Related papers: Exponential ergodicity of the jump-diffusion CIR p…
We are concerned with the absolute continuity of stationary distributions corresponding to some piecewise deterministic Markov process, being typically encountered in biological models. The process under investigation involves a…
We provide a class of diffusion processes for continuous time-varying multivariate angular data with explicit transition probability densities, enabling exact likelihood inference. The presented diffusions are time-reversible and can be…
The maximum likelihood approach is adapted to the problem of estimation of drift and diffusion functions of stochastic processes from measured time series. We reconcile a previously devised iterative procedure [Kleinhans et al., Physics…
We examine diffusion-limited aggregation for a one-dimensional random walk with long jumps. We achieve upper and lower bounds on the growth rate of the aggregate as a function of the number of moments a single step of the walk has. In this…
This paper considers a portfolio optimization problem in which asset prices are represented by SDEs driven by Brownian motion and a Poisson random measure, with drifts that are functions of an auxiliary diffusion factor process. The…
This paper derives the exact transition density and cumulative distribution function of a linear combination of two independent Cox-Ingersoll-Ross (CIR) processes. By combining the Poisson Gamma mixture representation of the noncentral…
This paper studies the steady-state properties of the Join the Shortest Queue model in the Halfin-Whitt regime. We focus on the process tracking the number of idle servers, and the number of servers with non-empty buffers. Recently,…
Stochastic processes of interacting particles with varying length are relevant e.g. for several biological applications. We try to explore what kind of new physical effects one can expect in such systems. As an example, we extend the…
We propose an approach to approximate the boundary crossing probabilities for general one-dimensional diffusion processes, and derive the convergence rate for this approximation scheme. There results are based on the explicit expression of…
General theorems for existence and uniqueness of viscosity solutions for Hamilton-Jacobi-Bellman quasi-variational inequalities (HJBQVI) with integral term are established. Such nonlinear partial integro-differential equations (PIDE) arise…
Flood front is the jump interface where fluids distribute discontinuously, whose interface condition is the theoretical basis of a mathematical model of the multiphase flow in porous medium. The conventional interface condition at the jump…
A numerical model was developed for flows involving an interface between a homogenous fluid and a porous medium. The numerical model is based on the finite volume method with body-fitted and multi-block grids. The Darcy-Forchheimer extended…
We give a complete and unified description -- under some stability assumptions -- of the functional scaling limits associated with some persistent random walks for which the recurrent or transient type is studied in [1]. As a result, we…
We study the diffusive limit approximation for a nonlinear radiative heat transfer system that arises in the modeling of glass cooling, greenhouse effects and in astrophysics. The model is considered with the reflective radiative boundary…
We study a one-dimensional exclusion process with a fixed jump length $I \ge 1$ in which a particle may advance or retreat $I$ sites provided all intermediate sites are vacant, with hopping rates of Arrhenius type depending on the local…
For continuous-time Markov jump processes on irreducible networks with time-independent rate constants, we employ a transition-based formalism to express the long-time precision of a single integrated current over an observable channel in…
Laplace transforms for integrals of stochastic processes have been known in analytically closed form for just a handful of Markov processes: namely, the Ornstein-Uhlenbeck, the Cox-Ingerssol-Ross (CIR) process and the exponential of…
In this study, we consider the exponential utility maximization problem in the context of a jump-diffusion model. To solve the problem, we rely on the dynamic programming principle and we derive from it a quadratic BSDE with jumps. Since…
In this paper a concentration inequality is proved for the deviation in the ergodic theorem in the case of discrete time observations of diffusion processes. The proof is based on the geometric ergodicity property for diffusion processes.…
In this paper we consider two processes driven by diffusions and jumps. The jump components are Levy processes and they can both have finite activity and infinite activity. Given discrete observations we estimate the covariation between the…