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11.
We prove the hydrodynamical limit for weakly asymmetric simple exclusion processes. A large deviation property with respect to this limit is established for the symmetric case. We treat also the situation where a slow reaction (creation and annihilation of particles) is present. 相似文献
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This work is concerned with the existence and uniqueness of a strong Markov process that has continuous sample paths and the following additional properties:
- (i) The state space is an infinite two-dimensional wedge, and the process behaves in the interior of the wedge like an ordinary Brownian motion.
- (ii) The process reflects instantaneously at the boundary of the wedge, the angle of reflection being constant along each side.
- (iii) The amount of time that the process spends at the comer of the wedge is zero (i.e., the set of times for which the process is at the comer has Lebesgue measure zero).
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Srinivasa R. S. Varadhan 《Letters in Mathematical Physics》2009,88(1-3):175-185
We explore the behavior under scaling limits of large systems using methods from the theory large deviations. This is carried out through the examination of a few examples. 相似文献
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We consider a family {u? (t, x, ω)}, ? < 0, of solutions to the equation ?u?/?t + ?Δu?/2 + H (t/?, x/?, ?u?, ω) = 0 with the terminal data u?(T, x, ω) = U(x). Assuming that the dependence of the Hamiltonian H(t, x, p, ω) on time and space is realized through shifts in a stationary ergodic random medium, and that H is convex in p and satisfies certain growth and regularity conditions, we show the almost sure locally uniform convergence, in time and space, of u?(t, x, ω) as ? → 0 to the solution u(t, x) of a deterministic averaged equation ?u/?t + H?(?u) = 0, u(T, x) = U(x). The “effective” Hamiltonian H? is given by a variational formula. © 2007 Wiley Periodicals, Inc. 相似文献
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