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The Large Deviation Principle of Local Processes - Arcones (2003) (Correct)
....for example Bahadur [5] We consider functional large deviations, i.e. we consider the large deviation principle (LDP) for sequences of stochastic processes T , where T is an arbitrary index parameter. In the situation in (1. 3) T = For an introduction to the LDP see Deuschel and Stroock [7]. We consider stochastic processes as elements of l (T ) l (T ) is the Banach space consisting of the bounded functions defined in T with the norm #x## = sup t#T x(t) We will use the following definition. Definition 1.1. Given a sequence of stochastic processes T , a sequence of ....
J. D. Deuschel, and D. W. Stroock, Large Deviations. Academic Press, Inc., Boston, 1989.
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....consider the moderate deviations of sums of i.i.d. random vectors with values in a separable Banach space. Our results are stated as functional large deviations with a Gaussian rate function. General references on (functional) large deviations are Bahadur [4] Varadhan [23] Deuschel and Stroock [9] and Shwartz and Weiss [21] We consider stochastic processes as elements of l (T ) where T is an index set. l (T ) is the Banach space consisting of the bounded functions defined in T with the norm #x## x(t) We will use the following definition: Definition 1.1. Given a sequence of ....
J. D. Deuschel, and D. W. Stroock, Large Deviations. Academic Press, Inc., Boston, MA. 1989.
The Large Deviation Principle for Stochastic Processes. II - Arcones (2003) (Correct)
....where the infimum is attained when x j = c# , for some constant c. Theorem 5.9 is proved. 22 Arcones M. A. 6. The LDP for Poisson processes. In this section, we present several results on the LDP for Poisson processes. By the Cramer theorem (see for example Theorem 1. 26 in [13]) if is a sequence of independent identically distributed r.v. s with Poisson distribution and mean n, then satisfies the LDP with speed n and rate function h(x) sup ##R (x# 1) It is easy to see that h(x) # x ln 1, if x # 0; if x 0. 6.1) We will use the fact that if ....
Deuschel J.-D., Stroock D.W. Large Deviations. Boston, MA: Academic Press, 1989, 307 p.
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J. D. Deuschel, and D. W. Stroock, Large Deviations. (1989), Academic Press, Inc., Boston, MA.
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