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Teor. Veroyatnost. i Primenen., 1972, Volume 17, Issue 1, Pages 167–172 (Mi tvp4215)  

This article is cited in 1 scientific paper (total in 1 paper)

Short Communications

Representations of Itô Processes

M. P. Ershov


Abstract: Let $(\Omega,\mathscr{F},\mathbf{P})$ be a complete probability space. By an Itô process relative to an increasing family $\{\mathscr{F}_t\}$ of sub-$\sigma$-algebras of $\mathscr{F}$, we mean a process $\xi$ of the form
$$ \xi_t=\xi_0+\int_0^t\alpha_s ds+\int_0^t \beta_s dW_s $$
where $\alpha,\beta$ are measurable processes well adapted to $\{\mathscr{F}_t\}$, $\displaystyle\int_0^t (|\alpha_s|+\beta_{s}^2)ds<\infty$ $\forall t$ a.s., and $W$ is a standard Wiener process with respect to $\mathscr{F}$. We study conditions under which an Itô process $\xi$ relative to $\{\mathscr{F}_t\}$ is also an Itô process relative to a family $\{\mathscr{G}_t\}$ of “simpler” $\sigma$-algebras: $\mathscr{G}_t\subseteq\mathscr{F}_t$ for each $t$.

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English version:
Theory of Probability and its Applications, 1972, 17:1, 165–169

Bibliographic databases:

Received: 27.05.1970

Citation: M. P. Ershov, “Representations of Itô Processes”, Teor. Veroyatnost. i Primenen., 17:1 (1972), 167–172; Theory Probab. Appl., 17:1 (1972), 165–169

Citation in format AMSBIB
\Bibitem{Ers72}
\by M.~P.~Ershov
\paper Representations of It\^o Processes
\jour Teor. Veroyatnost. i Primenen.
\yr 1972
\vol 17
\issue 1
\pages 167--172
\mathnet{http://mi.mathnet.ru/tvp4215}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=300339}
\zmath{https://zbmath.org/?q=an:0301.60056}
\transl
\jour Theory Probab. Appl.
\yr 1972
\vol 17
\issue 1
\pages 165--169
\crossref{https://doi.org/10.1137/1117016}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. V. Selivanov, “On time changes for Lévy processes”, Russian Math. Surveys, 58:2 (2003), 388–389  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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