Analytic stochastic processes

Modelling MAS with Finite Analytic Stochastic Processes

The Multi-Agent paradigm is becoming increasingly popular as a way of capturing complex control processes with stochastic properties. Many existing modelling tools are not flexible enough for these purposes, possibly because many of the modelling frameworks available inherit their structure from single agent frameworks. This paper proposes a new family of modelling frameworks called FASP, which...

Stochastic Processes

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

x 6∈S cxf(x) 2 < ε. Of course g has finite support since g(x) = 0 for x 6∈ S. u t Exercise 2. (*) Recall that the operator norm of an operator T : U → W is define ||T || = supu 6=0 {||Tu||/||u||}. Show the following: • The transition matrix P is a self-adjoint operator from L(V ) into itself. • The operator norm of P is at most 1. • ||P|| ≤ ||P ||. • ||P || = ||P ||. Solution (exercise 2). Sinc...