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In this section we will apply the Young integral and rough path integral of local time defined in sections 2 and 3 to prove a useful extension to Itˆ o’s formula.. Assume the
The behaviour of the horizontal projection of the random walk is less obvious: in Sections 3, 4 and 5 we prove that the expected values of the horizontal distance, of its
L´evy V´ehel, Large deviation spectrum of a class of additive processes with correlated non-stationary increments.. L´evy V´ehel, Multifractality of
We introduce the concept of a mild solution for the right Hudson-Parthasarathy quantum stochastic differential equation, prove existence and uniqueness results, and show the
Our proof of Theorem 1.1 is based on estimates for the structure function, i.e., the spatial Fourier transform of the correlation function with respect to h·i , the
By the way, we also prove that the Häggström-Pemantle non-coexistence result "except perhaps for a denumerable set" can be extended to families of stochastically
In this section we use the large deviation results for the discrete time Markov chain con- sidered in Sections 3, 4 and 5 to obtain the empirical measure LDP for two very
Using translation-invariance and symmetries of the system they proved that the answer to Question 1 is positive in the case that the initial quantities of resource have a