Brownian motionsEigenfunctions, Lévy LaplacianSemigroupWhite noise distributions60H40By using an infinite sequence of independent Brownian motions, a stochastic expression is obtained for semigroups generated by sums of Lévy Laplacians acting on a class of S-transforms of white noise distributions....
be independent brownian motions on \((\omega ,\mathcal {f},\mathbb {p})\) . for each \(i\ge 1\) , denote by \({\mathbb {f}}^i:=\{{\mathcal {f}}^i_t\}_{t\in [0,t]}\) the \(\mathbb {p}\) -completion of the filtration generated by \(w^i\) and let \(\...
In this paper, we give a stochastic expression of a semigroup generated by a sum of the Lévy Laplacians acting on a class of S-transforms of white noise distributions in terms of an infinite sequence of independent Brownian motions.Kimiaki...
The exchange rate as well as the foreign and domestic zero coupon bond prices are assumed to follow geometric Brownian motions.The emphasis is devoted to the discretely sampled Asian option. It is shown how the value of this option can be approximated as the sum of Black-Scholes options. The...