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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Controlled Markov Processes and Viscosity Solutions of Nonlinear Evolution

Controlled Markov Processes and Viscosity Solutions of Nonlinear Evolution

Fleming, Wendell H.

Paperback

Series: Publications of the Scuola Normale Superiore

Probability & Statistics

Currently unavailable to order

ISBN10: 8876422501
ISBN13: 9788876422508
Publisher: Springer Nature
Published: Oct 1 1988
Pages: 68
Weight: 0.40
Height: 0.23 Width: 6.77 Depth: 9.48
Language: English
These notes are based on a series of lectures delivered at the Scuola Normale Superiore in March 1986. They are intended to explore some connections between the theory of control of Markov stochastic processes and certain classes of nonlinear evolution equations. These connections arise by considering the dynamic programming equation associated with a stochastic control problem. Particular attention is given to controlled Markov diffusion processes on finite dimensional Euclidean space. In that case, the dynamic programming equation is a nonlinear partial differential equation of second order elliptic or parabolic type. For deterministic control the dynamic programming equation reduces to first order. From the viewpoint of nonlinear evolution equations, the interest is in whether one can find some stochastic control problem for which the given evolution equation is the dynamic programming equation. Classical solutions to first order or degenerate second order elliptic/parabolic equations with given boundary Cauchy data do not usually exist. One must instead consider generalized solutions. Viscosity solutions methods have substantially extended the theory.

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