Preface to the revised edition Remarks on notation 1. Basic examples 2. Characterization and existence 3. Stable processes and their extensions 4. The Levy-Ito decomposition of sample functions 5. Distributional properties of Levy processes 6. Subordination and density transformation 7. Recurrence and transience 8. Potential theory for Levy processes 9. Wiener-Hopf factorizations 10. More distributional properties Supplement Solutions to exercises References and author index Subject index.

Lévy processes and infinitely divisible distributions

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/63B506EB85D6875966CE63BA0336BC2F/S0025557200190515a.pdf/div-class-title-span-class-italic-lie-groups-and-lie-algebras-chapters-1-3-span-by-n-bourbaki-pp-450-dm-98-1989-isbn-3-540-50218-1-springer-div.pdf

Lie groups and Lie algebras (chapters 1-3 ), by N. Bourbaki. Pp 450. DM 98. 1989. ISBN 3-540-50218-1 (Springer)

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Principles Of Random Walk

‘groupes et algebres de lie’ chapters 2, 3

Martingale Hardy Spaces And Their Applications In Fourier Analysis

We prove $\ell ^p\left( {\mathbb {Z}}^d\right) $ bounds for $p\in (1, \infty )$, of r-variations $r\in (2, \infty )$, for discrete averaging operators and truncated singular integrals of Radon type. We shall present a new powerful method which allows us to deal with these operators in a unified way and obtain the range of parameters of p and r which coincide with the ranges of their continuous counterparts.

\ell ^p\left( \mathbb {Z}^d\right) -estimates for discrete operators of Radon type: variational estimates

We prove $\ell^p\big(\mathbb Z^d\big)$ bounds for $p\in(1, \infty)$, of $r$-variations $r\in(2, \infty)$, for discrete averaging operators and truncated singular integrals of Radon type. We shall present a new powerful method which allows us to deal with these operators in a unified way and obtain the range of parameters of $p$ and $r$ which coincide with the ranges of their continuous counterparts.

L^p(Z^d)-estimates for discrete operators of Radon type: Variational estimates

(x) : n∈ N.Moreover, one does not need to ﬁnd a dense class of functions for which the pointwise convergence holdswhich sometimes might be a diﬃcult problem.Variational estimates were the subject of many papers, see [6, 7, 8, 17] and the references therein. Letus notice that Theorem A for the truncated singular integral immediately implies that the singular integralalong the primesT f(x) =X

Variational estimates for averages and truncated singular integrals along the prime numbers

We establish a higher dimensional counterpart of Bourgain's pointwise ergodic theorem along an arbitrary integer-valued polynomial mapping. We achieve this by proving variational estimates $V_r$ on $L^p$ spaces for all $1

Bartosz Trojan

Papers

\ell ^p\left( \mathbb {Z}^d\right) -estimates for discrete operators of Radon type: variational estimates

L^p(Z^d)-estimates for discrete operators of Radon type: Variational estimates

Variational estimates for averages and truncated singular integrals along the prime numbers

Discrete maximal functions in higher dimensions and applications to ergodic theory

Cotlar’s Ergodic Theorem Along the Prime Numbers