Displaying similar documents to “Non-differentiability of Feynman paths”

Revisiting the sample path of Brownian motion

S. James Taylor (2006)

Banach Center Publications

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Brownian motion is the most studied of all stochastic processes; it is also the basis for stochastic analysis developed in the second half of the 20th century. The fine properties of the sample path of a Brownian motion have been carefully studied, starting with the fundamental work of Paul Lévy who also considered more general processes with independent increments and extended the Brownian motion results to this class. Lévy showed that a Brownian path in d (d ≥ 2) dimensions had zero...

Marking (1, 2) points of the brownian web and applications

C. M. Newman, K. Ravishankar, E. Schertzer (2010)

Annales de l'I.H.P. Probabilités et statistiques

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The brownian web (BW), which developed from the work of Arratia and then Tóth and Werner, is a random collection of paths (with specified starting points) in one plus one dimensional space–time that arises as the scaling limit of the discrete web (DW) of coalescing simple random walks. Two recently introduced extensions of the BW, the brownian net (BN) constructed by Sun and Swart, and the dynamical brownian web (DyBW) proposed by Howitt and Warren, are (or should be) scaling limits...

On Truncated Variation of Brownian Motion with Drift

Rafał Łochowski (2008)

Bulletin of the Polish Academy of Sciences. Mathematics

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We introduce the concept of truncated variation of Brownian motion with drift, which differs from regular variation by neglecting small jumps (smaller than some c > 0). We estimate the expected value of the truncated variation. The behaviour resembling phase transition as c varies is revealed. Truncated variation appears in the formula for an upper bound for return from any trading based on a single asset with flat commission.

Convergence to the brownian Web for a generalization of the drainage network model

Cristian Coletti, Glauco Valle (2014)

Annales de l'I.H.P. Probabilités et statistiques

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We introduce a system of one-dimensional coalescing nonsimple random walks with long range jumps allowing paths that can cross each other and are dependent even before coalescence. We show that under diffusive scaling this system converges in distribution to the Brownian Web.