We prove existence, uniqueness and gradient estimates of stochastic differential utility as a solution of the Cauchy problem for the following equation in ℝ3: ∂xxu + u∂yu - ∂tu = f (·,u), where f is Lipschitz continuous. We also characterize the solution in the vanishing viscosity sense. © 2002 Elsevier Science (USA). All rights reserved.
Antonelli F., Pascucci A. (2002). On the viscosity solutions of a stochastic differential utility problem. JOURNAL OF DIFFERENTIAL EQUATIONS, 186(1), 69-87 [10.1016/S0022-0396(02)00026-8].
On the viscosity solutions of a stochastic differential utility problem
Pascucci A.
2002
Abstract
We prove existence, uniqueness and gradient estimates of stochastic differential utility as a solution of the Cauchy problem for the following equation in ℝ3: ∂xxu + u∂yu - ∂tu = f (·,u), where f is Lipschitz continuous. We also characterize the solution in the vanishing viscosity sense. © 2002 Elsevier Science (USA). All rights reserved.File in questo prodotto:
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