Stochastic linear maps and transition probability

Stochastic Linear Maps and T R a N S I T I O N Probability

Some aspects of the transition probability P(w, u) between states w, ~, on unital *-algebras are discussed. It is shown that P increases under the action of any stochastic linear map T, i.e., P(Tco, Tp) >~ P(co, u). Some properties of P are derived in starting from a recently-proved characterization of the quantity in question.

Linear Operators with Compact Supports, Probability Measures and Milyutin Maps

The notion of a regular operator with compact supports between function spaces is introduced. On that base we obtain a characterization of absolute extensors for 0-dimensional spaces in terms of regular extension operators having compact supports. Milyutin maps are also considered and it is established that some topological properties, like paracompactness, metrizability and k-metrizability, ar...

Using linear and non-linear kriging interpolators to produce probability maps

Probability maps are used to define areas with high and low certainty of exceeding a threshold value. The most popular methods for creating these maps are variants of indicator kriging. However, such methods are questionable when the data exhibit a trend or contain measurement errors, the latter of which is common in most data sets. This paper presents an alternative approach that maps the risk...

A Survey of Invertibility and Spectrum Preserving Linear Maps

Transition probability bounds for the stochastic stability robustness of continuous- and discrete-time Markovian jump linear systems

This paper considers the robustness of stochastic stability of Markovian jump linear systems in continuousand discrete-time with respect to their transition rates and probabilities respectively. The continuous-time (discrete-time) system is described via a continuous-valued state vector and a discrete-valued mode which varies according to a Markov process (chain). By using stochastic Lyapunov f...