15 citations · 103 across the 25 of their papers we have counts for
26 papers
Interacting particle systems with continuous spins
Viktor Bezborodov, Luca Di Persio, Martin Friesen +1
We study a general class of interacting particle systems over a countable state space where on each site the particle mass follows a stochastic differen…
Limit theorems for time averages of continuous-state branching processes with immigration
Mariem Abdellatif, Martin Friesen, Peter Kuchling +1
In this work we investigate limit theorems for the time-averaged process where is a subcritical continuous-state branchi…
Stationary Covariance Regime for Affine Stochastic Covariance Models in Hilbert Spaces
Martin Friesen, Sven Karbach
We study the long-time behavior of affine processes on positive self-adjoiont Hilbert-Schmidt operators which are of pure-jump type, conservative and have finite second moment. For…
Volterra square-root process: Stationarity and regularity of the law
Martin Friesen, Peng Jin
The Volterra square-root process on is an affine Volterra process with continuous sample paths. Under a suitable integrability condition on the resolvent of the se…
Regularity of transition densities and ergodicity for affine jump-diffusion processes
Martin Friesen, Peng Jin, Jonas Kremer +1
In this paper we study the transition density and exponential ergodicity in total variation for an affine process on the canonical state space $\mathbb{R}_{\geq0}^{m}\times\mathbb{…
On a class of stochastic partial differential equations with multiple invariant measures
Balint Fárkas, Martin Friesen, Barbara Rüdiger +1
In this work we investigate the long-time behavior, that is the existence and characterization of invariant measures as well as convergence of transition probabilities, for Markov…
On uniqueness and stability for the Enskog equation
Martin Friesen, Barbara Rüdiger, Padmanabhan Sundar
The time-evolution of a moderately dense gas in a vacuum is described in classical mechanics by a particle density function obtained from the Enskog equation. Based on a McKean-Vla…
Spontaneous wave formation in stochastic self-driven particle systems
Martin Friesen, Hanno Gottschalk, Barbara Rüdiger +1
Waves and oscillations are commonly observed in the dynamics of self-driven agents such as pedestrians or vehicles. Interestingly, many factors may perturb the stability of space h…
On the anisotropic stable JCIR process
Martin Friesen, Peng Jin
We investigate the anisotropic stable JCIR process which is a multi-dimensional extension of the stable JCIR process but also a multi-dimensional analogue of the classical JCIR pro…
Ergodicity of affine processes on the cone of symmetric positive semidefinite matrices
Martin Friesen, Peng Jin, Jonas Kremer +1
This article investigates the long-time behavior of conservative affine processes on the cone of symmetric positive semidefinite -matrices. In particular, for conservati…
Long-time behavior for subcritical measure-valued branching processes with immigration
Martin Friesen
In this work we study the long-time behavior for subcritical measure-valued branching processes with immigration on the space of tempered measures. Under some reasonable assumption…
Exponential ergodicity for stochastic equations of nonnegative processes with jumps
Martin Friesen, Peng Jin, Jonas Kremer +1
In this work, we study ergodicity of continuous time Markov processes on state space obtained as unique strong solutions to stochastic equations…
Boundary behavior of multi-type continuous-state branching processes with immigration
Martin Friesen, Peng Jin, Barbara Rüdiger
In this article we provide a sufficient condition for a continuous-state branching process with immigration (CBI process) to not hit its boundary, i.e. for non-extinction. Our resu…
Weak-coupling limit for ergodic environments
Martin Friesen, Yuri Kondratiev
The main aim of this work is to establish an averaging principle for a wide class of interacting particle systems in the continuum. This principle is an important step in the analy…
Stochastic equation and exponential ergodicity in Wasserstein distances for affine processes
Martin Friesen, Peng Jin, Barbara Rüdiger
This work is devoted to the study of conservative affine processes on the canonical state space R_+^m \times \R^nm + n > 0$. We show that each affine process can be…
Existence of densities for stochastic differential equations driven by Lévy processes with anisotropic jumps
Martin Friesen, Peng Jin, Barbara Rüdiger
We study existence of densities for solutions to stochastic differential equations with Hölder continuous coefficients and driven by a -dimensional Lévy process $Z=(Z_{t})_{t\ge…
Existence of densities for multi-type CBI processes
Martin Friesen, Peng Jin, Barbara Rüdiger
Let X be a multi-type continuous-state branching process with immigration (CBI process) on state space . Denote by , , the law of . We provide s…
On Stochastic Cucker-Smale flocking dynamics
Martin Friesen, Oleksandr Kutoviy
We present a stochastic version of the Cucker-Smale flocking dynamics based on a markovian -particle system of pair interactions with unbounded and, in general, non-Lipschitz co…
Nonlinear perturbations of evolution systems in scales of Banach spaces
Martin Friesen, Oleksandr Kutoviy
A variant of the abstract Cauchy-Kovalevskaya theorem is considered. We prove existence and uniqueness of classical solutions to the nonlinear, non-autonomous initial value problem…
The Enskog process for hard and soft potentials
Martin Friesen, Barbara Rüdiger, Padmanabhan Sundar
The density of a moderately dense gas evolving in a vacuum is given by the solution of an Enskog equation. Recently we have constructed in [ARS17] the stochastic process that corre…
Stochastic averaging for a spatial population model in random environment
Martin Friesen, Yuri Kondratiev
In this work we study the non-equilibrium Markov state evolution for a spatial population model on the space of locally finite configurations over $\mathbb{R…
Stochastic averaging principle for spatial Markov evolutions in the continuum
Martin Friesen, Yuri Kondratiev
We study a spatial birth-and-death process on the phase space of locally finite configurations over . Dynamics is described by an non-equilibrium evo…
Non-equilibrium dynamics for a Widom-Rowlinson type model with mutations
Martin Friesen
A dynamical version of the Widom-Rowlinsom model in the continuum is considered. The dynamics is modelled by a spatial two-component birth-and-death Glauber process where particles…
Evolution of states and mesoscopic scaling for two-component birth-and-death dynamics in continuum
Martin Friesen, Oleksandr Kutoviy
Two coupled spatial birth-and-death Markov evolutions on are obtained as unique weak solutions to the associated Fokker-Planck equations. Such solutions are construc…