Geodesic
$\sigma$-localization and $\sigma$-martingales
Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 1, pp. 177-188

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This paper introduces the concept of $\sigma$-localization, which is a generalization of localization in the general theory of stochastic processes. The $\sigma$-localized class derived from the set of martingales is the class of $\sigma$-martingales, which plays an important role in mathematical finance. These processes and the corresponding $\sigma$-martingale measures are considered in detail. By extending the stochastic integral with respect to compensated random measures, a canonical representation of $\sigma$-martingales as for local martingales is derived.
Keywords: $\sigma$-localization, stochastic integral, canonical representation, $\sigma$-martingale measure.
Mots-clés : $\sigma$-martingale 
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     author = {J. Kallsen},
     title = {$\sigma$-localization and $\sigma$-martingales},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {177--188},
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     url = {http://geodesic.mathdoc.fr/item/TVP_2003_48_1_a11/}
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J. Kallsen. $\sigma$-localization and $\sigma$-martingales. Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 1, pp. 177-188. http://geodesic.mathdoc.fr/item/TVP_2003_48_1_a11/