This paper presents the uniform concentration inequality for stochastic integral of marked point processes. We developed a new chaining method to obtain results. Our main result is presented under an entropy condition partitioning index set integrands. improvement work van de Geer on exponential inequalities martingales in 1995. As applications result, we also obtained functional indexed empiri...

We establish an analog Hardy inequality with sharp constant involving exponential weight function. The special case of this inequality (for n = 2) leads to a direct proof of Onofri inequality on S.

In this work, we study the tradeoffs between the error probabilities of classical-quantum channels and the blocklength n when the transmission rates approach the channel capacity at a rate slower than 1/ √ n, a research topic known as moderate deviation analysis. We show that the optimal error probability vanishes under this rate convergence. Our main technical contributions are a tight quantum...

Option pricing and hedging in a complete market are well-studied with nice results using martingale theories. However, they remain as open questions in incomplete markets. In particular, when the underlying processes involve jumps, there could be infinitely many martingale measures which give an interval of no-arbitrage prices instead of a unique one. Consequently, there is no martingale repres...

We obtain general weak existence and stability results for stochastic convolution equations with jumps under mild regularity assumptions, allowing non-Lipschitz coefficients singular kernels. Our approach relies on convergence in Lp spaces. The main tools are new a priori estimates Sobolev–Slobodeckij norms of the solution, as well novel martingale problem that is equivalent to original equatio...

The problems of almost sure a.s. stability and a.s. stabilization are investigated for hybrid stochastic systems HSSs with time-varying delays. The different time-varying delays in the drift part and in the diffusion part are considered. Based on nonnegative semimartingale convergence theorem, Hölder’s inequality, Doob’s martingale inequality, and Chebyshev’s inequality, some sufficient conditi...

This paper deals with the quantized H∞ control problem for uncertain networked control system with Markovian jumps and time delays. In the study, networkinduced delays and limited communication capacity due to signal quantization are both taken into consideration. The system contains time delays and Markovian jumps with partially known transition probabilities. By linear inequality approach, a ...

We suggest two versions of the Hardy--Littlewood--Sobolev inequality for discrete time martingales. In one version, fractional integration operator is a martingale transform, however, it may vanish if filtration excessively irregular; second version lacks property while being analytically meaningful an arbitrary filtration.