stochastic control

The field of stochastic control has developed greatly since the 1970s, particularly in its applications to finance.

A crucial distinction is between deterministic and stochastic control models.

Stochastic control deals with control design with uncertainty in the model.

Robert Merton used stochastic control to study optimal portfolios of safe and risky assets.

Building up market making strategies typically involves precise modeling of the target market microstructure together with stochastic control techniques.

More precisely, a Markov Decision Process is a discrete time stochastic control process.

An extremely well-studied formulation in stochastic control is that of linear quadratic Gaussian control.

His main research interests are in mathematical finance, contract theory, stochastic control theory, and stochastic differential equations.

Witsenhausen's counterexample, shown in the figure below, arises in a deceptively simple toy problem in decentralized stochastic control.

Many other researchers provided solutions using concepts from several control areas such as robust control, optimal stochastic control, model predictive control, fuzzy logic etc.

Existence of optimal stochastic control laws, SIAM Journal on Control 9(?)

He was elected IEEE Fellow (1990) for "contributions to the structure of telephone connecting networks, stochastic control, and nonlinear filtering".

Stochastic control aims to design the time path of the controlled variables that performs the desired control task with minimum cost, somehow defined, despite the presence of this noise.

His main field of interest is stochastic analysis, including stochastic control, optimal stopping, stochastic ordinary and partial differential equations and applications, particularly to physics, biology and finance.

The idea of solving a control problem by applying Bellman's principle of optimality and then working out backwards in time an optimizing strategy can be generalized to stochastic control problems.

S. S. Sritharan,"Deterministic and stochastic control of viscous flow with linear, monotone and hyper viscosities," Applied Mathematics and Optimization, Vol.

In typical stochastic control problems, it is assumed that there exist random noise and disturbances in the model and the controller, and the control design must take into account these random deviations.

István Gyöngy (born 1951) is a Hungarian mathematician working in the fields of stochastic differential equations, stochastic partial differential equations and their applications to nonlinear filtering and stochastic control.

Stochastic Optimal Control: The Discrete-Time Case (1978, co-authored with S. E. Shreve), a mathematically complex work, establishing the measure-theoretic foundations of dynamic programming and stochastic control.

In probability theory, the Mabinogion sheep problem or Mabinogian urn is a problem in stochastic control introduced by , who named it after a herd of magic sheep in the Welsh epic Mabinogion.

Stochastic control or stochastic optimal control is a subfield of control theory that deals with the existence of uncertainty either in observations of the data or in the things that drive the evolution of the data.

And in 2008 he received the Richard E. Bellman Control Heritage Award from the American Automatic Control Council, "for pioneering contributions to stochastic control, hybrid systems and the unification of theories of control and computation".

At the beginning of his career (starting from 1963) he, in collaboration with Dynkin, worked on nonlinear stochastic control theory, making advances in the study of convex, nonlinear partial equations of 2nd order (i.e. Bellman equations), which were examined with stochastic methods.

Soner co-authored a book, with Wendell Fleming, on viscosity solutions and stochastic control; Controlled Markov Processes and Viscosity Solutions (Springer-Verlag) in 1993, which was listed among the most-cited articles on computer science by Thomson Science in 2004.