A STRONG COMPARISON RESULT FOR THE BELLMAN EQUATION ARISING IN STOCHASTIC EXIT TIME CONTROL PROBLEMS AND ITS APPLICATIONS

[1]  H. Ishii,et al.  A New Formulation of State Constraint Problems for First-Order PDEs , 1996 .

[2]  H. Ishii.  Hamilton-Jacobi Equations with Discontinuous Hamiltonians on Arbitrary Open Sets , 1985 .

[3]  G. Barles,et al.  Discontinuous solutions of deterministic optimal stopping time problems , 1987 .

[4]  H. Ishii.  Perron’s method for Hamilton-Jacobi equations , 1987 .

[5]  G. Barles,et al.  Convergence of approximation schemes for fully nonlinear second order equations , 1990, 29th IEEE Conference on Decision and Control.

[6]  P. L. Linos.  Optimal control of diffustion processes and hamilton-jacobi-bellman equations part I: the dynamic programming principle and application , 1983 .

[7]  G. Barles,et al.  Comparison principle for dirichlet-type Hamilton-Jacobi equations and singular perturbations of degenerated elliptic equations , 1990 .

[8]  H. W. Knobloch.  On optimal control problems with state space constraints , 1975 .

[9]  P. Lions.  Optimal control of diffusion processes and hamilton–jacobi–bellman equations part 2 : viscosity solutions and uniqueness , 1983 .

[10]  G. Barles,et al.  The Dirichlet problem for semilinear second-order degenerate elliptic equations and applications to stochastic exit time control problems , 1995 .

[11]  Eduardo D. Sontag,et al.  Mathematical Control Theory: Deterministic Finite Dimensional Systems , 1990 .

[12]  Hitoshi Ishii,et al.  A boundary value problem of the Dirichlet type for Hamilton-Jacobi equations , 1989 .

[13]  A. Bensoussan.  Stochastic control by functional analysis methods , 1982 .

[14]  P. Lions.  Optimal control of diffusion processes and Hamilton-Jacobi-Bellman equations, Part I , 1983 .

[15]  P. Lyons.  Neumann Type Boundary Conditions for Hamilton-Jacobi Equations. , 1985 .

[16]  G. Barles,et al.  Exit Time Problems in Optimal Control and Vanishing Viscosity Method , 1988 .

[17]  N. Karoui.  Les Aspects Probabilistes Du Controle Stochastique , 1981 .

[18]  W. Fleming,et al.  Controlled Markov processes and viscosity solutions , 1992 .

[19]  G. Barles,et al.  Uniqueness and the maximum principle for quasilinear elliptic equations with quadratic growth conditions , 1995 .

[20]  N. Krylov.  Controlled Diffusion Processes , 1980 .

[21]  H. Soner.  Optimal control with state-space constraint I , 1986 .

[22]  G. Barles.  Solutions de viscosité des équations de Hamilton-Jacobi , 1994 .