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math.PR2011
Vertical martingales, stochastic calculus and harmonic sections
Simão Stelmastchuk
This work is about a new class of martingales: the vertical martingales. We construct the vertical martingale for smooth submersions and we develop a stochastic calculus for one. F…
math.PR2011
Martingales in Reductive Homogeneous spaces
S. N. Stelmastchuk
The subject of this work is to study martingales in a reductive homogeneous space with respect to a symmetric connection. Our basic idea is to view homogenous spaces as principal f…
math.PR2011
The Itô exponential on Lie Groups
Simão N. Stelmastchuk
Let be a Lie Group with a left invariant connection . Denote by $\g$ the Lie algebra of , which is equipped with a connection $\nabla^{\g}$. Our main is to intro…