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Small deviations of iterated processes in the space of trajectories

Andrei Frolov (2013)

Open Mathematics

We derive logarithmic asymptotics of probabilities of small deviations for iterated processes in the space of trajectories. We find conditions under which these asymptotics coincide with those of processes generating iterated processes. When these conditions fail the asymptotics are quite different.

Spatial trajectories

Rafael V. Chacon, Yves Le Jan, John B. Walsh (1981)

Séminaire de probabilités de Strasbourg

Statistical causality and adapted distribution

Ljiljana Petrović, Sladjana Dimitrijević (2011)

Czechoslovak Mathematical Journal

In the paper D. Hoover, J. Keisler: Adapted probability distributions, Trans. Amer. Math. Soc. 286 (1984), 159–201 the notion of adapted distribution of two stochastic processes was introduced, which in a way represents the notion of equivalence of those processes. This very important property is hard to prove directly, so we continue the work of Keisler and Hoover in finding sufficient conditions for two stochastic processes to have the same adapted distribution. For this purpose we use the concept...

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