This book lays the foundations for a theory on almost periodic stochastic processes and their applications to various stochastic differential equations, functional differential equations with delay, partial differential equations, and difference equations. It is in part a sequel of authors recent work on almost periodic stochastic difference and differential equations and has the particularity to be the first book that is entirely devoted to almost periodic random processes and their applications. The topics treated in it range from existence, uniqueness, and stability of solutions for abstract stochastic difference and differential equations.
George Y. H. Chi (1969), “Nonlinear prediction and multiplicity of generalized random processes.” At University of California, Riverside: Vera ... “Besicovitch - Orlicz spaces of almost periodic functions.” Michael D. Brennan (1978), ...
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( see Besicovitch ( 3 ] ) , one notes here that the same relaxation is available for the $ 2 almost PC processes . ... T ) = rît + T , t ) is a uniformly continuous s ? almost periodic function , it is then uniformly almost periodic .
Bedouhene, F., Mellah, O., Raynaud de Fitte, P: Bochner–almost periodicity for stochastic processes. Stoch. Anal. Appl. 30(2), 322–342 (2012) 2. Bezandry, P., Diagana, T.: Almost Periodic Stochastic Processes. Springer, New York (2011) ...
Lemma 1.5 Let hypothesis of Lemma 1.4 hold and, for process X therein, hypothesis of Lemma 1.1 at Z(t,x) = xx" also ... Definition 1.12 Markov process is called stationary or periodic (quasiperiodic, almost-periodic) if and only if it ...
... acts on a stochastic process, say {ξ(t,ω),t ∈R,ω ∈ }, and is an average over the variable ω. In the time-variant nonstochastic framework (for ACS time series), the expectation operator is the almost-periodic component extraction ...
D. Araya, R. Castro, C. Lizama, Almost automorphic solutions of difference equations. ... Periodic Functions (Dover Publications, Newburyport, 1954) P. Bezandry, T. Diagana, Almost Periodic Stochastic Processes (Springer, New York, ...
Chapter 9 Almost Periodic Functions and Weakly Stationary Stochastic Processes It is a basic idea for the classical theory of Fourier series to express periodic functions as compositions of harmonic waves. This idea can be successfully ...
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[ 21 ] Cenuşă , G. , Properties of mean and of covariance of an almost periodic in probability stochastic process ( in Romanian ) , Stud . Cerc . Mat . ( Bucharest ) , 32 ( 1980 ) , 4 , 377-383 . ( 22 ] Cenuşă , G. , Random vector ...