Stability and Existence of Diffusions with Discontinuous or Rapidly Growing Drift Terms

摘要

Stochastic differential equations whose drift terms do not satisfy the usual (Ito) Lipschitz or linear growth conditions in the state occur frequently as models in stochastic control theory. Local stability properties are useful for proving global existence for ordinary differential equations whose right hand sides grow too fast or are not Lipschitz in the state. Here, the author uses a local stochastic stability property to prove global existence, stability, ergodicity, the strong Markov and other properties, for a class of diffusions which occur frequently as models. (Author)