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Maximal displacement for bridges of random walks in a random environment

Nina Gantert, Jonathon Peterson (2011)

Annales de l'I.H.P. Probabilités et statistiques

It is well known that the distribution of simple random walks on ℤ conditioned on returning to the origin after 2n steps does not depend on p=P(S1=1), the probability of moving to the right. Moreover, conditioned on {S2n=0} the maximal displacement maxk≤2n|Sk| converges in distribution when scaled by √n (diffusive scaling). We consider the analogous problem for transient random walks in random environments on ℤ. We show that under the quenched law Pω (conditioned on the environment ω), the maximal...

Mean stability of a stochastic difference equation

Viorica Mariela Ungureanu, Sui Sun Cheng (2008)

Annales Polonici Mathematici

A simple personal saving model with interest rate based on random fluctuation of national growth rate is considered. We establish connections between the mean stochastic stability of our model and the deterministic stability of related partial difference equations. Then the asymptotic behavior of our stochastic model is studied. Although the model is simple, the techniques for obtaining its properties are not, and we make use of the theory of abstract Banach algebras and weighted spaces. It is hoped...

Moderate deviations for a Curie–Weiss model with dynamical external field

Anselm Reichenbachs (2013)

ESAIM: Probability and Statistics

In the present paper we prove moderate deviations for a Curie–Weiss model with external magnetic field generated by a dynamical system, as introduced by Dombry and Guillotin-Plantard in [C. Dombry and N. Guillotin-Plantard, Markov Process. Related Fields 15 (2009) 1–30]. The results extend those already obtained for the Curie–Weiss model without external field by Eichelsbacher and Löwe in [P. Eichelsbacher and M. Löwe, Markov Process. Related Fields 10 (2004) 345–366]. The Curie–Weiss model with...

Moderate deviations for I.I.D. random variables

Peter Eichelsbacher, Matthias Löwe (2003)

ESAIM: Probability and Statistics

We derive necessary and sufficient conditions for a sum of i.i.d. random variables – where , but – to satisfy a moderate deviations principle. Moreover we show that this equivalence is a typical moderate deviations phenomenon. It is not true in a large deviations regime.

Moderate Deviations for I.I.D. Random Variables

Peter Eichelsbacher, Matthias Löwe (2010)

ESAIM: Probability and Statistics

We derive necessary and sufficient conditions for a sum of i.i.d. random variables – where , but – to satisfy a moderate deviations principle. Moreover we show that this equivalence is a typical moderate deviations phenomenon. It is not true in a large deviations regime.

Moderate deviations for two sample t-statistics

Hongyuan Cao (2007)

ESAIM: Probability and Statistics

Let X1,...,Xn1 be a random sample from a population with mean µ1 and variance , and X1,...,Xn1 be a random sample from another population with mean µ2 and variance independent of {Xi,1 ≤ i ≤ n1}. Consider the two sample t-statistic . This paper shows that ln P(T ≥ x) ~ -x²/2 for any x := x(n1,n2) satisfying x → ∞, x = o(n1 + n2)1/2 as n1,n2 → ∞ provided 0 < c1 ≤ n1/n2 ≤ c2 < ∞. If, in addition, E|X1|3 < ∞, E|Y1|3 < ∞, then holds uniformly in x ∈ (O,o((n1 + n2)1/6))

Moment inequalities for sums of certain independent symmetric random variables

P. Hitczenko, S. Montgomery-Smith, K. Oleszkiewicz (1997)

Studia Mathematica

This paper gives upper and lower bounds for moments of sums of independent random variables which satisfy the condition , where are concave functions. As a consequence we obtain precise information about the tail probabilities of linear combinations of independent random variables for which for some fixed 0 < r ≤ 1. This complements work of Gluskin and Kwapień who have done the same for convex functions N.

Monte Carlo Random Walk Simulations Based on Distributed Order Differential Equations with Applications to Cell Biology

Andries, Erik, Umarov, Sabir, Steinberg, Stanly (2006)

Fractional Calculus and Applied Analysis

Mathematics Subject Classification: 65C05, 60G50, 39A10, 92C37In this paper the multi-dimensional Monte-Carlo random walk simulation models governed by distributed fractional order differential equations (DODEs) and multi-term fractional order differential equations are constructed. The construction is based on the discretization leading to a generalized difference scheme (containing a finite number of terms in the time step and infinite number of terms in the space step) of the Cauchy problem for...

Moyennes harmoniques

Fernando Alcalde Cuesta (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

Nous introduisons une notion de moyenne harmonique pour une marche aléatoire sur une relation d’équivalence mesurée graphée, qui généralise la notion classique de moyenne invariante. Pour les graphages à géométrie bornée, une telle moyenne existe toujours. Nous prouvons qu’une moyenne harmonique devient invariante lorsque la marche aléatoire sur presque toute orbite jouit de bonnes propriétés asymptotiques telles que la propriété de Liouville ou la récurrence.

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