The Stochastic Stationary Root Model

Non-Stationary Stochastic Optimization

We consider a non-stationary variant of a sequential stochastic optimization problem, in which the underlying cost functions may change along the horizon. We propose a measure, termed variation budget, that controls the extent of said change, and study how restrictions on this budget impact achievable performance. We identify sharp conditions under which it is possible to achieve long-run avera...

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(...

Stationary Solutions of the Stochastic Differential Equation

For a given bivariate Lévy process (Ut, Lt)t≥0, necessary and sufficient conditions for the existence of a strictly stationary solution of the stochastic differential equation dVt = Vt− dUt + dLt are obtained. Neither strict positivity of the stochastic exponential of U nor independence of V0 and (U,L) are assumed and noncausal solutions may appear. The form of the stationary solution is determ...

Stationary Solutions for Stochastic Damped

We consider the stochastic damped Navier-Stokes equations in R (d = 2, 3), assuming as in our previous work [4] that the covariance of the noise is not too regular, so Itô calculus cannot be applied in the space of finite energy vector fields. We prove the existence of an invariant measure when d = 2 and of a stationary solution when d = 3.

Stochastic Games and Stationary Strategies