# On a class of stochastic partial differential equations with multiple invariant measures

@article{Farkas2021OnAC, title={On a class of stochastic partial differential equations with multiple invariant measures}, author={B{\'a}lint Farkas and Martin Friesen and Barbara R{\"u}diger and Dennis Schroers}, journal={Nonlinear Differential Equations and Applications NoDEA}, year={2021}, volume={28} }

In this work we investigate the long-time behavior for Markov processes obtained as the unique mild solution to stochastic partial differential equations in a Hilbert space. We analyze the existence and characterization of invariant measures as well as convergence of transition probabilities. While in the existing literature typically uniqueness of invariant measures is studied, we focus on the case where the uniqueness of invariant measures fails to hold. Namely, introducing a generalized…

## 2 Citations

### Volterra square-root process: Stationarity and regularity of the law

- Mathematics
- 2022

. The Volterra square-root process on R m + is an aﬃne Volterra process with continuous sample paths. Under a suitable integrability condition on the resolvent of the second kind associated with the…

### A Stochastic Model of Economic Growth in Time-Space

- Mathematics, EconomicsSIAM J. Control. Optim.
- 2022

We deal with an infinite horizon, infinite dimensional stochastic optimal control problem arising in the study of economic growth in time-space. Such problem has been the object of various papers in…

## References

SHOWING 1-10 OF 45 REFERENCES

### Jump-diffusions in Hilbert spaces: existence, stability and numerics

- Mathematics
- 2008

By means of an original approach, called ‘method of the moving frame’, we establish existence, uniqueness and stability results for mild and weak solutions of stochastic partial differential…

### Stochastic equation and exponential ergodicity in Wasserstein distances for affine processes

- MathematicsThe Annals of Applied Probability
- 2020

This work is devoted to the study of conservative affine processes on the canonical state space $D = $R_+^m \times \R^n$, where $m + n > 0$. We show that each affine process can be obtained as the…

### Invariant measures for stochastic evolution equations with Hilbert space valued Lévy noise

- Mathematics
- 2005

Existence of invariant measures for semi-linear stochastic evolution equations in separable real Hilbert spaces is considered, where the noise is generated by Hilbert space valued Lévy processes. It…

### Stochastic Volterra integral equations and a class of first-order stochastic partial differential equations

- MathematicsStochastics
- 2022

We investigate stochastic Volterra equations and their limiting laws. The stochastic Volterra equations we consider are driven by a Hilbert space valued Lévy noise and integration kernels may have…

### Subgeometric rates of convergence of Markov processes in the Wasserstein metric

- Mathematics
- 2014

We establish subgeometric bounds on convergence rate of general Markov processes in the Wasserstein metric. In the discrete time setting we prove that the Lyapunov drift condition and the existence…

### Ergodicity of the 2D Navier-Stokes equations with degenerate stochastic forcing

- Mathematics
- 2004

The stochastic 2D Navier-Stokes equations on the torus driven by degenerate noise are studied. We characterize the smallest closed invariant subspace for this model and show that the dynamics…

### Asymptotic coupling and a general form of Harris’ theorem with applications to stochastic delay equations

- Mathematics
- 2009

There are many Markov chains on infinite dimensional spaces whose one-step transition kernels are mutually singular when starting from different initial conditions. We give results which prove unique…

### Stochastic Partial Differential Equations with Lévy Noise: An Evolution Equation Approach

- Mathematics
- 2007

Introduction Part I. Foundations: 1. Why equations with Levy noise? 2. Analytic preliminaries 3. Probabilistic preliminaries 4. Levy processes 5. Levy semigroups 6. Poisson random measures 7.…