\mathfrak F'_t)$, $0\le t<\infty$, which may be obtained from some Wiener process by means of a continuous random time change. Finally we prove that sample functions of a continuous submartingale (martingale) either have infinite variation or nondecrease (are constant) on every interval.
Full text:
PDF file (2013 kB)
English version:
Theory of Probability and its Applications, 1965, 10:3, 401–410
Bibliographic databases:
Received: 04.02.1964
Citation:
K. È. Dambis, “On decomposition of continuous submartingales”, Teor. Veroyatnost. i Primenen., 10:3 (1965), 438–448; Theory Probab. Appl., 10:3 (1965), 401–410
Citation in format AMSBIB
\Bibitem{Dam65}
\by K.~\`E.~Dambis
\paper On decomposition of continuous submartingales
\jour Teor. Veroyatnost. i Primenen.
\yr 1965
\vol 10
\issue 3
\pages 438--448
\mathnet{http://mi.mathnet.ru/tvp540}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=202179}
\zmath{https://zbmath.org/?q=an:0141.15102}
\transl
\jour Theory Probab. Appl.
\yr 1965
\vol 10
\issue 3
\pages 401--410
\crossref{https://doi.org/10.1137/1110048}
Linking options:
http://mi.mathnet.ru/eng/tvp540 http://mi.mathnet.ru/eng/tvp/v10/i3/p438
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
This publication is cited in the following articles:
-
Zhou H.-l., Wang Sh.-ya., “A Computation of the Price of Convertible Bonds with Changes of Numeraire and Changes of Time”, Advances in Business Intelligence and Financial Engineering, Advances in Intelligent Systems Research, 5, 2008, 142–148
-
Engelbert H.-J., Peskir G., “Stochastic Differential Equations For Sticky Brownian Motion”, Stochastics, 86:6 (2014), 993–1021
|
Number of views: |
This page: | 321 | Full text: | 137 | First page: | 4 |
|