Stochastic Flows and Jump-Diffusions

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.

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.