Some expansion theorems for stochastic processes. II.

Some Inference Theorems in Stochastic Processes

Stochastic Processes ( Fall 2014 ) Spectral representations and ergodic theorems for stationary stochastic processes Stationary stochastic processes

A stochastic process X is strongly stationary if its fdds are invariant under time shifts, that is, for any (finite) n, for any t0 and for all t1, ..., tn ∈ T , (Xt1 , ..., Xtn) and (Xt1+t0 , ..., Xtn+t0) have the same distribution. A stochastic process X is weakly stationary if its mean function is constant and its covariance function is invariant under time shifts. That is, for all t ∈ T , E(...

Stochastic Processes (stochastik Ii)

Approximation Theorems for Random Permanents and Associated Stochastic Processes

The limit theorems for certain stochastic processes generated by permanents of random matrices of independent columns with exchangeable components are established. The results are based on the martingale decomposition of a random permanent function similar to the one known for U -statistics and on relating the components of this decomposition to some multiple stochastic integrals.

Some Strong Deviation Theorems for Dependent Stochastic Sequence

The upper and lower bounds of the sequence of sums 1 an ∑n k=1[ Xk−μk,n bn ] are obtained, where {bn, n ∈ N} are regularly vary functions and {an, n ∈ N} are real constants satisfying an → ∞ as n → ∞. Some strong deviation theorems for arbitrary continuous random sequence {Xn, n ∈ N} are obtained under suitable conditions. Mathematics Subject Classification: 60F15