Asymptotic Expansions for Symmetric Statistics with Degenerate Kernels

Asymptotic expansions for degenerate parabolic equations

Article history: Received 14 May 2014 Accepted after revision 26 September 2014 Available online 11 October 2014 Presented by Olivier Pironneau We prove asymptotic convergence results for some analytical expansions of solutions to degenerate PDEs with applications to financial mathematics. In particular, we combine short-time and global-in-space error estimates, previously obtained in the unifo...

Asymptotic Expansions of Symmetric Standard Elliptic Integrals

Symmetric standard elliptic integrals are considered when one of their parameters is larger than the others. Distributional approach is used for deriving five convergent expansions of these integrals in inverse powers of the respective five possible asymptotic parameters. Four of these expansions involve also a logarithmic term in the asymptotic variable. Coefficients of these expansions are ob...

Toeplitz Quantization and Asymptotic Expansions for Real Bounded Symmetric Domains

An analogue of the star product, familiar from deformation quantization, is studied in the setting of real bounded symmetric domains. The analogue turns out to be a certain invariant operator, which one might call star restriction, from functions on the complexification of the domain into functions on the domain itself. In particular, we establish the usual (i.e. semiclassical) asymptotic expan...

Asymptotic Expansions for Integrals

Asymptotic Expansions with Oscillating CoeÆcients

In recent years, Computer Algebra has seen signi cant advances on a wide range of fronts. One of the many areas of development has been Symbolic Asymptotics. The exp{log functions are those de ned by expressions built from the rational numbers Q and the variable, x, using arithmetic operations and the functions exp and log, with the understanding that the latter is only applied to arguments whi...