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Your search keyword '"Weak convergence"' showing total 4 results
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4 results on '"Weak convergence"'

1. Large deviation principle for the stochastic Cahn-Hilliard/Allen-Cahn equation with fractional noise.

Author

Gregory, Amali Paul Rose, Suvinthra, Murugan, and Balachandran, Krishnan

Subjects
*LARGE deviations (Mathematics), *STOCHASTIC partial differential equations, *RIESZ spaces, *PERTURBATION theory, *EQUATIONS, *NOISE
Abstract

In this work, we consider the stochastic Cahn-Hilliard/Allen-Cahn equation with fractional noise, which is fractional in time and white in space. We obtain the existence, uniqueness, and Hölder regularity of the solution. Also, using a weak convergence approach, we prove that the law of solution associated with the above equation with a small perturbation satisfies the large deviation principle in the Hölder norm. [ABSTRACT FROM AUTHOR]

Published
2024
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2. LARGE DEVIATIONS FOR STOCHASTIC GENERALIZED POROUS MEDIA EQUATIONS DRIVEN BY LÉVY NOISE.

Author

WEINA WU and JIANLIANG ZHAI

Subjects
*POROUS materials, *LARGE deviations (Mathematics), *SELFADJOINT operators, *SCHRODINGER operator, *NOISE
Abstract

We establish a large deviation principle (LDP) for a class of stochastic porous media equations driven by Lévy-type noise on a σ-finite measure space (E,B(E),μ), with the Laplacian replaced by a negative definite self-adjoint operator. One of the main contributions of this paper is that we do not assume the compactness of embeddings in the corresponding Gelfand triple, and to compensate for this generalization, a new procedure is provided. This is the first paper to deal with LDPs for stochastic evolution equations with Lévy noise without compactness conditions. The coefficient Ψ is assumed to satisfy nondecreasing Lipschitz nonlinearity, so an important physical problem covered by this case is the Stefan problem. Numerous examples of negative definite self-adjoint operators are applicable to our results, for example, for open E⊂Rd, L= Laplacian or fractional Laplacians, i.e., L=-(-Δ)α, α∈(0,1], generalized Schrödinger operators, i.e., L=Δ+2∇ρ/ρ⋅∇, Laplacians on fractals is also included. [ABSTRACT FROM AUTHOR]

Published
2024
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3. Large-population asymptotics for the maximum of diffusive particles with mean-field interaction in the noises.

Author

Kolliopoulos, Nikolaos, Sanchez, David, and Xiao, Amy

Subjects
*PARTICLE interactions, *DISTRIBUTION (Probability theory), *NOISE, *COMPUTER simulation
Abstract

We study the N → ∞ limit of the normalized largest component in some systems of N diffusive particles with mean-field interaction. By applying a universal time change, the interaction in noises is transferred to the drift terms, and the asymptotic behavior of the maximum becomes well-understood due to existing results in the literature. We expect that the normalized maximum in the original setting has the same limiting distribution as that of i.i.d copies of a solution to the corresponding McKean–Vlasov SDE and we present some results and numerical simulations that support this conjecture. [ABSTRACT FROM AUTHOR]

Published
2024
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4. Two-time-scale stochastic functional differential equations with wideband noises and jumps.

Author

Liu, Yuanyuan and Wen, Zhexin

Subjects
*FUNCTIONAL differential equations, *STOCHASTIC differential equations, *STOCHASTIC systems, *HYBRID systems, *MARKOV processes, *MARKOVIAN jump linear systems, *PHASE space, *NOISE
Abstract

This work examines a class of path-dependent stochastic systems which are hybrid with wideband noise, Poisson jumps and a singularly perturbed Markov chain. The addition of multi-scale Markov chain allows for modeling of discrete events with both fast and slow fluctuation. While this more realistic approach presents analytical challenges due to the non-Markovian formulation resulting from the wideband noise and the singularly perturbed Markov chain. By virtue of the weak convergence method and Itô functional formula, we prove that as ɛ → 0 , we obtain a Markovian switching jump diffusion. Finally, we offer several examples to illustrate our findings. • This is the first time to consider a class of stochastic systems with hybrid switching, wideband noise, Poisson jumps as well as time-delay perturbations. • Two-time-scale Markovian chain can describe the systems with both strong and weak interactions, which becomes really helpful when we dealt with a large-scale system. • Our problem is path-dependent and its phase space is infinite-dimensional, functional Itô formula expected to be applied to deal with such complex situation. • By virtue of the weak convergence method and Itô functional formula, we get the limit system for the singularly perturbed functional systems. • Integro-differential systems, Ginzburg–Landau equations and Replicator dynamics are presented to illustrate our findings. [ABSTRACT FROM AUTHOR]

Published
2024
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