Jack Baczynski

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Filtering deals with the optimal estimation of signals from their noisy observations. The standard setting consists of a pair of random processes (X,Y ) = (Xt, Yt)t≥0, where the signal component X is to be estimated at a current time t > 0 on the basis of the trajectory of Y , observed up to t. Under the minimal mean square error criterion, the optimal(More)
Under the structural assumption of stochastic stability, we prove existence of maximal solution for a certain perturbed algebraic Riccati equation in infinite dimensional Banach space. The positive perturbation operator is as it appears in control problems involving Markov jump linear systems with infinite countable state space.
In this paper, we deal with a perturbed algebraic Riccati equation in an infinite dimensional Banach space. Besides the interest in its own right, this class of equations appears, for instance, in the optimal control problem for infinite Markov jump linear systems (from now on iMJLS). Here, infinite or finite has to do with the state space of theMarkov(More)
We propose a second order accurate numerical finite difference method to replace the classical schemes used to solve PDEs in financial engineering. We name it Modified Fully Implicit method. The motivation for doing so stems from the accuracy loss while trying to stabilize the solution via the up-wind scheme in the convective term as well as the fact that(More)
A new concept of risk sensitivity is given which unveils a wide class of functions not detected as risk sensitive in the classical scenario. Benefiting from the broadening of this class beyond the classical real-valued convex format, the concept allows, for instance, to further inroads concerning risk sensitive optimal control problems as did Jacobson(More)