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Limiting laws associated with Brownian motion perturbed by its maximum, minimum and local time, II

2006
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Studia scientiarum mathematicarum Hungarica (Print)
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Proof of Theorem 1.1 Let s > 0 and Γ s ∈ F s fixed. Using the definition of Q F x,t (Γ s ) and the Markov property we have : Property (1.7) and inequality (1.8) allow us to apply the dominated convergence theorem : 1.3 In this paper, we investigate four cases of examples involving respectively for (A t ) : • the unilateral maximum (resp. minimum) S t (resp. I t ) : We also consider, in the same case study the two-dimensional process (S t , t). • (L 0 t ; t ≥ 0) the local time at 0 of (X t ) t≥0

doi:10.1556/sscmath.43.2006.3.3
fatcat:qt23vlsj5jhkpbxr6i2ibb3e7y