MULTIPLE MARKOV GENERALIZED GAUSSIAN PROCESSES AND THEIR DUALITIES

作者：Si Si^*

来源：Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2010, 13(1): 99-110.

DOI：10.1142/S0219025710003961

• Gaussian processes
• generalized processes
• canonical representation
• multiple Markov property
• duality

A stochastic process describes evolutional random phenomena towards future. Corresponding with this direction, there will be a process describing, as it were, backward evolution from future to present. The dual process is a realization of this fact.
We restrict our attention to Gaussian processes for which multiple Markov property is well investigated. This property expresses way of dependence of involved randomness as time goes by. We can therefore expect that such a process with multiple Markov property would present an exact form of the dual process.
We shall show that having defined generalized Gaussian process with multiple Markov property, we can construct the dual process satisfying the properties that we claim. The analysis for this can be done in the space of Hida distributions.

• 出版日期2010-3