Evolutionary predictions from invariant physical measures of dynamic processes

Evolutionary predictions from invariant physical measures of dynamic processes.

The invariant physical measure of a dynamic process comprises the information necessary to compute statistical quantities of the system. It allows us to replace time averages over the system's trajectory by integrals over state-space. In particular, it allows us to compute the long-term growth rate of a fluctuating population and hence to make evolutionary predictions. This is explained here us...

Computing Physical Invariant Measures

| We consider the problem of describing the long term behaviour of a dynamical system in a statistical sense. For many chaotic systems, the asymptotic distribution of points in a trajectory fT i (x)g 1 i=0 often appears to be independent of x. We present new results on the numerical approximation of this common asymptotic distribution, called the physical invariant measure of T.

Distribution-Invariant Dynamic Risk Measures

The paper provides an axiomatic characterization of dynamic risk measures for multi-period financial positions. For the special case of a terminal cash flow, we require that risk depends on its conditional distribution only. We prove a representation theorem for dynamic risk measures and investigate their relation to static risk measures. Two notions of dynamic consistency are proposed. A key i...

INVARIANT MEASURES FOR MARKOV PROCESSES(i)

Convergence of Invariant Measures of Truncation Approximations to Markov Processes

Let Q be the Q-matrixof an irreducible, positive recurrent Markov process on a countable state space. We show that, under a number of conditions, the stationary distributions of the n × n north-west corner augmentations of Q converge in total variation to the stationary distribution of the process. Twoconditions guaranteeing such convergence include exponential ergodicity and stochastic monoton...