In this paper we study the stationary distributions for reflected diffusions with jumps in the positive orthant. Under the assumption that the stationary distribution possesses a density in R+ that satisfies certain finiteness conditions, we characterize the Fokker-Planck equation. We then provide necessary and sufficient conditions for the existence of a product-form distribution for diffusion...

We consider the boundary crossing problem for time-homogeneous diffusions and general curvilinear boundaries. Bounds are derived for the approximation error of the one-sided (upper) boundary crossing probability when replacing the original boundary by a different one. In doing so we establish the existence of the firstpassage time density and provide an upper bound for this function. In the cas...

We study distorted survival probabilities related to risks in incomplete markets. The risks are modeled as diffusion processes, and the distortions are of general type. We establish a connection between distorted survival probabilities of the original risk process and distortion-free survival probabilities of new pseudo risk diffusions; the latter turns out to be diffusions with killing or spli...

Diffusions with random switching are stochastic processes that consist of a diffusion process Xt and a continuous Markov jump process Yt. Both components interact with each other as Yt controls the dynamical regimes of Xt and Xt effects the transition rate of Yt. This type of systems includes a wide range of models used in various fields, and many applications require the transition rates of Yt...

This paper provides a countable representation for a class of infinite-dimensional diffusions which extends the infinitely-many-neutral-alleles model and is related to the two-parameter PoissonDirichlet process. By means of Gibbs sampling procedures, we define a reversible Moran-type population process. The associated process of ranked relative frequencies of types is shown to converge in distr...

Abstract: Most previous contributions on BSDEs, and the related theories of nonlinear expectation and dynamic risk measures, have been in the framework of continuous time diffusions or jump diffusions. Using solutions of BSDEs on spaces related to finite state, continuous time Markov Chains, we develop a theory of nonlinear expectations in the spirit of (15). We prove basic properties of these ...

The nonlocal electrodynamics of accelerated systems is discussed in connection with the development of Lorentz-invariant nonlocal field equations. Nonlocal Maxwell’s equations are presented explicitly for certain linearly accelerated systems. In general, the field equations remain nonlocal even after accelerated motion has ceased. PACS numbers: 03.30.+p, 11.10.Lm

We consider reflected jump-diffusions in the orthant R + with timeand state-dependent drift, diffusion and jump-amplitude coefficients. Directions of reflection upon hitting boundary faces are also allow to depend on time and state. Pathwise comparison results for this class of processes are provided, as well as absolute continuity properties for their associated regulator processes responsible...

We propose a new solution method for optimal stopping problems with random discounting for linear diffusions whose state space has a combination of natural, absorbing, or reflecting boundaries. The method uses a concave characterization of excessive functions for linear diffusions killed at a rate determined by a Markov additive functional and reduces the original problem to an undiscounted opt...

The functional quantization problem for one-dimensional Brownian diffusions on [0, T ] is investigated. First, the existence of optimal n-quantizers for every n ≥ 1 is established, based on an existence result for random vectors taking their values in abstract Banach spaces. Then, one shows under rather general assumptions that the rate of convergence of the L-quantization error is O((log n)− 1...