Adaptive weak approximation of diffusions with jumps

• This work develops Monte Carlo Euler adaptive time stepping methods for the weak approximation problem of jump diffusion driven stochastic differential equations. The main result is the derivation of a new expansion for the omputational error, with computable leading order term in a posteriori form, based on stochastic flows and discrete dual backward problems which extends the results in [STZ]. These expansions lead to efficient and accurate computation of error estimates. Adaptive algorithms for either stochastic time steps or quasi-deterministic time steps are described. Numerical examples show the performance of the proposed error approximation and of the described adaptive time-stepping methods.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

diffusions with jumps

weak approximation

error control

Euler-Maruyama method

a posteriori error estimates

backward dual functions

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