Occupation Measures of Singularly Perturbed Markov Chains with Absorbing States

This paper develops asymptotic properties of singularly perturbed Markov chains with inclusion of absorbing states.It focuses on both unscaled and scaled occupation measures.Under mild conditions,a mean-square estimate is obtained.By averaging the fast components,we obtain an aggregated process.Although the aggregated process itself may be non-Markovian,its weak limit is a Markov chain with much smaller state space.Moreover,a suitably scaled sequence consisting of a component of scaled occupation measures and a component of the aggregated process is shown to converge to a pair of processes with a switching diffusion component.

The Multifractal Analysis of the Occupation Measure of a Lévy Process

We introduce the results on the multifractal structure of the occupation measures of a Brownian Motion, a stable process, a general subordinator and a stochastic process derived from random reordering of the Cantor set. We also introduced an interesting and powerful technique to investigate the multifractal spectrum.

Large deviation principle of occupation measures for non-linear monotone SPDEs

Using the hyper-exponential recurrence criterion,we establish the occupation measures’large deviation principle for a class of non-linear monotone stochastic partial differential equations(SPDEs)driven by Wiener noise,including the stochastic p-Laplace equation,the stochastic porous medium equation and the stochastic fast-diffusion equation.We also propose a framework for verifying hyper-exponential recurrence,and apply it to study the large deviation problems for strong dissipative SPDEs.These SPDEs can be stochastic systems driven by heavy-tailedα-stable process.

Multifractal structure of the product measure of two independent general subordinators'occupation measures

In this paper, we mainly investigate the multifractal spectrum of the random measure derived from two independent general subordinators.

ABSOLUTE CONTINUITIES OF EXIT MEASURES AND TOTAL WEIGHTED OCCUPATION TIME MEASURES FOR SUPER-α-STABLE PROCESSES

Suppose X is a super-α-stable process in R^d, （0 〈 α〈 2）, whose branching rate function is dr, and branching mechanism is of the form ψ（z） = z^1＋β （0 〈0 〈β ≤1）. Let Xγ and Yγ denote the exit measure and the total weighted occupation time measure of X in a bounded smooth domain D, respectively. The absolute continuities of Xγ and Yγ are discussed.

Spectrum Occupancy Measurement and Analysis

This paper analyzes current spectrum utilization from all aspects based on related methods of spectrum measurement. The measurement results show that some spectrum resources are not used effectively due to current fixed spectrum allocation policy, and the spectrum occupancy varies dramatically in terms of time and space. These results provide basis for the development of next generation wireless communication technologies such as Cognitive Radio (CR).

A Functional LIL for Integrated α Stable Process

Let {X（t）,t ∈ R＋} be an integrated α stable process. In this paper, a functional law of the iterated logarithm （LIL） is derived via estimating the small ball probability of X. As a corollary,, the classical Chung LIL of X is obtained. Furthermore, some results about the weighted occupation measure of X（t） are established.

A Functional LIL for m-Fold Integrated Brownian Motion

Let {Xm（t）, t∈R＋} be an m-Fold integrated Brownian motion. In this paper, with the help of small ball probability estimate, a functional law of the iterated logarithm （LIL） for Xm（t） is established. This extends the classic Chung type liminf result for this process. Furthermore, a result about the weighted occupation measure for Xm（t） is also obtained.

CONVERGENCE OF CONTROLLED MODELS FOR CONTINUOUS-TIME MARKOV DECISION PROCESSES WITH CONSTRAINED AVERAGE CRITERIA

This paper attempts to study the convergence of optimal values and optimal policies of continuous-time Markov decision processes(CTMDP for short)under the constrained average criteria. For a given original model M_∞of CTMDP with denumerable states and a sequence {M_n} of CTMDP with finite states, we give a new convergence condition to ensure that the optimal values and optimal policies of {M_n} converge to the optimal value and optimal policy of M_∞as the state space Snof Mnconverges to the state space S_∞of M_∞, respectively. The transition rates and cost/reward functions of M_∞are allowed to be unbounded. Our approach can be viewed as a combination method of linear program and Lagrange multipliers.