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The Annals of probability, ISSN 0091-1798, 7/2003, Volume 31, Issue 3, pp. 1228 - 1240
.... In this paper we show that a self-normalized version of Donsker's theorem holds only under the assumption that X belongs to the domain of attraction of the normal law... 
Mathematical theorems | Central limit theorem | Statistical theories | Probability theory | Partial sums | Mathematical moments | Random variables | Probabilities | Law of sines | Self-normalized sums | Arc sine law | Donsker's theorem | arc sine law | STATISTICS & PROBABILITY | self-normalized sums | 60F17 | 60F05 | 62E20
Journal Article
ELECTRONIC COMMUNICATIONS IN PROBABILITY, ISSN 1083-589X, 2020, Volume 25
We compute the Wassertein-1 (or Kantorovitch-Rubinstein) distance between a random walk in R-d and the Brownian motion. The proof is based on a new estimate of... 
STEINS METHOD | Wasserstein distance | STATISTICS & PROBABILITY | Malliavin calculus | Stein's method | Donsker theorem
Journal Article
Statistics and Probability Letters, ISSN 0167-7152, 07/2019, Volume 150, pp. 1 - 8
In this paper we study a Donsker type theorem for the fractional Poisson process (fPp... 
Fractional Poisson process | Donsker type theorem | Skorohod topology | Long memory | Random walk | LEVY PROCESSES | STATISTICS & PROBABILITY | PARAMETERS | ROSENBLATT PROCESS | Memory
Journal Article
中国科学:数学英文版, ISSN 1674-7283, 2012, Volume 55, Issue 11, pp. 2285 - 2296
Journal Article
Journal of mathematical analysis and applications, ISSN 0022-247X, 2019, Volume 477, Issue 2, pp. 1133 - 1156
... convex functionals on Wasserstein-1. We retrieve dual transportation inequalities as a Corollary and we provide examples where the theorem can be used to easily prove dual expressions like the celebrated Donsker-Varadhan variational formula... 
Fenchel-Moreau-Rockafellar theorem | Conjugate duality | Donsker-Varadhan variational formula | Optimal control | Wasserstein metric | Partially observable Markov decision processes | Markov processes | Neurosciences | Mathematics - Probability
Journal Article
The Annals of probability, ISSN 0091-1798, 7/2005, Volume 33, Issue 4, pp. 1422 - 1451
Journal Article
The Annals of probability, ISSN 0091-1798, 7/2015, Volume 43, Issue 4, pp. 1777 - 1822
.... It is based on stochastic fixed-point equations, where probability metrics can be used to obtain contraction properties and allow the application of Banach's fixed-point theorem... 
Functional limit theorem | Zolotarev metric | Recursive distributional equation | Contraction method | Donsker's invariance principle | PARTIAL MATCH QUERIES | TREES | QUICKSORT | LIMIT-THEOREM | RANDOM QUADTREES | contraction method | STATISTICS & PROBABILITY | RECURSIVE ALGORITHMS | recursive distributional equation | 68Q25 | 60C05 | Donsker’s invariance principle | 60G18 | 60F17
Journal Article
International Journal of Uncertainty, Fuzziness and Knowlege-Based Systems, ISSN 0218-4885, 02/2018, Volume 26, Issue 1, pp. 27 - 42
Journal Article
Modern Stochastics: Theory and Applications, ISSN 2351-6046, 09/2017, Volume 4, Issue 3, pp. 189 - 198
...])$. This approach is used to simplify the proof of the self-normalized Donsker theorem in Cs\"{o}rg\H{o} et al. (2003). Some notes on spheres with respect... 
Mathematics - Probability | Brownian motion | Poincaré–Borel lemma | Donsker theorem | self-normalized sums
Journal Article
Alea, ISSN 1980-0436, 2015, Volume 12, Issue 1, pp. 1 - 23
We consider a class of continuous time Markov chains on a compact metric space that admit an invariant measure strictly positive on open sets together with... 
Donsker-varadhan theorem | Phonon boltzmann equation | Empirical flow | Large deviations | PROCESS EXPECTATIONS | LARGE TIME | THEOREM | Phonon Boltzmann equation | DYNAMICS | STATISTICS & PROBABILITY | Donsker-Varadhan theorem | EQUATION
Journal Article
Discrete and continuous dynamical systems. Series B, ISSN 1531-3492, 2014, Volume 19, Issue 6, pp. 1549 - 1562
This paper considers binomial approximation of continuous time stochastic processes. It is shown that, under some mild integrability conditions, a process can... 
Complete market | Incomplete market | Binomial approximation | Discretzation of Ito equations | Stochastic processes | Donsker theorem | binomial approximation | discretzation of Ito equations | MATHEMATICS, APPLIED | MARKET | STATISTICS | THEOREMS | EQUATIONS | complete market | MODEL | incomplete market
Journal Article
Markov Processes and Related Fields, ISSN 1024-2953, 2014, Volume 20, Issue 1, pp. 167 - 172
... among Gaussian processes. In this note, making use of the Mallows distance and for 1 < alpha <= 2, we derive the classical Donsker's theorem for alpha-stable Levy motions. 
Stable laws | Donsker's theorem | Mallows distance | CONVERGENCE | STATISTICS & PROBABILITY | stable laws | LAWS
Journal Article
Statistics and Probability Letters, ISSN 0167-7152, 02/2013, Volume 83, Issue 2, pp. 588 - 595
.... The limit in law is a certain continuous state-space branching process (CSBP). In the present work, we obtain a Central Limit Theorem, thus completing Bertoin’s work. 
Branching process | Lévy-Itô decomposition | Donsker’s invariance principle | Skorohod’s representation | Skorohod's representation | Donsker's invariance principle | Lévy-ItÔ decomposition | STATISTICS & PROBABILITY | Levy-Ito decomposition | Probability | Mathematics
Journal Article
Electronic Journal of Statistics, ISSN 1935-7524, 2012, Volume 6, pp. 2486 - 2518
.... We obtain a uniform central limit theorem with root nrate on the assumption that the smoothness of the functionals is larger than the illposedness of the problem, which is given by the polynomial... 
Distribution function | Fourier multipliers | Deconvolution | Smoothed empirical processes | Efficiency | Donsker theorem | RATES | efficiency | LINEAR FUNCTIONALS | STATISTICS & PROBABILITY | smoothed empirical processes | ASYMPTOTIC NORMALITY | distribution function
Journal Article
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