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2 results

Stochastic differential games involving impulse controls *
Feng Zhang
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 17 / Issue 3 / July 2011

Published online by Cambridge University Press:

23 April 2010, pp. 749-760

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July 2011
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A zero-sum stochastic differential gameproblem on infinite horizon with continuous and impulse controls isstudied. We obtain the existence of the value of the game andcharacterize it as the unique viscosity solution of the associatedsystem of quasi-variational inequalities. We also obtain averification theorem which provides an optimal strategy of the game.

Almost sure properties of controlled diffusionsand worst case properties of deterministic systems
Martino Bardi, Annalisa Cesaroni
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 14 / Issue 2 / April 2008

Published online by Cambridge University Press:

20 March 2008, pp. 343-355

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April 2008
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We compare a general controlled diffusion process with a deterministic systemwhere a second controller drives the disturbance against the firstcontroller. We show that the two models are equivalent withrespect to two properties: the viability (or controlledinvariance, or weak invariance) of closed smooth sets, and theexistence of a smooth control Lyapunov function ensuring thestabilizability of the system at an equilibrium.

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2 results

Stochastic differential games involving impulse controls*

Almost sure properties of controlled diffusionsand worst case properties of deterministic systems

Stochastic differential games involving impulse controls *