Kac functional and Schrödinger equation
A simple proof of Doob's convergence theorem
Note on last exit decomposition
The gauge and conditional gauge theorem
Pedagogic notes on the barrier theorem
On stopped Feynman-Kac functionals
Remark on the conditional gauge theorem
Some universal field equations
On the Exponential Formulas of Semi-Group Theory.
A generalization of an inequality in the elementary theory of numbers.
The lifetime of conditional brownian motion in the plane
Sul problema del ritorno all’equilibrio
Si considera, sul gruppo degli interi, una passeggiata aleatoria uscente dall’origine, i cui passi ammettano due soli possibili valori: uno strettamente negativo, l’altro strettamente positivo. Nel caso particolare in cui il primo di questi valori sia , si dà un’espressione esplicita per la legge del primo istante di ritorno nell’origine.
Probabilistic approach in potential theory to the equilibrium problem
A complete form of the classical theorem by Gauss-M. Riesz-Frostman is given for a large of Markov processes without the usual hypothesis of duality. The idea leads to a probabilistic solution of Robin’s problem and it is based on the last exit time from a transient set.
Remarks on equilibrium potential and energy
This note discusses to problem of the minimization of energy by the equilibrium measure obtained by the method of last exit in reference Ann. Inst. Fourier, 23-3 (1973), 313–322.
A new setting for potential theory. I
We consider a transient Hunt process in which the potential density satisfies the conditions: (a) for each , is finite continuous in ; (b) iff . In earlier papers Chung established an equilibrium principle, and Rao obtained a Riesz of decomposition for excessive functions. We now begin a deeper study under these conditions, including the uniqueness of the decomposition and Hunt’s hypothesis (B).
Borel et la martingale de Saint-Pétersbourg
On se propose d’examiner sur un exemple, le paradoxe de Saint-Pétersbourg, la façon dont Borel « expose » la science de son temps. La première partie indique sommairement la place singulière de la vulgarisation dans l’œuvre de Borel. Les deux parties suivantes présentent dans l’ordre chronologique les contributions boréliennes au paradoxe de Saint-Pétersbourg qui s’échelonnent sur plus de cinquante ans ; elles indiquent comment Borel aborde le problème en le replaçant dans une réflexion au long...
Borel and the St. Petersburg martingale.
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