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an it？ formula for an accretive operatorit 公式粘连的运营商
Axioms 2012, 1, 4-8; doi:10.3390/axioms1010004
OPEN ACCESS
axioms
ISSN 2075-1680
/journal/axioms
Communication
ˆ
An Ito Formula for an Accretive Operator
´ ´
Remi Leandre
´ ´ ´
Laboratoire de Mathematiques, Universite de Franche-Comte, route de Gray, Besanc¸on 25030,
France; E-Mail: Remi.leandre@univ-fcomte.fr; Tel.: +33-03 81 66 63 3
Received: 21 November 2011; in revised form: 12 March 2012 / Accepted: 13 March 2012 /
Published: 21 March 2012
ˆ
Abstract: We give an Ito formula associated to a non-linear semi-group associated to a
m-accretive operator.
ˆ
Keywords: non-linear semi-group; Ito formula
1. Introduction
ˆ
Let us recall the Ito formula in the Stratonovich Calculus [1]. Let be a one dimensional Brownian
motion and be a smooth function on . Then
(1)
where we consider the Stratonovich differential.
In [2,3], we have remarked that the couple is a diffusion on whose generator can be
ˆ
easily computed. This leads to an interpretation inside the semi-group theory of the I
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