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III: 07, 137-142, LNM 88 (1969)

**HUBER, Catherine**

Un aspect de la loi du logarithme itéré pour des variables aléatoires indépendantes et équidistribuées (Independence)

A refinement of the classical law of the iterated logarithm for i.i.d. random variables, under regularity assumptions on the tail of the common distribution

Keywords: Law of the iterated logarithm

Nature: Original

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VI: 04, 72-89, LNM 258 (1972)

**CHATTERJI, Shrishti Dhav**

Un principe de sous-suites dans la théorie des probabilités (Measure theory)

This paper is devoted to results of the following kind: any sequence of random variables with a given weak property contains a subsequence which satisfies a stronger property. An example is due to Komlós: any sequence bounded in $L^1$ contains a subsequence which converges a.s. in the Cesaro sense. Several results of this kind, mostly due to the author, are presented without detailed proofs

Comment: See 1302 for extensions to the case of Banach space valued random variables. See also Aldous,*Zeit. für W-theorie,* **40**, 1977

Keywords: Subsequences, Central limit theorem, Law of the iterated logarithm

Nature: Exposition

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VIII: 10, 134-149, LNM 381 (1974)

**KNIGHT, Frank B.**

Existence of small oscillations at zeros of brownian motion (Brownian motion)

The one-dimensional Brownian motion path is shown to have an abnormal behaviour (an ``iterated logarithm'' upper limit smaller than one) at uncountably many times on his set of zeros

Comment: This result may be compared to Kahane,*C.R. Acad. Sci.* **248**, 1974

Keywords: Law of the iterated logarithm, Local times

Nature: Original

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XII: 17, 148-161, LNM 649 (1978)

**LÉPINGLE, Dominique**

Sur le comportement asymptotique des martingales locales (Martingale theory)

This paper is devoted to the extension of well-known statements (the strong law of large numbers, the Borel-Cantelli lemma, and the easier half of the law of the iterated logarithm) to right-continuous local martingales. An interesting technical point is the definition of a family of exponential supermartingales

Keywords: Law of large numbers, Borel-Cantelli lemma, Exponential martingales, Law of the iterated logarithm

Nature: Original

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XV: 03, 11-37, LNM 850 (1981)

**LEDOUX, Michel**

La loi du logarithme itéré bornée dans les espaces de Banach (Banach space valued random variables)

To be completed

Keywords: Law of the iterated logarithm

Nature: Original

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XLV: 10, 277-300, LNM 2078 (2013)

**DONEY, R. A.**; **VAKEROUDIS, S.**

Windings of Planar Stable Processes (Theory of processes)

Keywords: Stable processes, Lévy processes, Brownian motion, windings, exit time from a cone, Spitzer's Theorem, skew-product representation, Lamperti's relation, Law of the Iterated Logarithm for small times

Nature: Original

Un aspect de la loi du logarithme itéré pour des variables aléatoires indépendantes et équidistribuées (Independence)

A refinement of the classical law of the iterated logarithm for i.i.d. random variables, under regularity assumptions on the tail of the common distribution

Keywords: Law of the iterated logarithm

Nature: Original

Retrieve article from Numdam

VI: 04, 72-89, LNM 258 (1972)

Un principe de sous-suites dans la théorie des probabilités (Measure theory)

This paper is devoted to results of the following kind: any sequence of random variables with a given weak property contains a subsequence which satisfies a stronger property. An example is due to Komlós: any sequence bounded in $L^1$ contains a subsequence which converges a.s. in the Cesaro sense. Several results of this kind, mostly due to the author, are presented without detailed proofs

Comment: See 1302 for extensions to the case of Banach space valued random variables. See also Aldous,

Keywords: Subsequences, Central limit theorem, Law of the iterated logarithm

Nature: Exposition

Retrieve article from Numdam

VIII: 10, 134-149, LNM 381 (1974)

Existence of small oscillations at zeros of brownian motion (Brownian motion)

The one-dimensional Brownian motion path is shown to have an abnormal behaviour (an ``iterated logarithm'' upper limit smaller than one) at uncountably many times on his set of zeros

Comment: This result may be compared to Kahane,

Keywords: Law of the iterated logarithm, Local times

Nature: Original

Retrieve article from Numdam

XII: 17, 148-161, LNM 649 (1978)

Sur le comportement asymptotique des martingales locales (Martingale theory)

This paper is devoted to the extension of well-known statements (the strong law of large numbers, the Borel-Cantelli lemma, and the easier half of the law of the iterated logarithm) to right-continuous local martingales. An interesting technical point is the definition of a family of exponential supermartingales

Keywords: Law of large numbers, Borel-Cantelli lemma, Exponential martingales, Law of the iterated logarithm

Nature: Original

Retrieve article from Numdam

XV: 03, 11-37, LNM 850 (1981)

La loi du logarithme itéré bornée dans les espaces de Banach (Banach space valued random variables)

To be completed

Keywords: Law of the iterated logarithm

Nature: Original

Retrieve article from Numdam

XLV: 10, 277-300, LNM 2078 (2013)

Windings of Planar Stable Processes (Theory of processes)

Keywords: Stable processes, Lévy processes, Brownian motion, windings, exit time from a cone, Spitzer's Theorem, skew-product representation, Lamperti's relation, Law of the Iterated Logarithm for small times

Nature: Original