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An exact bound for tail probabilities for a class of conditionally symmetric bounded martingales
Lietuvos Matematikos Rinkinys, 2023 We consider the class, say ℳn,sym, of martingales Mn = X1 + ⋯ + Xn with conditionally symmetric bounded differences Xk such that |Xk | ≤ 1. We find explicitly a solution, say Dn(x), of the variational problem Dn(x) ≝ sup Mn ∈ℳn,sym ℙ {Mn ≥ x}.
Dainius Dzindzalieta
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Exponential inequalities for the supremum of some counting processes and their square martingales
Comptes Rendus. Mathématique, 2021 We establish exponential inequalities for the supremum of martingales and square martingales obtained from counting processes, as well as for the oscillation modulus of these processes. Our inequalities, that play a decisive role in the control of errors
Le Guével, Ronan
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Concentration Inequalities and Optimal Number of Layers for Stochastic Deep Neural Networks
IEEE Access, 2023 We state concentration inequalities for the output of the hidden layers of a stochastic deep neural network (SDNN), as well as for the output of the whole SDNN.
Michele Caprio, Sayan Mukherjee
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On the martingale property of certain local martingales [PDF]
Probability Theory and Related Fields, 2010 Appendix on local time of diffusions added; 27 pages, 1 figure; to appear in ...
Mijatovic, A, Urusov, M
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Conformable Fractional Martingales and Some Convergence Theorems
Mathematics, 2021 In this paper, we define conformable Lebesgue measure and conformable fractional countable martingales. Some convergence theorems are proved.
Ma’mon Abu Hammad
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Axioms, 2022 In this paper, we focus on a family of backward stochastic differential equations (BSDEs) with subdifferential operators that are driven by infinite-dimensional martingales. We shall show that the solution to such infinite-dimensional BSDEs exists and is
Pei Zhang +2 more
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Asymptotic normality of recursive algorithms via martingale difference arrays [PDF]
Discrete Mathematics & Theoretical Computer Science, 2001 We propose martingale central limit theorems as an tool to prove asymptotic normality of the costs of certain recursive algorithms which are subjected to random input data. The recursive algorithms that we have in mind are such that if input data of size
Werner Schachinger
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A Berry–Esseen bound of order $\protect \frac{1}{\protect \sqrt{n}} $ for martingales
Comptes Rendus. Mathématique, 2020 Renz [13] has established a rate of convergence $1/\sqrt{n}$ in the central limit theorem for martingales with some restrictive conditions. In the present paper a modification of the methods, developed by Bolthausen [2] and Grama and Haeusler [6], is ...
Wu, Songqi +3 more
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A functional limit law for the profile of plane-oriented recursive trees. [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 We give a functional limit law for the normalized profile of random plane-oriented recursive trees. The proof uses martingale convergence theorems in discrete and continuous-time. This complements results of Hwang (2007).
Henning Sulzbach
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Martingale-like sequences in Banach lattices
Modern Stochastics: Theory and Applications, 2018 Martingale-like sequences in vector lattice and Banach lattice frameworks are defined in the same way as martingales are defined in [Positivity 9 (2005), 437–456].
Haile Gessesse, Alexander Melnikov
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