Abstract
Suppose X is a semimartingale on a differential manifold M with a linear connection Γ. The main purpose of this paper is to show that the „Ito integral“ (with respect to Γ) of a differential form along the path of X is the limit in probability of certain Riemann sums, constructed in a natural way using the exponential map in differential geometry. For this, we study the deviation between the stochastic development of X in the tangent space at some point, and the image of X under the inverse of the exponential map at the point.
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