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Itô's formula has been celebrated as a fundamental extension of the classical Leibnitz-Newton formula and forms a cornerstone to what is known today as stochastic calculus. In recent years, there have been further extensions of this formula which essentially weaken further the smoothness of the function to which the formula is applied at the cost of an additional term involving integration over a two dimensional field which has been labeled local time-space. As of yet the full potential of local time-space calculus and its applications has neither been realized nor properly understood. The current proposal aimed at bringing together researchers who in some way have touched on this currently unchartered territory in order to examine its importance as both a pure and applied field of study as well as to establish the state of the art in the current literature and identify new road map of research.
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Nathalie Eisenbaum, Andreas E. Kyprianou, Ana-Maria Matache, Goran Peskir, Mini-Workshop: Local Time-Space Calculus with Applications. Oberwolfach Rep. 1 (2004), no. 2, pp. 1343–1370DOI 10.4171/OWR/2004/26