We introduce jumptime unraveling as a distinct description of open quantum systems. As our starting point, we consider jump trajectories, which emerge, physically, from continuous measurements, or, formally, the Markovian master equations. If stochastically evolving trajectories are ensemble-averaged at specific times, resulting states solutions to associated equation. demonstrate that can also...

Discrete-time coupled algebraic Riccati equations that arise in quadratic optimal control and -control of Markovian jump linear systems are considered. First, the L_ equations that arise from the quadratic optimal control problem are studied. The matrix cost is only assumed to be hermitian. Conditions for existence of the maximal hermitian solution are derived in terms of the concept of mean sq...

In this paper a bond market model and the related term structure of interest rates are studied where prices of zero coupon bonds are driven by a jump-diffusion process. A criterion is derived on the deterministic forward rate volatilities under which the short rate process is Markovian. In the case that the volatilities depend on the short rate sufficient conditions are presented for the existe...

A Bayes type formula is derived for the non-linear filter where the observation contains both general Gaussian noise as well as Cox noise whose jump intensity depends on the signal. This formula extends the well know Kallianpur-Striebel formula in the classical non-linear filter setting. We also discuss Zakai type equations for both the unnormalized conditional distribution as well as unnormali...

In this paper, we provide a new framework for mean square stability of stochastic jump linear systems via optimal transport. The Wasserstein metric which defines an optimal transport cost between probability density functions enables the stability analysis. Without any assumptions on the nature of the underlying jump process, the convergence of the Wasserstein distance guarantees the mean squar...