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The major results of the paper are in Section 4. We expand integral polynomials to integral power series with respect to the integral root basis and extend the duality
We remark that the nodes and the corresponding coefficients of this formula do not depend to the function f for which we approximate the weighted integral by using the multiple
But the Malliavin calculus for Gaussian processes can be adapted to it, Skorohod stochastic integrals can be defined, and it will allow us to derive an Itˆ o formula when the
Moreover, we show that the resulting stochastic integral satisfies a change of variable formula with a correction term that is an ordinary Itô integral with respect to a Brownian
Key words: infinite divisibility, Lévy measure, O -subexponentiality, dominated variation, expo- nential class.. AMS 2000 Subject Classification: Primary 60E07;
The following theorem completes a recent accumulation of results concerning extended version of Itˆ o’s formula for one dimensional L´evy processes.. As it has been done in [6],
Following the same line of reasoning it is more useful to use this formula rather than the trace expressed in terms of occupation states for the computation of some specific
With the help of the Cauchy problem solution we construct a nonlinear evolution operator and the corresponding left inverse operator in explicit form for the nonlinear FPKE.. In
