We consider the time-inhomogeneous Markovian jump process introduced by John S. Bell [4] for a lattice quantum field theory, which runs on the associated configuration space. Its jump rates, tailored to give the process the quantum distribution |Ψt| at all times t, typically exhibit singularities. We establish the existence of a unique such process for all times, under suitable assumptions on t...

We study the stochastic Hamilton–Jacobi–Bellman (HJB) equation with jump, which arises from a non-Markovian optimal control problem recursive utility cost functional. The solution to is predictable triplet of random fields. show that value function problem, under some regularity assumptions, HJB equation; and classical this characterizes control. With additional assumptions on coefficients, an ...

We study partial information, possibly non-Markovian, singular stochastic control of jump diffusions and obtain general maximum principles. The results are used to find connections between singular stochastic control, reflected BSDEs and optimal stopping in the partial information case. Mathematics Subject Classification 2010: 93E20, 60H07, 60H10, 60HXX, 60J75

This paper investigates robust adaptive switching controller design for Markovian jump nonlinear systems with unmodeled dynamics and Wiener noise. The concerned system is of strict-feedback form, and the statistics information of noise is unknown due to practical limitation. With the ordinary input-to-state stability ISS extended to jump case, stochastic Lyapunov stability criterion is proposed...

This paper considers H∞ performance for Markovian jump systems with Time-varying delays. The systems under consideration involve disturbance signal, Markovian switching and timevarying delays. By using a new Lyapunov-Krasovskii functional and a convex optimization approach, a delay-dependent stability condition in terms of linear matrix inequality (LMI) is addressed, which guarantee asymptotica...

This paper examines the problem of designing a robust H∞ state-feedback controller for a class of nonlinear two-time scale systems with Markovian Jumps described by a Takagi-Sugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, LMI-based sufficient conditions for the uncertain Markovian jump nonlinear two-time scale systems to have an H∞ performance are derived. The propo...

This paper examines the problem of designing a robust H∞ state-feedback controller for a class of nonlinear two-time scale systems with Markovian Jumps described by a Takagi-Sugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, LMI-based sufficient conditions for the uncertain Markovian jump nonlinear two-time scale systems to have an H∞ performance are derived. The propo...

This paper examines the problem of designing a robust H∞ state-feedback controller for a class of nonlinear two-time scale systems with Markovian Jumps described by a Takagi-Sugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, LMI-based sufficient conditions for the uncertain Markovian jump nonlinear two-time scale systems to have an H∞ performance are derived. The propo...

We consider a solution xt to a generic Markovian jump diffusion and show that for any t0 > 0 the law of xt0 has a C ∞ density with respect to Lebesgue measure under a uniform version of Hörmander’s conditions. Unlike previous results in the area the result covers a class of infinite activity jump processes. The result is accompolished by using carefully crafted refinements to the classical argu...

The critical value of the reaction rate able to sustain the propagation of an invasive front is obtained for general non-Markovian biased random walks with reactions. From the Hamilton-Jacobi equation corresponding to the mean field equation we find that the critical reaction rate depends only on the mean waiting time and on the statistical properties of the jump length probability distribution...