演講訊息 TALKS

摘要: Under the condition that the diffusion coefficients are uniformly elliptic, we study the Euler scheme of (non-Markovian) stochastic differential equations. While the strong approximation (i.e. approximation in Lp) and the weak approximation (i.e. approximation in terms of expectation) have been well studied, we study an approximation which has not been very much touched so far-- the approximation of probability densities. We are concerned with the following problems: do the corresponding densities converge and, if they do, in which Holder space the convergence takes place? Using differential analysis on the Wiener space (Malliavin's stochastic calculus of variations), especially Watanabe's theory of pullback of distributions and fractional Sobolev space over the Wiener space, we answer the above problems. To this end we localize fractional calculus of Wiener functionals. We obtain the relation between the Holder indexes of the spaces in which the convergence can take place and those of the spaces in which the coefficients lay in.