Markov chain approximation method

In <a href="/facts/Numerical_methods/QT9cYa9z">numerical methods</a> for <a href="/facts/Stochastic_differential_equations/ol9a9WNq">stochastic differential equations</a>, the Markov chain approximation method (MCAM) belongs to the several numerical (schemes) approaches used in <a href="/facts/Stochastic_control_theory/ETvJLl24">stochastic control theory</a>. Regrettably the simple adaptation of the deterministic schemes for matching up to stochastic models such as the Runge–Kutta method does not work at all.
It is a powerful and widely usable set of ideas, due to the current infancy of stochastic control it might be even said 'insights.' for numerical and other approximations problems in <a href="/facts/Stochastic_processes/Ng1n1dnB">stochastic processes</a>. They represent counterparts from deterministic control theory such as <a href="/facts/Optimal_control_theory/9SmcQHjJ">optimal control theory</a>.
The basic idea of the MCAM is to approximate the original controlled process by a chosen controlled markov process on a finite state space. In case of need, one must as well approximate the cost function for one that matches up the <a href="/facts/Markov_chain/5oP5hntk">Markov chain</a> chosen to approximate the original stochastic process.

Markov chain approximation method open-in-new

Markov chain approximation method