A note on asymptotic expansions for sums over a weakly dependent random field with application to the Poisson and Strauss processes

1993 ◽  
Vol 45 (2) ◽  
pp. 353-360 ◽  
Author(s):  
J. L. Jensen
Keyword(s):  
Random Field ◽  
Asymptotic Expansions ◽  
Weakly Dependent

scholarly journals Higher order asymptotics for large deviations — Part II

2020 ◽  
pp. 2150025
Author(s):  
Kasun Fernando ◽  
Pratima Hebbar
Keyword(s):  
Large Deviations ◽  
Asymptotic Expansions ◽  
Continuous Time ◽  
Compact Manifold ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Hörmander Condition ◽  
Additive Functionals ◽  
Higher Order Asymptotics ◽  
Weakly Dependent

We obtain asymptotic expansions for the large deviation principle (LDP) for continuous time stochastic processes with weakly-dependent increments. As a key example, we show that additive functionals of solutions of stochastic differential equations (SDEs) satisfying Hörmander condition on a [Formula: see text]-dimensional compact manifold admit these asymptotic expansions of all orders.

scholarly journals On maxima of stationary fields

2019 ◽  
Vol 56 (4) ◽  
pp. 1217-1230
Author(s):  
N. Soja-Kukieła
Keyword(s):  
Random Field ◽  
Random Fields ◽  
General Setting ◽  
Extremal Index ◽  
New Method ◽  
Mixing Condition ◽  
Translation Invariant ◽  
Stationary Random Field ◽  
Maximum Field ◽  
Weakly Dependent

AbstractLet $\{X_{\textbf{n}} \colon \textbf{n}\in{\mathbb Z}^d\}$ be a weakly dependent stationary random field with maxima $M_{A} :=, \sup\{X_{\textbf{i}} \colon \textbf{i}\in A\}$ for finite $A\subset{\mathbb Z}^d$ and $M_{\textbf{n}} := \sup\{X_{\textbf{i}} \colon \mathbf{1} \leq \textbf{i} \leq \textbf{n} \}$ for $\textbf{n}\in{\mathbb N}^d$ . In a general setting we prove that ${\mathbb{P}}(M_{(N_1(n),N_2(n),\ldots, N_d(n))} \leq v_n)$ $= \exp(\!- n^d {\mathbb{P}}(X_{\mathbf{0}} > v_n , M_{A_n} \leq v_n)) + {\text{o}}(1)$ for some increasing sequence of sets $A_n$ of size $ {\text{o}}(n^d)$ , where $(N_1(n),N_2(n), \ldots,N_d(n))\to(\infty,\infty, \ldots, \infty)$ and $N_1(n)N_2(n)\cdots N_d(n)\sim n^d$ . The sets $A_n$ are determined by a translation-invariant total order $\preccurlyeq$ on ${\mathbb Z}^d$ . For a class of fields satisfying a local mixing condition, including m-dependent ones, the main theorem holds with a constant finite A replacing $A_n$ . The above results lead to new formulas for the extremal index for random fields. The new method for calculating limiting probabilities for maxima is compared with some known results and applied to the moving maximum field.

THE METHOD OF MULTISCALE ASYMPTOTIC EXPANSIONS FOR THE PROBLEM OF HEAT EXCHANGE IN COMPOSITE PLANE WALL WITH STATIONARY RANDOM FIELDS

2011 ◽  
Vol 25 (01) ◽  
pp. 143-151 ◽  
Author(s):  
WEN-MING HE ◽  
XIAO-FEI GUAN ◽  
XIN-JUN ZHANG
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Heat Exchange ◽  
Random Field ◽  
Asymptotic Expansions ◽  
Random Fields ◽  
Plane Wall ◽  
Stationary Random Fields ◽  
Stationary Random Field ◽  
Element Method

In this paper, we discuss the problem of heat exchange in a composite plane wall whose heat transmitting coefficient is a stationary random field. We present a method of multiscale asymptotic expansions and the corresponding finite element method to solve the problem.

Comparison of random field strengths in (1-x)SrTiO3-xBiFeO3 and (1-x)SrTiO3-xBaTiO3 relaxor ferroelectrics by means of acoustic emission

2020 ◽  
Vol 92 (2) ◽  
pp. 20401
Author(s):  
Evgeniy Dul'kin ◽  
Michael Roth
Keyword(s):  
Acoustic Emission ◽  
Random Field ◽  
Electric Fields ◽  
Bias Field ◽  
Relaxor Ferroelectrics ◽  
External Bias ◽  
Field Strengths

In relaxor (1-x)SrTiO3-xBiFeO3 ferroelectrics ceramics (x = 0.2, 0.3 and 0.4) both intermediate temperatures and Burns temperatures were successfully detected and their behavior were investigated in dependence on an external bias field using an acoustic emission. All these temperatures exhibit a non-trivial behavior, i.e. attain the minima at some threshold fields as a bias field enhances. It is established that the threshold fields decrease as x increases in (1-x)SrTiO3-xBiFeO3, as it previously observed in (1-x)SrTiO3-xBaTiO3 (E. Dul'kin, J. Zhai, M. Roth, Phys. Status Solidi B 252, 2079 (2015)). Based on the data of the threshold fields the mechanisms of arising of random electric fields are discussed and their strengths are compared in both these relaxor ferroelectrics.

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