On some stochastic parabolic differential equations in a Hilbert space.
On Special Case of Multiple Hypotheses Optimal Testing for Three Differently Distributed Random Variables
2000 Mathematics Subject Classification: 62P30.In this paper by using theory of large deviation techniques (LDT), the problem of hypotheses testing for three random variables having different distributions from three possible distributions is solved. Hypotheses identification for two objects having different distributions from two given probability distributions was examined by Ahlswewde and Haroutunian. We noticed Sanov's theorem and its applications in hypotheses testing.
On spectral bandwidth of a stationary random process
The irregularity coefficient is one of the numerical characteristics of the spectral bandwith of a stationary random process. Its basic properties are investigated and the application to the dichotomic classification of a process into narrow-band and wide-band ones is given. Further, its behaviour is analyzed for sufficiently wide classes of stationary processes whose spectral densities frequently appear both in theory and applications.
On spectral measures of strings and excursions of quasi-diffusions
On spectral type of nonanticipative transformation of Wiener process
On stability for numerical approximations of stochastic ordinary differential equations.
On standard normal convergence of the multivariate Student -statistic for symmetric random vectors.
On stationarity of a multiple doubly stochastic model
On stationary distributions for the KPP equation with branching noise
On statistically convergent sequences of real numbers
On stochastic differential equations in a configuration space.
On stochastic differential equations with locally unbounded drift
We study the regularizing effect of the noise on differential equations with irregular coefficients. We present existence and uniqueness theorems for stochastic differential equations with locally unbounded drift.
On Stochastic Differential Equations with Reflecting Boundary Condition in Convex Domains
Let D be an open convex set in and let F be a Lipschitz operator defined on the space of adapted càdlàg processes. We show that for any adapted process H and any semimartingale Z there exists a unique strong solution of the following stochastic differential equation (SDE) with reflection on the boundary of D: , t ∈ ℝ⁺. Our proofs are based on new a priori estimates for solutions of the deterministic Skorokhod problem.
On stochastic Euler equation in .
On Stochastic Orders
On stochastic properties of past varentropy with applications
To have accuracy in the extracted information is the goal of the reliability theory investigation. In information theory, varentropy has recently been proposed to describe and measure the degree of information dispersion around entropy. Theoretical investigation on varentropy of past life has been initiated, however details on its stochastic properties are yet to be discovered. In this paper, we propose a novel stochastic order and introduce new classes of life distributions based on past varentropy....
On stopped Feynman-Kac functionals
On Strassen's theorem on stochastic domination.
On strictly sparse subsets of a free group.
On strong ergodicity of inhomogeneous products of finite stochastic matrices