This paper studies the H∞ filtering problem of stochastic linear systems subject to Markovian jump and multiplicative noise. The transition probabilities are considered be uncertain. A unified form filters is constructed for both continuous-time discrete-time systems. With new decoupling technique coupling terms between Lyapunov matrices parameters, sufficient conditions stability performance e...

The jump behavior of an infinitely active Itô semimartingale can be conveniently characterized by a activity index Blumenthal–Getoor type, typically assumed to constant in time. We study Markovian semimartingales with non-constant, state-dependent and non-vanishing continuous diffusion component. A nonparametric estimator for the functional is proposed shown asymptotically normal under combined...

Deep neural networks (DNNs) with ReLU activation function are proved to be able express viscosity solutions of linear partial integrodifferential equations (PIDEs) on state spaces possibly high dimension d. Admissible PIDEs comprise Kolmogorov for high-dimensional diffusion, advection, and pure jump Lévy processes. We prove such arising from a class jump-diffusions [Formula: see text], that any...

We establish an integration by parts formula for the random functionals of a continuous-time Markov chain, based on partial differentiation with respect to jump times. In comparison with existing methods, our approach does not rely on the Girsanov theorem and it imposes less restrictions on the choice of directions of differentiation, while assuming additional continuity conditions on the consi...

This paper considers the problems of stability, stabilization and H∞ control via memoryless state feedback for uncertain discrete-time Markovian jump linear systems with mode-dependent time delays. Based on linear matrix inequalities, delay-dependent solutions are obtained by using a descriptor model transformation of the system and by applying a new bounding technique for cross terms. Numerica...

Addressed is the problem of state estimation for dynamic Markovian jump systems (MJS) with unknown transitional probability matrix (TPM) of the embedded Markov chain governing the system jumps. Based on recent authors’ results, proposed is a new TPM-estimation algorithm that utilizes stochastic simulation methods (viz. Bayesian sampling) for finite mixtures’ estimation. Monte Carlo simulation r...

The problem of delay-dependent stochastic stability for neutral Markovian jump systems with mixed delays is investigated in this paper. Combined the new constructed Lyapunov functional with the introduced free matrices, and using the analysis technique of matrix inequalities, the delay-dependent stability conditions are obtained. The obtained results are formulated in terms of LMIs, which can b...

This paper aims to study stability in distribution of Markovian switching jump diffusions. The main motivation stems from and stabilizing hybrid systems which there is no trivial solution. An explicit criterion for derived. effects Markov chains, Brownian motions, Poisson jumps are revealed. Based on these criteria, stabilization problems stochastic differential equations with developed.