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The Dean-Kawasaki equation with non-local singular interactions and correlated noise will be introduced, which describes the evolution of the density function for a system of finitely many particles g...
In this talk, we present the pointwise convergence of one-point large deviations rate functions (LDRFs) of the spatial finite difference method and further the fully discrete method based on the tempo...
For ergodic SDEs, their ergodic limits are usually approximated by the suitable means of numerical methods. To reveal the numerical asymptotic behavior, we study the large deviations principle (LDP) f...
In this lecture, I will talk about how to control the deviation of the occupation-time profile conditioned on disconnection so that this conditioning makes the model exhibit a phenomenon generally kno...
In this lecture, I will discuss how ``tilted interlacements’’ and ``solidification of porous surfaces’’, two specific realizations of the change-of-measure and coarse graining ideas respectively, prod...
In this lecture, I will discuss how tilting and coarse graining, two key ideas in modern probability, come into play in deriving respectively the lower and upper bounds of the asymptotic probability i...
In this lecture, I will talk about the large deviation problems in random interlacements, in particular the LDP of the occupation measure, and discuss its relations to sharp asymptotic probabilities o...
The deviations of hourly f 0 F 2 from monthly medians for 20 stations in Europe during the period 1958-1998 are studied. Spectral analysis is used to show that, both for original data (for each hour) ...
We derive a large deviation result for the log-likelihood ratio for testing simple hypotheses in locally stationary Gaussian processes. This result allows us to find explicitly the rates of exponentia...
Consider the problem of numerically computing the exponential rate at which the tail of the hitting time of a Markov chain to a given set decreases to zero. One approach involves computing the solutio...
We consider the problem of optimal allocation of computing budget to maximize the probability of correct selection in the ordinal optimization setting. This problem has been studied in the literature ...
Consider a simulation estimator α(c) based on expending c units of computer time, to estimate a quantity α. One measure of efficiency is to attempt to minimize P(|α(c)−α|>ε) for large c. This he...
The theory of large deviations for random walks is important both in its own right and as a starting point for establishing large deviations for more complex models (such as ìsmall noisdi§usion...
This paper develops central limit theorems (CLT's) and large deviations results for additive functionals associated with reflecting disions in which the functional may include a term associated with t...
Numerical simulations of the evolution of the channel power response to power adjustments in constant gain amplified degree-2 ROADM networks demonstrate novel persistent and periodic distant-dependent...

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