Stochastic Differential Systems Analysis and FilteringWiley, 1987 M06 22 - 570 páginas Gives applied methods for studying stochastic differential systems--in particular, the methods for finding the finite-dimensional distributions of the state vector and of the output of such systems, and also the estimation methods of the state and of the parameters of differential systems based on observations (filtering and extrapolation theory). Also studied are stochastic differential equations of general type with arbitrary processes and independent increments. The equations with Wiener processes are considered as a special case. The construction of stochastic differential systems in the book is based on Pugachev's equations for finite-dimensional characteristic functions of the processes determined by stochastic differential equations. Includes end-of-chapter problems. |
Contenido
ferential system | 1 |
PROBLEMS | 9 |
RANDOM FUNCTIONS | 44 |
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a₁ admissible filters b₁ characteristic function coefficients components conditionally optimal filter Consequently considered corresponding covariance function covariance matrix equal to zero Example expectation expression finite-dimensional distributions g₁ h₁ independent increments initial condition input interval Itô equation Itô integral k₁ m.s. continuous m.s. derivative m.s. integral m.s. limit m₁ non-linear normally distributed obtained output parameters Poisson process posterior problem process with independent process with uncorrelated process Z(t Pugachev random function X(t random process random variables random vector represents right-hand side Section semi-invariants sequence shaping filter solution spectral density stationary linear system stationary process stationary random function stochastic differential equation stochastic integral t₁ t₂ theorem transfer function transformation U₁ uncorrelated increments V₁ V₂ variance vector random function W₁ white noise Wiener process X₁ Y₁ Z₁ Z₂ Σ Σ