Titlebook: Seminaire de Probabilites XXXV; J. Azéma,M. émery,M. Yor Book 2001 Springer-Verlag Berlin Heidelberg 2001 Brownian motions.Measure.Probabi

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The Principle of Variation for Relativistic Quantum Particles,ween jump Markov processes. After renormalizing the multiplicative functional, the principle of variation of stochastic processes is applied in constructing Schr?dinger processes of pure-jumps which describe the movement of relativistic quantum particles.

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Quantum stochastic calculus for the uniform measure and Boolean convolution,ors and creators. These processes include the Boolean Brownian and Poisson processes obtained by replacing the classical convolution by its Boolean counterpart, and a family of Bernoulli processes. Using a quantum stochastic calculus constructed by time changes, we complete the existing non-commutat

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Some remarks on the martingales satisfying the structure equation ,ere . is a real parameter..Moreover, using the Bouleau-Yor extension of Ito’s formula to a real function F satisfying: . with ., we obtain inequalites of Burkholder-Davis-Gundy’s type for these martingales.

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