Displaying similar documents to “On Multi-Dimensional Random Walk Models Approximating Symmetric Space-Fractional Diffusion Processes”

Monte Carlo Random Walk Simulations Based on Distributed Order Differential Equations with Applications to Cell Biology

Andries, Erik, Umarov, Sabir, Steinberg, Stanly (2006)

Fractional Calculus and Applied Analysis

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Mathematics Subject Classification: 65C05, 60G50, 39A10, 92C37 In this paper the multi-dimensional Monte-Carlo random walk simulation models governed by distributed fractional order differential equations (DODEs) and multi-term fractional order differential equations are constructed. The construction is based on the discretization leading to a generalized difference scheme (containing a finite number of terms in the time step and infinite number of terms in the space step)...

Discrete Models of Time-Fractional Diffusion in a Potential Well

Gorenflo, R., Abdel-Rehim, E. (2005)

Fractional Calculus and Applied Analysis

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Mathematics Subject Classification: 26A33, 45K05, 60J60, 60G50, 65N06, 80-99. By generalization of Ehrenfest’s urn model, we obtain discrete approximations to spatially one-dimensional time-fractional diffusion processes with drift towards the origin. These discrete approximations can be interpreted (a) as difference schemes for the relevant time-fractional partial differential equation, (b) as random walk models. The relevant convergence questions as well as the behaviour...

Upper tails of self-intersection local times of random walks: survey of proof techniques

Wolfgang König (2010)

Actes des rencontres du CIRM

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The asymptotics of the probability that the self-intersection local time of a random walk on ℤ d exceeds its expectation by a large amount is a fascinating subject because of its relation to some models from Statistical Mechanics, to large-deviation theory and variational analysis and because of the variety of the effects that can be observed. However, the proof of the upper bound is notoriously difficult and requires various sophisticated techniques. We survey some heuristics and some...