We prove existence, uniqueness and gradient estimates of stochastic differential utility as a solution of the Cauchy problem for the following equation in R-3: partial derivative(xx)u + upartial derivative(y)u - partial derivative(t)u = f((.),u), where f is Lipschitz continuous. We also characterize the solution in the vanishing viscosity sense.
On the viscosity solutions of a stochastic differential utility problem
ANTONELLI, FABIO;
2002-01-01
Abstract
We prove existence, uniqueness and gradient estimates of stochastic differential utility as a solution of the Cauchy problem for the following equation in R-3: partial derivative(xx)u + upartial derivative(y)u - partial derivative(t)u = f((.),u), where f is Lipschitz continuous. We also characterize the solution in the vanishing viscosity sense.File in questo prodotto:
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