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Canonical Decompositions of Certain Generalized Brownian Bridges
Brownian motion Brownian bridge Canonical decomposition Volterra transform
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2009/4/29
We define a generalized Brownian bridge and we provide some information about its filtration. Two decompositions of this process as a semi-martingale are given. The first one is a Volterra decompositi...
Boundary Crossings of Brownian Motion
Brownian motion with trend boundary crossing probability large deviations
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2009/4/27
Let B be a standard Brownian motion and let b_gamma be a piecewise linear continuous boundary function. In this paper we obtain an exact asymptotic expansion of P{ B(t)< b_gamma(t), forall tin [0,1]} ...