Path-Dependent Hamilton–Jacobi Equations: The Minimax Solutions Revised

Amplitude Equations for Time-Dependent Solutions of the McKendrick Equations

The well-known McKendrick equations model the dynamical behavior of age-dependent populations. These equations govern, at time t, the number of individuals of age a in a population, known as the population density, and arise from a conservation law subject to constitutive assumptions for the maternity and mortality rates. In this paper, multiple scale analysis and bifurcation theory are applied...

Revised-Path Dependence

In this paper, we define a class of revised-path dependent processes and characterize some of their basic properties. A process exhibits revised-path dependence if the current outcome causes the value of a past outcome to be revised. This revision could be an actual change to that outcome or a reinterpretation. We characterize a revised-path dependent process called the accumulation process: in...

Improving the Accuracy of the Solutions of Riccati Equations

An overview of Viscosity Solutions of Path-Dependent PDEs

This paper provides an overview of the recently developed notion of viscosity solutions of path-dependent partial differential equations. We start by a quick review of the CrandallIshii notion of viscosity solutions, so as to motivate the relevance of our definition in the path-dependent case. We focus on the wellposedness theory of such equations. In particular, we provide a simple presentatio...

Two iterative algorithms for finding minimax solutions

Two iterative minimax algorithms are presented with associated convergence theorems. Both algorithms consists of iterative procedures based on a sequence of finite parameter sets; in general these finite parameter sets are subsets of an infinite parameter space. To show their applicabilities, several commonly used examples are presented. It is also shown that minimax problems with or without fi...