Stochastische Processen in de Fysica: verschil tussen versies
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| Regel 9: | Regel 9: | ||
===17 juni 2015=== | ===17 juni 2015=== | ||
Vraag 1: Consider a continuous time Markov process with state space K = {1, 2, . . . , M} and | Vraag 1: Consider a continuous time Markov process with state space K = {1, 2, . . . , M} and | ||
with transition rates k(x, x + 1) = q except for x = M, k(x, x − 1) = p except for x = 1. All other transition rates are zero. Determine the stationary distribution as a function of p, q and M. Is there detailed balance? | with transition rates k(x, x + 1) = q except for x = M, k(x, x − 1) = p except for x = 1. All other transition rates are zero. Determine the stationary distribution as a function of p, q and M. Is there detailed balance?\\ | ||
Vraag 2: | Vraag 2: | ||
Versie van 20 aug 2015 13:49
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Algemeen
Dit vak vervangt het deel van Wiskundige Methoden gegeven door Professor Maes over Markovketens. Het is daarnaast ook iets uitgebreider geworden met wat meer leerstof over Brownian Motion en een klein deel Non-Equilibrium Physics.
Examens Stochastische Processen
2014-2015
17 juni 2015
Vraag 1: Consider a continuous time Markov process with state space K = {1, 2, . . . , M} and with transition rates k(x, x + 1) = q except for x = M, k(x, x − 1) = p except for x = 1. All other transition rates are zero. Determine the stationary distribution as a function of p, q and M. Is there detailed balance?\\ Vraag 2: