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Asymptotic theory for approximate martingale estimating functions is generalised to diffusions with finite-activity jumps, when the sampling frequency and terminal sampling time go to infinity. Rate optimality and efficiency are of…
This paper introduces test and estimation procedures for abrupt and gradual changes in the entire jump behaviour of a discretely observed Ito semimartingale. In contrast to existing work we analyse jumps of arbitrary size which are not…
We prove density and current fluctuations for two examples of symmetric, interacting particle systems with anomalous diffusive behavior: the zero-range process with long jumps and the zero-range process with degenerated bond disorder. As an…
Self-chemophoresis is an appealing and quite successful interpretation of the motility exhibited by certain chemically active colloidal particles suspended in a solution of their "fuel": the particle has a phoretic response to…
We study jump-diffusion processes with parameters switching at random times. Being motivated by possible applications, we characterise equivalent martingale measures for these processes by means of the relative entropy. The minimal entropy…
This paper is the first part of a series of papers on filtering for partially observed jump diffusions satisfying a stochastic differential equation driven by Wiener processes and Poisson martingale measures. The coefficients of the…
Swimming bacteria detect chemical gradients by performing temporal comparisons of recent measurements of chemical concentration. These comparisons are described quantitatively by the chemotactic response function, which we expect to…
For one-dimensional Jump-Drift and Jump-Diffusion processes converging towards some steady state, the large deviations of a long dynamical trajectory are described from two perspectives. Firstly, the joint probability of the empirical…
In this paper we present a hydrodynamic approach to describe the motion of migrating bacteria as a special class of self-propelled systems. Analytical and numerical calculations has been performed to study the behavior of our model in the…
The purpose of this paper is to investigate properties of self-exciting jump processes. We derive the Laplace transform of SDE driven self-exciting processes with independent, identically distributed jump sizes. By using this Laplace…
We consider a rate control problem for an $N$-particle weakly interacting finite state Markov process. The process models the state evolution of a large collection of particles and allows for multiple particles to change state…
This work develops asymptotic properties of a class of switching jump diffusion processes. The processes under consideration may be viewed as a number of jump diffusion processes modulated by a random switching mechanism. The underlying…
Random metastability occurs when an externally forced or noisy system possesses more than one state of apparent equilibrium. This work investigates fluctuations in a class of random dynamical systems, arising from randomly perturbing a…
Piecewise-deterministic Markov processes form a general class of non-diffusion stochastic models that involve both deterministic trajectories and random jumps at random times. In this paper, we state a new characterization of the jump rate…
We discuss diffusion properties of a dynamical system, which is characterised by long-tail distributions and finite correlations. The particle velocity has the stable L\'evy distribution; it is assumed as a jumping process (the kangaroo…
Biochemical reactions can happen on different time scales and also the abundance of species in these reactions can be very different from each other. Classical approaches, such as deterministic or stochastic approach, fail to account for or…
This paper studies a stylized model of local interaction where agents choose from an ever increasing set of vertically ranked actions, e.g. technologies. The driving forces of the model are infrequent upward shifts (``updates''), followed…
We investigate the two-points correlation function for several boundary-driven interacting particle systems. Our goal is to show that the time evolution of that correlation function is solution to a partial differential equation that can be…
We investigate the evolution of particle ensembles in open chaotic hydrodynamical flows. Active processes of the type A+B --> 2B and A+B --> 2C are considered in the limit of weak diffusion. As an illustrative advection dynamics we consider…
Current models of phoretic transport rely on molecular forces creating a "diffuse" particle-fluid interface. We investigate theoretically an alternative mechanism, in which a diffuse interface emerges solely due to a non-vanishing…