Ergodicity of stochastically forced large scale geophysical flows.
On some regularity properties of solutions to stochastic evolution equations in Hilbert spaces
Fixed precision estimation of a normal mean
On analyticity of Ornstein-Uhlenbeck semigroups
Let be a transition semigroup of the Hilbert space-valued nonsymmetric Ornstein-Uhlenbeck process and let denote its Gaussian invariant measure. We show that the semigroup is analytic in if and only if its generator is variational. In particular, we show that the transition semigroup of a finite dimensional Ornstein-Uhlenbeck process is analytic if and only if the Wiener process is nondegenerate.
Fixed precision estimation of the mean of a sequence of independent normal random variables
The author presents a review of solutions to the problem of constructing a fixed precision estimate of the mean in the Gaussian case. The conclusion is that no satisfactory solution exists. No new results are given.
Confidence interval with specified precision for the mean value in a sequence of Gaussian variables
Consider the class C of real-valued stochastic processes of the form Xt=m+mt+ξt, with discrete t=1,2,⋯, such that mt→0 and the ξt are random variables with normal distributions N(0,σt), where σt→0. Required is a sequence of estimators m^t for the parameter m, determined by X1,⋯,Xt and a stopping rule τ, such that for every ε>0 and 0
Review: Z. Govindarajulu; The sequential statistical analysis of hypothesis testing, point and interval estimation, and decision theory
The article contains no abstract
Hypercontractivity of solutions to Hamilton-Jacobi equations
We show that solutions to some Hamilton-Jacobi Equations associated to the problem of optimal control of stochastic semilinear equations enjoy the hypercontractivity property.
Existence, uniqueness and ergodicity for the stochastic quantization equation
Existence, uniqueness and ergodicity of weak solutions to the equation of stochastic quantization in finite volume is obtained as a simple consequence of the Girsanov theorem.
Uniform exponential ergodicity of stochastic dissipative systems
We study ergodic properties of stochastic dissipative systems with additive noise. We show that the system is uniformly exponentially ergodic provided the growth of nonlinearity at infinity is faster than linear. The abstract result is applied to the stochastic reaction diffusion equation in with .
Exponential ergodicity of semilinear equations driven by Lévy processes in Hilbert spaces
We study convergence to the invariant measure for a class of semilinear stochastic evolution equations driven by Lévy noise, including the case of cylindrical noise. For a certain class of equations we prove the exponential rate of convergence in the norm of total variation. Our general result is applied to a number of specific equations driven by cylindrical symmetric α-stable noise and/or cylindrical Wiener noise. We also consider the case of a "singular" Wiener process with unbounded covariance...
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