Kolmogorov equations are second order parabolic equations with a finite or an infinite number of variables. They are deeply connected with stochastic differential equations in finite or infinite dimensional spaces. They arise in many fields as Mathematical Physics, Chemistry and Mathematical Finance. These equations can be studied both by probabilistic and by analytic methods, using such tools as Gaussian measures, Dirichlet Forms, and stochastic calculus. The following courses have been delivered: N.V. Krylov presented Kolmogorov equations coming from finite-dimensional equations, giving...
Kolmogorov equations are second order parabolic equations with a finite or an infinite number of variables. They are deeply connected with stochastic ...
This book covers the optimal control of solutions of fully observable Ito-type stochastic differential equations. It proves the validity of the Bellman differential equation for payoff functions and develops rules for optimal control strategies.
This book covers the optimal control of solutions of fully observable Ito-type stochastic differential equations. It proves the validity of the Bel...
Stochastic control theory is a relatively young branch of mathematics. The beginning of its intensive development falls in the late 1950s and early 1960s. During that period an extensive literature appeared on optimal stochastic control using the quadratic performance criterion (see references in W onham 76J). At the same time, Girsanov 25J and Howard 26J made the first steps in constructing a general theory, based on Bellman's technique of dynamic programming, developed by him somewhat earlier 4J. Two types of engineering problems engendered two different parts of stochastic control...
Stochastic control theory is a relatively young branch of mathematics. The beginning of its intensive development falls in the late 1950s and early 19...
