For a spider diffusion with controlled, local-time-dependent branch selection, the value function is characterized as the unique viscosity solution of a HJB system with a nonlinear local-time Kirchhoff boundary condition.
Comparison principle for Walsh's spider HJB equations with non linear local time Kirchhoff's boundary transmission
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
The main purpose of this work is to obtain a comparison principle for viscosity solutions of a system of elliptic Walsh's spider Hamilton-Jacobi-Bellman equations, possessing a new boundary condition called non linear local-time Kirchhoff's transmission. The main idea is to build test functions at the neighborhood of the vertex solutions of ODE, with well-designed coefficients. The key point is to impose a 'local-time' derivative at the vertex absorbing the error term induced by - what we decide to call here - the Kirchhoff's speed of the Hamiltonians.
citation-role summary
method 1
citation-polarity summary
fields
math.AP 1years
2025 1verdicts
CONDITIONAL 1roles
method 1polarities
use method 1representative citing papers
citing papers explorer
-
Stochastic scattering control of spider diffusion governed by an optimal diffraction probability measure selected from its own local-time
For a spider diffusion with controlled, local-time-dependent branch selection, the value function is characterized as the unique viscosity solution of a HJB system with a nonlinear local-time Kirchhoff boundary condition.