Infinite dimensional stochastic differential equations of Ornstein-Uhlenbeck type

  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},

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

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

. 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

. 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

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

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

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

  • F. Žák
  • 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

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

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

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



On the Ornstein-Uhlenbeck Operator in Spaces of Continuous Functions

We study the realization of the Ornstein-Uhlenbeck operator A in the space of the uniformly continuous and bounded functions in Rn. We prove that it generates a semigroup which is neither strongly

Singular dissipative stochastic equations in Hilbert spaces

Existence of solutions to martingale problems corresponding to singular dissipative stochastic equations in Hilbert spaces are proved for any initial condition. The solutions for the single starting

Countable Systems of Degenerate Stochastic Differential Equations with Applications to Super-Markov Chains

We prove well-posedness of the martingale problem for an infinite-dimensional degenerate elliptic operator under appropriate Holder continuity conditions on the coefficients. These martingale

An analytic approach to existence and uniqueness for martingale problems in infinite dimensions

Abstract. We prove existence and uniqueness for a class of martingale problems in a Hilbert space. We solve the associated Kolmogorov equation and prove that the corresponding semigroup is determined

Hölder norm estimates for elliptic operators on finite and infinite-dimensional spaces

We introduce a new method for proving the estimate Equation Omitted. Where u solves the equation Δu − λu = f. The method can be applied to the Laplacian on R ∞ . It also allows us to obtain similar

On the Ornstein-Uhlenbeck operator in ² spaces with respect to invariant measures

We consider a class of elliptic and parabolic differential operators with unbounded coefficients in Rn, and we study the properties of the realization of such operators in suitable weighted L2 spaces.

Multidimensional Diffusion Processes

Preliminary Material: Extension Theorems, Martingales, and Compactness.- Markov Processes, Regularity of Their Sample Paths, and the Wiener Measure.- Parabolic Partial Differential Equations.- The

Diffusions and Elliptic Operators

Stochastic Differential Equations.- Representations of Solutions.- Regularity of Solutions.- One-dimensional Diffusions.- Nondivergence form Operators.- Martingale Problems.- Divergence Form

Infinite-dimensional elliptic equations with Hölder-continuous coefficients

Infinite-dimensional elliptic equations, with Hölder-continuous coe cients are here studied by purely analytic methods. In particular, Schauder estimates for solutions of such equations are derived.

Perturbations of Ornstein—Uhlenbeck Operators: an Analytic Approach

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: