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 Teor. Veroyatnost. i Primenen., 1972, Volume 17, Issue 1, Pages 173–178 (Mi tvp4216)

Short Communications

On the Absolute Continuity of Measures Corresponding to Diffusion Type Processes

M. P. Ershov

Moscow

Abstract: In the paper, conditions are studied under which the measures corresponding to Wiener processes with different drifts are equivalent. The main theorem assepts that, if the drift coefficient (measurable with respect to the past of the observation process) is square integrable a.s. at both «observation-process» and «Wiener-process point», then the measures of the process are equivalent.
The result is applied to the existence and uniqueness of a weak of the stochastic equation $d\xi=\gamma(t,\xi) dt+dW$.

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English version:
Theory of Probability and its Applications, 1972, 17:1, 169–174

Bibliographic databases:

Citation: M. P. Ershov, “On the Absolute Continuity of Measures Corresponding to Diffusion Type Processes”, Teor. Veroyatnost. i Primenen., 17:1 (1972), 173–178; Theory Probab. Appl., 17:1 (1972), 169–174

Citation in format AMSBIB
\Bibitem{Ers72} \by M.~P.~Ershov \paper On the Absolute Continuity of Measures Corresponding to Diffusion Type Processes \jour Teor. Veroyatnost. i Primenen. \yr 1972 \vol 17 \issue 1 \pages 173--178 \mathnet{http://mi.mathnet.ru/tvp4216} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=394850} \zmath{https://zbmath.org/?q=an:0315.60043} \transl \jour Theory Probab. Appl. \yr 1972 \vol 17 \issue 1 \pages 169--174 \crossref{https://doi.org/10.1137/1117017} 

• http://mi.mathnet.ru/eng/tvp4216
• http://mi.mathnet.ru/eng/tvp/v17/i1/p173

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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. Yu. M. Kabanov, R. Sh. Liptser, A. N. Shiryaev, “Absolute continuity and singularity of locally absolutely continuous probability distributions. II”, Math. USSR-Sb., 36:1 (1980), 31–58
2. Cherny A., Urusov M., “On the absolute continuity and singularity of measures on filtered spaces: Separating times”, From Stochastic Calculus to Mathematical Finance: The Shiryaev Festschrift, 2006, 125–168