Provides systematic treatment of the Malliavin calculus on the WienerPoisson space, introducing Sobolev norms Uses the flow property of the solution of stochastic differential equations and application to dual jump-diffusions Is a study of fundamental solutions through stochastic analysis without the aid of partial differential equations

Autorentext
Kunita was an invited speaker at the ICM 1986.

Zusammenfassung

Inhalt

Preface.- Introduction.- 1.Probability distributions and stochastic processes.- 2.Stochastic integrals based on Wiener processes and Poisson random measures.- 3.Stochastic differential equations and stochastic flows.- 4.Diffusions, jump-diffusions and heat equations.- 5.Malliavin calculus for Wiener processes and Poisson random measures.- 6.Smooth densities and heat kernels.- 7.Jump-diffusions on manifolds and smooth densities.- Bibliography.- Index.