# Infinite dimensional stochastic differential equations of Ornstein-Uhlenbeck type

@article{Athreya2005InfiniteDS, title={Infinite dimensional stochastic differential equations of Ornstein-Uhlenbeck type}, author={Siva Athreya and Richard F. Bass and Maria Gordina and Edwin Perkins}, journal={Stochastic Processes and their Applications}, year={2005}, volume={116}, pages={381-406} }

## 17 Citations

### Schauder estimates for Kolmogorov equations in Banach spaces associated with stochastic reaction-diffusion equations

- Mathematics
- 2011

We consider some reaction-diffusion equations perturbed by white noise and prove Schauder estimates for the elliptic problem associated with the generator of the corresponding transition semigroup,…

### Schauder regularity results in separable Hilbert spaces

- Mathematics
- 2022

. We prove Schauder type estimates for solutions of stationary and evolution equa- tions driven by weak generators of transition semigroups associated to a semilinear stochastic partial diﬀerential…

### Schauder estimates for stationary and evolution equations associated to stochastic reaction-diffusion equations driven by colored noise

- Mathematics
- 2022

. We consider stochastic reaction-diﬀusion equations with colored noise and prove Schauder type estimates, which will depend on the color of the noise, for the stationary and evolution problems…

### Stochastic evolution equations driven by stable processes

- Mathematics

Existence and uniqueness of pathwise and weak (martingale) solutions of stochastic evolution equations driven by stable processes are established. AMS Subject Classification: Primary 60H15 Secondary…

### Stochastic evolution equations driven by Lévy processes

- Mathematics
- 2011

Existence of weak (martingale) solutions and pathwise uniq ueness are established for stochastic evolution equations driven by Lévy processe s.

### Nonlinear effects in the regularity problems for infinite dimensional evolutions of unbounded spin systems

- Mathematics
- 2006

We study the regularity problems for unbounded spin systems of anharmonic oscillators, that approximate multi-dimensional Euclidean field theories. The main attention is paid to the effect of…

### Exponential ergodicity of infinite system of interating diffusions

- Mathematics, Computer Science
- 2014

A new probabilistic strategy for proving exponential ergodicity for interacting diffusion processes on unbounded lattice is developed and implemented and exponential convergence in the uniform norm is proved.

### Existence of equilibrium for infinite system of interacting diffusions

- Mathematics
- 2015

ABSTRACT We develop and implement new probabilistic strategy for proving basic results about long-time behavior for interacting diffusion processes on unbounded lattice. The concept of the solution…

### On Weak Uniqueness for Some Degenerate SDEs by Global Lp Estimates

- Mathematics
- 2013

We prove uniqueness in law for possibly degenerate SDEs having a linear part in the drift term. Diffusion coefficients corresponding to non-degenerate directions of the noise are assumed to be…

### Kolmogorov Equations for Stochastic PDE's with Multiplicative Noise

- Mathematics
- 2007

where g is a real function of class C bounded together with its derivatives of order less or equal to 2 and W is a cylindrical Wiener process in H (see below for a precise definition). Existence and…

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We are given a separable Hilbert spaceH(with norm I and inner product (•, •)), two linear operators A:D(A) C H — H,C:H Hand a nonlinear mappingF: H H, such that: