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By Don S Lemons; Paul Langevin

ISBN-10: 0801868661

ISBN-13: 9780801868665

ISBN-10: 080186867X

ISBN-13: 9780801868672

ISBN-10: 0801876389

ISBN-13: 9780801876387

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Additional info for An introduction to stochastic processes in physics : containing "On the theory of Brownian motion" by Paul Langevin, translated by Anthony Gythiel

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Mean{X n } = µ and var{X 1 } = var{X 2 } = . . var{X n } = σ 2 . The net displacement is given by X = X 1 + X 2 + · · · + X n . a. Find mean{X }, var{X }, and X 2 as a function of n. PROBLEMS 21 b. A steady wind blows the Brownian particle, causing its steps to the right to be larger than those to the left. That is, the two possible outcomes of each step are X 1 = xr and X 2 = − xl where xr > xl > 0. Assume the probability of a step to the right is the same as the probability of a step to the left.

3) returns a unique value of q(t + dt) for each q(t). Many of the familiar processes of classical physics belong to the class of timedomain and process-variable continuous, smooth, and Markov sure processes. In the next section we investigate a particular random process that is continuous (in both senses) and Markov but neither smooth nor sure. Such continuous, Markov, random processes incrementally, but powerfully, generalize the wellbehaved, sure processes of classical physics they most closely resemble.

A. Compute mean{X i } and var{X i } in terms of the constants Vo , and V . b. Determine mean{N }, var{N }, and the coefficient of variation var{N }/ mean{N } in terms of No , Vo , and V . 1 Brownian Motion Described We are ready to use our knowledge of how random variables add and multiply to model the simplest of all physical processes—a single particle at rest. If at one instant a particle occupies a definite position and has zero velocity, it will, according to Newton’s first law of motion, continue to occupy the same position as long as no forces act on it.

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An introduction to stochastic processes in physics : containing "On the theory of Brownian motion" by Paul Langevin, translated by Anthony Gythiel by Don S Lemons; Paul Langevin


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