Habib Salehi

Random Perturbation Methods with Applications in Science and Engineering

Introduction.- Ergodic Theorems.- Convergence Properties of Stochastic Processes.- Averaging.- Normal Deviation.- Diffusion Approximation.- Stability.- Markov Chains with Random Transition Probabilities.- Randomly Perturbed Mechanical Systems.- Dynamical Systems on a Torus.- The Phase Locked Loop.- Models in Population Biology.- Genetics.- Appendices.- Index.

Spatially homogeneous random evolutions

Spatially homogeneous random evolutions arise in the study of the growth of a population in a spatially homogeneous random environment. The random evolution is obtained as the solution of a bilinear stochastic evolution equation. The main results are concerned with the asymptotic behavior of the solution for large times. In particular, conditions for the existence of a stationary random field are established. Furthermore space-time renormalization limit theorems are obtained which lead to either Gaussian or non-Gaussian generalized processes depending on the case under consideration.

Random nonlinear equations and monotonic nonlinearities

Abstract The question of existence of random solutions of nonlinear random operator equations involving a monotonic nonlinearity is discussed.

Measurability of Generalized Inverses of Random Linear Operators

Let

Interpolation of q-variate weakly stationary stochastic processes over a locally compact abelian group

( {\Omega ,\mathcal{B}} )

On optimal filtering of multitarget tracking systems based on point processes observations

be a measurable space,

On singularity and Lebesgue type decomposition for operator-valued measures

{\rm X},Y

Continuous time periodically correlated processes: Spectrum and prediction

be separable Hilbert spaces. Let T be a random linear operator from

Operator-Valued wide-sense Markov processes and solutions of infinite-dimensional linear differential systems driven by white noise

\Omega \times {\rm X}

An averaging principle for dynamical systems in Hilbert space with Markov random perturbations

into Y. Let