An isometric embedding of the g(t)-Brownian motion with application in stability and homotopy group
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In this work, we construct a [Formula: see text]-Brownian motion via an isometric embedding, whose approach permit to define the Laplace operator associated with parametrized metric [Formula: see text], for every [Formula: see text]. We present an Itô formula for stochastic flow acting on time-dependent tensor fields, in particular to the metric [Formula: see text] and consequently to the norm of a stochastic process in [Formula: see text]. We use this approach to study stability by [Formula: see text]th moment exponent of [Formula: see text]-Brownian motion and its applications on homotopy groups.
2009 ◽
Vol 201
(2)
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pp. 205-211
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2007 ◽
Vol 44
(02)
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pp. 393-408
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2021 ◽
Vol 1740
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pp. 012016
2012 ◽
Vol 2
(2)
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pp. 281-319
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