Stationary solutions of SPDEs with locally monotone coefficients satisfy the Freidlin-Wentzell LDP, from which the LDP for invariant measures follows by contraction, covering reaction-diffusion, Burgers, Navier-Stokes, and MHD equations.
Extinction time and the total mass of the continuous-state branching processes with competition
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Sufficient conditions are given for CIMBI processes to avoid the boundary entirely and for hitting it almost surely (diffusion case) or with positive probability (finite-activity jumps) under small constant immigration.
Nonnegative weak martingale solutions exist for the stochastic thin-film equation, and their L^∞ norm converges in square mean to the initial mean multiplied by a geometric Wiener process-like random factor.
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Large deviation principles for the stationary solutions and invariant measures of a class of SPDE with locally monotone coefficients
Stationary solutions of SPDEs with locally monotone coefficients satisfy the Freidlin-Wentzell LDP, from which the LDP for invariant measures follows by contraction, covering reaction-diffusion, Burgers, Navier-Stokes, and MHD equations.
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Boundary behavior of continuous-state interacting multi-type branching processes with immigration
Sufficient conditions are given for CIMBI processes to avoid the boundary entirely and for hitting it almost surely (diffusion case) or with positive probability (finite-activity jumps) under small constant immigration.
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Long Time Behavior of Stochastic Thin Film Equation
Nonnegative weak martingale solutions exist for the stochastic thin-film equation, and their L^∞ norm converges in square mean to the initial mean multiplied by a geometric Wiener process-like random factor.