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Endowing the manifold with a connection establishes a natural relation with the horizontal part of the frame bundle. This lends itself to the definition of horizontal semimartingales by generalizing the horizontal lift of smooth curves on manifolds. Following this, a one-to-one correspondence between Euclidean semimartingales and manifold-valued ones are obtained through horizontal lift.

Furthermore, this one-to-one correspondence allows for a notion of manifold valued martingales to be defined. Their relation to diffusion processes are examined and an equivalent definition is obtained by means of diffusion theory. Write a review. See any care plans, options and policies that may be associated with this product. Email address. Please enter a valid email address. Walmart Services. Get to Know Us. Customer Service.

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