非对称Dirichlet型的扰动及其结合的Markov过程

该文研究非对称Ｄｉｒｉｃｈｌｅｔ型的扰动及其结合的Ｍａｒｋｏｖ过程．讨论一般状态空间上的拟正则Ｄｉｒｉｃｈｌｅｔ型（ε,犇（ε））关于光滑符号测度μ的扰动,这里μ＝μ＋ －μ－ ,μ＋ 为光滑测度,μ－ 属于Ｋａｔｏ类,证明了扰动型（εμ,犇（εμ））犺 结合犿 胎紧犿 特别标准的Ｍａｒｋｏｖ过程．     

Markov Chain Approximations for Symmetric Jump Processes

Markov chain approximations of reversible jump processes are investigated. Tightness results and a central limit theorem are established. Moreover, given the generator of a reversible jump process with state space ℝ ^d , the approximating Markov chains are constructed explicitly. As a byproduct we obtain a definition of the Sobolev space H ^α/2(ℝ ^d ), α∈(0,2), that is equivalent to the standard one.      

Markov Chain Approximation of Pure Jump Processes

We prove the weighted endpoint estimates for some multilinear operators related to certain singular integral operators on some Hardy and Herz type Hardy spaces.     

On Multidimensional Generalized Diffusion Processes

We construct a multidimensional generalized diffusion process with the drift coefficient that is the (generalized) derivative of a vector-valued measure satisfying an analog of the Hölder condition with respect to volume. We prove the existence and continuity of the density of transition probability of this process and obtain standard estimates for this density. We also prove that the trajectories of the process are solutions of a stochastic differential equation.     

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In this paper, we extend the previous Markov-modulated reflected Brownian motion model discussed in [1] to a Markov-modulated reflected jump diffusion process, where the jump component is described as a Markov-modulated compound Poisson process. We compute the joint stationary distribution of the bivariate Markov jump process. An abstract example with two states is given to illustrate how the stationary equation described as a system of ordinary integro-differential equations is solved by choosing appropriate boundary conditions. As a special case, we also give the sationary distribution for this Markov jump process but without Markovian regime-switching.     

Game Theoretic Decentralized Feedback Controls in Markov Jump Processes

This paper studies a decentralized routing problem over a network, using the paradigm of mean-field games with large number of players. Building on a state-space extension technique, we turn the problem into an optimal control one for each single player. The main contribution is an explicit expression of the optimal decentralized control which guarantees the convergence both to local and to global equilibrium points. Furthermore, we study the stability of the system also in the presence of a delay which we model using an hysteresis operator. As a result of the hysteresis, we prove existence of multiple equilibrium points and analyze convergence conditions. The stability of the system is illustrated via numerical studies.     

Markov Jump Processes in Estimating Sharing of Identity by Descent

Identity by descent(IBD) sharing is a very important genomic feature in population genetics which can be used to reconstruct recent demographic history.In this paper we provide a framework to estimate IBD sharing for a demographic model called two-population model with migration.We adopt the structured coalescent theory and use a continuous-time Markov jump process {X(t),t≥0} to describe the genealogical process in such model.Then we apply Kolmogorov backward equation to calculate the distributi...     

Boundary Crossing Probabilities of Jump Diffusion Processes to Time-Dependent Boundaries

Methodology and Computing in Applied Probability - The finite Markov chain imbedding technique has been used to compute the boundary crossing probabilities of one and higher-dimensional Brownian...     

On the Nonexplosion and Explosion for Nonhomogeneous Markov Pure Jump Processes

In this paper, we obtain new drift-type conditions for nonexplosion and explosion for nonhomogeneous Markov pure jump processes in Borel state spaces. The conditions are sharp; e.g., the one for nonexplosion is necessary if the state space is in addition locally compact and the Q-function satisfies weak Feller-type and local boundedness conditions. We comment on the relations of our conditions with the existing ones in the literature and demonstrate some possible applications.     

Local Times of Markov Processes Approximated by a Generalized Iterated Brownian Motion

Csáki et al.⁽⁵⁾ have given strong approximations of continuous additive functional of Brownian motion. We establish here an extension of these results for a large class of Markov processes.     

Generalized Solutions of Nonlinear Parabolic Equations and Diffusion Processes

We reduce the construction of a weak solution of the Cauchy problem for a quasilinear parabolic equation to the construction of a solution to a stochastic problem. Namely, we construct a diffusion process that allows us to obtain a probabilistic representation of a weak (in distributional sense) solution to the Cauchy problem for a nonlinear PDE.      

Construction of Generalized Diffusion Processes: the Resolvent Approach

In this paper, we define the generalized diffusion operator ■ for two suitable measures on the line, which includes the generators of the birth-death processes, the one-dimensional diffusion and the gap diffusion among others. Via the standard resolvent approach, the associated generalized diffusion processes are constructed.     

On Markov-Additive Jump Processes

In 1995, Pacheco and Prabhu introduced the class of so-called Markov-additive processes of arrivals in order to provide a general class of arrival processes for queueing theory. In this paper, the above class is generalized considerably, including time-inhomogeneous arrival rates, general phase spaces and the arrival space being a general vector space (instead of the finite-dimensional Euclidean space). Furthermore, the class of Markov-additive jump processes introduced in the present paper is embedded into the existing theory of jump processes. The best known special case is the class of BMAP arrival processes.     

Markov dilation of Diffusion Type Processes and Its Application to the Financial Mathematics

The Markov dilation of diffusion type processes is defined. Infinitesimal operators and stochastic differential equations for the obtained Markov processes are described. Some applications to the integral representation for functionals of diffusion type processes and to the construction of a replicating portfolio for a non-terminal contingent claim are considered.     

Reciprocal Class of Jump Processes

Processes having the same bridges as a given reference Markov process constitute its reciprocal class. In this paper we study the reciprocal class of compound Poisson processes whose jumps belong to a finite set \(\mathcal {A}\subset \mathbb {R}^{d}\). We propose a characterization of the reciprocal class as the unique set of probability measures on which a family of time and space transformations induces the same density, expressed in terms of the reciprocal invariants. The geometry of \(\mathcal {A}\) plays a crucial role in the design of the transformations, and we use tools from discrete geometry to obtain an optimal characterization. We deduce explicit conditions for two Markov jump processes to belong to the same class. Finally, we provide a natural interpretation of the invariants as short-time asymptotics for the probability that the reference process makes a cycle around its current state.     

Extremal Processes with One Jump

Convergence of a sequence of deterministic functions in the Skorohod topology implies convergence of the jumps. For processes with independent additive increments the fixed discontinuities converge. In this paper it will be shown that this is not true for processes with independent max-increments. The limit in of a sequence of stochastically continuous extremal processes may have fixed discontinuities. Our construction makes use of stochastically continuous extremal processes whose sample functions have only one jump.     

Harnack Inequalities for Jump Processes

We consider a class of pure jump Markov processes in R ^d whose jump kernels are comparable to those of symmetric stable processes. We establish a Harnack inequality for nonnegative functions that are harmonic with respect to these processes. We also establish regularity for the solutions to certain integral equations.     

Filtering of a Markov Jump Process with Counting Observations

This paper concerns the filtering of an R ^d -valued Markov pure jump process when only the total number of jumps are observed. Strong and weak uniqueness for the solutions of the filtering equations are discussed. Accepted 12 November 1999