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...
These lectures concentrate on fundamentals of the modern theory of linear elliptic and parabolic equations in H older spaces. Krylov shows that this theory - including some issues of the theory of nonlinear equations - is based on some general and extremely powerful ideas and some simple computations. The main object of study is the first boundary-value problems for elliptic and parabolic equations, with some guidelines concerning other boundary-value problems such as the Neumann or oblique derivative problems or problems involving higher-order elliptic operators acting on the boundary....
These lectures concentrate on fundamentals of the modern theory of linear elliptic and parabolic equations in H older spaces. Krylov shows that this t...
Focusing on one of the major branches of probability theory, this book treats the large class of processes with continuous sample paths that possess the Markov property. The exposition is based on the theory of stochastic analysis, which uses such notions as stochastic differentials and stochastic integrals.
Focusing on one of the major branches of probability theory, this book treats the large class of processes with continuous sample paths that possess t...
This text concentrates on the basic facts and ideas of the modern theory of linear elliptic and parabolic equations in Sobolev spaces. The main areas covered in this book are the first boundary-value problem for elliptic equations and the Cauchy problem for parabolic equations.
This text concentrates on the basic facts and ideas of the modern theory of linear elliptic and parabolic equations in Sobolev spaces. The main areas ...
