| 1. |
- Broman, Erik, 1977, et al.
(författare)
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Dynamical Stability of Percolation for Some Interacting Particle Systems and $\epsilon$--Stability
- 2006
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Ingår i: Annals of Probability. - : Institute of Mathematical Statistics. - 0091-1798 .- 2168-894X. ; 34, s. 539-576
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we will investigate dynamic stability of percolation for the stochastic Ising model and the contact process. We also introduce the notion of downwards and upwards $\epsilon$-- stability which will be a key tool for our analysis.
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| 2. |
- Broman, Erik, 1977
(författare)
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One-dependent trigonometric determinantal processes are two-block-factors
- 2005
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Ingår i: Annals of Probability. - : Institute of Mathematical Statistics. - 0091-1798 .- 2168-894X. ; 33:2, s. 601-609
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Tidskriftsartikel (refereegranskat)abstract
- Given a trigonometric polynomial f : [0, 1] → [0, 1] of degree m, one can define a corresponding stationary process {Xi}i ∈ℤ via determinants of the Toeplitz matrix for f. We show that for m = 1 this process, which is trivially one-dependent, is a two-block-factor. © Institute of Mathematical Statistics, 2005.
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| 3. |
- Broman, Erik, 1977
(författare)
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Stochastic domination for a hidden markov chain with applications to the contact process in a randomly evolving environment
- 2007
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Ingår i: Annals of Probability. - : Institute of Mathematical Statistics. - 0091-1798 .- 2168-894X. ; 35:6, s. 2263-2293
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Tidskriftsartikel (refereegranskat)abstract
- The ordinary contact process is used to model the spread of a disease in a population. In this model, each infected individual waits an exponentially distributed time with parameter 1 before becoming healthy. In this paper, we introduce and study the contact process in a randomly evolving environment. Here we associate to every individual an independent two-state, {0, 1}, background process. Given delta(0) < delta(1), if the background process is in state 0, the individual (if infected) becomes healthy at rate delta(0), while if the background process is in state 1, it becomes healthy at rate delta(1). By stochastically comparing the contact process in a randomly evolving environment to the ordinary contact process, we will investigate matters of extinction and that of weak and strong survival. A key step in our analysis is to obtain stochastic domination results between certain point processes. We do this by starting out in a discrete setting and then taking continuous time limits.
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| 4. |
- Buckdahn, Rainer, et al.
(författare)
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MEAN-FIELD BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS : A LIMIT APPROACH
- 2009
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Ingår i: Annals of Probability. - : Institute of Mathematical Statistics. - 0091-1798 .- 2168-894X. ; 37:4, s. 1524-1565
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Tidskriftsartikel (refereegranskat)abstract
- Mathematical mean-field approaches play an important role in different fields of Physics and Chemistry, but have found in recent works also their application in Economics, Finance and Game Theory. The objective of our paper is to investigate a special mean-field problem in a purely stochastic approach: for the solution (Y, Z) of a mean-field backward stochastic differential equation driven by a forward stochastic differential of McKean-Vlasov type with solution X we study a special approximation by the solution (X-N, Y-N, Z(N)) of some decoupled forward-backward equation which coefficients are governed by N independent copies of (X-N, Y-N, Z(N)). We show that the convergence speed of this approximation is of order 1/root N. Moreover, our special choice of the approximation allows to characterize the limit behavior of root N(X-N - X, Y-N - Y, Z(N) - Z). We prove that this triplet converges in law to the solution of some forward-backward. stochastic differential equation of mean-field type, which is not only governed by a Brownian motion but also by an independent Gaussian field.
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| 5. |
- Hult, Henrik, et al.
(författare)
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Extremal behavior of stochastic integrals driven by regularly varying Levy processes
- 2007
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Ingår i: Annals of Probability. - : Institute of Mathematical Statistics. - 0091-1798 .- 2168-894X. ; 35:1, s. 309-339
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Tidskriftsartikel (refereegranskat)abstract
- We study the extremal behavior of a stochastic integral driven by a multivariate Levy process that is regularly varying with index alpha > 0. For predictable integrands with a finite (alpha + delta)-moment, for some delta > 0, we show that the extremal behavior of the stochastic integral is due to one big jump of the driving Levy process and we determine its limit measure associated with regular variation on the space of cadlag functions.
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| 6. |
- Hwang, Hsien-Kuei, et al.
(författare)
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Local limit theorems for finite and infinite urn models
- 2008
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Ingår i: Annals of Probability. - 0091-1798 .- 2168-894X. ; 36:3, s. 992-1022
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Tidskriftsartikel (refereegranskat)abstract
- Local limit theorems are derived for the number of occupied urns in general finite and infinite urn models under the minimum condition that the variance tends to infinity. Our results represent an optimal improvement over previous ones for normal approximation.
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| 7. |
- Hägg, Jonas
(författare)
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Local Gaussian fluctuations in the Airy and Discrete PNG processes
- 2008
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Ingår i: Annals of Probability. - 0091-1798 .- 2168-894X. ; 36:3, s. 1059-1092
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Tidskriftsartikel (refereegranskat)abstract
- We prove that the Airy process, A(t), locally fluctuates like a Brownian motion. In the same spirit we also show that, in a certain scaling limit, the so-called discrete polynuclear growth process (PNG) behaves like a Brownian motion.
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| 8. |
- Janson, Svante
(författare)
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Rounding of continuous random variables and oscillatory asymptotics
- 2006
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Ingår i: Annals of Probability. - : Institute of Mathematical Statistics. - 0091-1798 .- 2168-894X. ; 34:5, s. 1807-1826
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Tidskriftsartikel (refereegranskat)abstract
- We study the characteristic function and moments of the integer-valued random variable [X + alpha], where X is a continuous random variables. The results can be regarded as exact versions of Sheppard's correction. Rounded variables of this type often occur as subsequence limits of sequences of integer-valued random variables. This leads to oscillatory terms in asymptotics for these variables, something that has often been observed, for example in the analysis of several algorithms. We give some examples, including applications to tries, digital search trees and Patricia tries.
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| 9. |
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| 10. |
- Jonasson, Johan, 1966, et al.
(författare)
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Dynamical models for circle covering: Brownian motion and Poisson updating
- 2008
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Ingår i: Annals of Probability. - 0091-1798 .- 2168-894X. ; 36, s. 739-764
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Tidskriftsartikel (refereegranskat)abstract
- We consider two dynamical variants of Dvoretzky’s classical problem of random interval coverings of the unit circle, the latter having been completely solved by L. Shepp. In the first model, the centers of the intervals perform independent Brownian motions and in the second model, the positions of the intervals are updated according to independent Poisson processes where an interval of length ℓ is updated at rate ℓ−α where α≥0 is a parameter. For the model with Brownian motions, a special case of our results is that if the length of the nth interval is c/n, then there are times at which a fixed point is not covered if and only if c<2 and there are times at which the circle is not fully covered if and only if c<3. For the Poisson updating model, we obtain analogous results with c<α and c<α+1 instead. We also compute the Hausdorff dimension of the set of exceptional times for some of these questions.
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