Asymptotic evaluation of certain markov process expectations for large time, I

Donsker, M. D.; Varadhan, S. R. S.

doi:10.1002/cpa.3160280102

Cited by 545 publications

(327 citation statements)

References 3 publications

(3 reference statements)

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“…Thus, the assertions of Theorems 2.3 and 2.4 follow from the well known results on large deviations (see [9], [10], [16] and [11]) in the same way as in the discrete time case.…”

Section: Continuous Time Casesupporting

confidence: 62%

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Nonconventional large deviations theorems

Kifer

Varadhan

2013

Probab. Theory Relat. Fields

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Abstract. We obtain large deviations theorems for both discrete time expressions of the form N n=1 F X(q 1 (n)), . . . , X(q ℓ (n)) and similar expressions of the form T 0 F X(q 1 (t)), . . . , X(q ℓ (t)) dt in continuous time. Here X(n), n ≥ 0 or X(t), t ≥ 0 is a Markov process satisfying Doeblin's condition, F is a bounded continuous function and q i (n) = in for i ≤ k while for i > k they are positive functions taking on integer values on integers with some growth conditions which are satisfied, for instance, when q i 's are polynomials of increasing degrees. Applications to some types of dynamical systems such as mixing subshifts of finite type and hyperbolic and expanding transformations will be obtained, as well.

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“…Thus, the assertions of Theorems 2.3 and 2.4 follow from the well known results on large deviations (see [9], [10], [16] and [11]) in the same way as in the discrete time case.…”

Section: Continuous Time Casesupporting

confidence: 62%

“…Differentiability of Q(W λ ) in λ follows from standard results on positive operatos (see, for instance, [20]) and we derive now Theorem 2.1 from well known "conventional" large deviations results (see, for instance, [9], [16] and Section 2.3 in [11]). …”

Section: 2mentioning

confidence: 73%

Nonconventional large deviations theorems

Kifer

Varadhan

2013

Probab. Theory Relat. Fields

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“…We infer from this identity that 14) which shows that p t (β, ·) is differentiable, and also yields (7.12). It is clear that…”

Section: Proof Of Theorem 712mentioning

confidence: 64%

“…(In fact, it is not difficult to see (3.26) for Y ≡ 0 by applying Donsker-Varadhan's large deviations [14]. Then, one can use Girsanov transformation to extend (3.26) to the case of smooth path Y.…”

Section: Path Localizationmentioning

confidence: 99%

Localization Transition for Polymers in Poissonian Medium

Comets

Yoshida

2013

Commun. Math. Phys.

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We study a model of directed polymers in random environment in dimension 1 + d, given by a Brownian motion in a Poissonian potential. We study the effect of the density and the strength of inhomogeneities, respectively the intensity parameter ν of the Poisson field and the temperature inverse β. Our results are: (i) fine information on the phase diagram, with quantitative estimates on the critical curve; (ii) pathwise localization at low temperature and/or large density; (iii) complete localization in a favourite corridor for large νβ 2 and bounded β.Short Title: Brownian Polymers

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“…Instead of precise deviations that have been studied in Féray et al [12]. Our large deviations and moderate deviations results are in the sense of Donsker-Varadhan [19], [3], [4], [5], [6]. Our proofs are probabilistic and require only elementary number theory results, in constrast to the analytical number theory approach in Radziwill [17].…”

Section: Introductionmentioning

confidence: 77%