Shopping Cart
You're getting the VIP treatment!
With the purchase of Kobo VIP Membership, you're getting 10% off and 2x Kobo Super Points on eligible items.
itemsitem
With the purchase of Kobo VIP Membership, you're getting 10% off and 2x Kobo Super Points on eligible items.
Save $16.51 (20% off) and earn Kobo Super Points!
You'll see how many points you'll earn before checking out. We'll award them after completing your purchase.
Or, get it for 34000 Kobo Super Points!
See if you have enough points for this eBook. Sign in
This book provides the mathematical foundations for the analysis of a class of degenerate elliptic operators defined on manifolds with corners, which arise in a variety of applications such as population genetics, mathematical finance, and economics. The results discussed in this book prove the uniqueness of the solution to the Martingale problem and therefore the existence of the associated Markov process.
Charles Epstein and Rafe Mazzeo use an "integral kernel method" to develop mathematical foundations for the study of such degenerate elliptic operators and the stochastic processes they define. The precise nature of the degeneracies of the principal symbol for these operators leads to solutions of the parabolic and elliptic problems that display novel regularity properties. Dually, the adjoint operator allows for rather dramatic singularities, such as measures supported on high codimensional strata of the boundary. Epstein and Mazzeo establish the uniqueness, existence, and sharp regularity properties for solutions to the homogeneous and inhomogeneous heat equations, as well as a complete analysis of the resolvent operator acting on Hölder spaces. They show that the semigroups defined by these operators have holomorphic extensions to the right half-plane. Epstein and Mazzeo also demonstrate precise asymptotic results for the long-time behavior of solutions to both the forward and backward Kolmogorov equations.
You can read this item using any of the following Kobo apps and devices: