@article{MTMT:34749280,
	title = {Reaction-diffusion equations on metric graphs with edge noise},
	url = {https://m2.mtmt.hu/api/publication/34749280},
	author = {Sikolya, Eszter},
	doi = {10.1007/s10476-024-00006-z},
	journal-iso = {ANAL MATH},
	journal = {ANALYSIS MATHEMATICA},
	unique-id = {34749280},
	issn = {0133-3852},
	abstract = {We investigate stochastic reaction-diffusion equations on finite metric graphs. On each edge in the graph a multiplicative cylindrical Gaussian noise driven reaction-diffusion equation is given. The vertex conditions are the standard continuity and generalized, non-local Neumann-Kirchhoff-type law in each vertex. The reaction term on each edge is assumed to be an odd degree polynomial, not necessarily of the same degree on each edge, with possibly stochastic coefficients and negative leading term. The model is a generalization of the problem in [14] where polynomials with much more restrictive assumptions are considered and no first order differential operator is involved. We utilize the semigroup approach from [15] to obtain existence and uniqueness of solutions with sample paths in the space of continuous functions on the graph.},
	year = {2024},
	eissn = {1588-273X},
	orcid-numbers = {Sikolya, Eszter/0000-0003-0636-4326}
}

@article{MTMT:34048342,
	title = {On the parabolic Cauchy problem for quantum graphs with vertex noise},
	url = {https://m2.mtmt.hu/api/publication/34048342},
	author = {Kovács, Mihály and Sikolya, Eszter},
	doi = {10.1214/23-EJP962},
	journal-iso = {ELECTRON J PROBAB},
	journal = {ELECTRONIC JOURNAL OF PROBABILITY},
	volume = {28},
	unique-id = {34048342},
	issn = {1083-6489},
	abstract = {We investigate the parabolic Cauchy problem associated with quantum graphs includ-ing Lipschitz or polynomial type nonlinearities and additive Gaussian noise perturbed vertex conditions. The vertex conditions are the standard continuity and Kirchhoff assumptions in each vertex. In the case when only Kirchhoff conditions are perturbed, we can prove existence and uniqueness of a mild solution with continuous paths in the standard state space 9-L of square integrable functions on the edges. We also show that the solution is Markov and Feller. Furthermore, assuming that the vertex values of the normalized eigenfunctions of the self-adjoint operator governing the problem are uniformly bounded, we show that the mild solution has continuous paths in the fractional domain space associated with the Hamiltonian operator, 9-L & alpha; for & alpha; < 14. This is the case when the Hamiltonian operator is the standard Laplacian perturbed by a potential. We also show that if noise is present in both type of vertex conditions, then the problem admits a mild solution with continuous paths in the fractional domain space 9-L & alpha; with & alpha; < -14 only. These regularity results are the quantum graph ana-logues obtained by da Prato and Zabczyk [9] in case of a single interval and classical boundary Dirichlet or Neumann noise.},
	year = {2023},
	eissn = {1083-6489},
	orcid-numbers = {Kovács, Mihály/0000-0001-7977-9114; Sikolya, Eszter/0000-0003-0636-4326}
}

@article{MTMT:32152022,
	title = {Corrigendum to "On the stochastic Allen–Cahn equation on networks with multiplicative noise" [Electron. J. Qual. Theory Differ. Equ. 2021, No. 7, 1–24]},
	url = {https://m2.mtmt.hu/api/publication/32152022},
	author = {Kovács, Mihály and Sikolya, Eszter},
	doi = {10.14232/ejqtde.2021.1.52},
	journal-iso = {ELECTRON J QUAL THEOR DIFFER EQUAT},
	journal = {ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS},
	unique-id = {32152022},
	issn = {1417-3875},
	abstract = {We reprove Proposition 3.8 in our paper that was published in [Electron. J. Qual. Theory Differ. Equ. 2021, No. 7, 1-24], to fill a gap in the proof of Corollary 3.7 where the density of one of the embeddings does not follow by the original arguments. We further carry out some minor corrections in the proof of Corollary 3.7, in Remark 3.1 and in the formula (3.23) of the original paper.},
	keywords = {Stochastic Allen-Cahn equation; analytic semigroups; stochastic evolution equations; stochastic reaction-diffusion equations on networks},
	year = {2021},
	eissn = {1417-3875},
	pages = {1-4},
	orcid-numbers = {Kovács, Mihály/0000-0001-7977-9114; Sikolya, Eszter/0000-0003-0636-4326}
}

@article{MTMT:32082271,
	title = {Stochastic reaction–diffusion equations on networks},
	url = {https://m2.mtmt.hu/api/publication/32082271},
	author = {Kovács, Mihály and Sikolya, Eszter},
	doi = {10.1007/s00028-021-00719-w},
	journal-iso = {J EVOL EQU},
	journal = {JOURNAL OF EVOLUTION EQUATIONS},
	volume = {21},
	unique-id = {32082271},
	issn = {1424-3199},
	year = {2021},
	eissn = {1424-3202},
	pages = {4213-4260},
	orcid-numbers = {Kovács, Mihály/0000-0001-7977-9114; Sikolya, Eszter/0000-0003-0636-4326}
}

@article{MTMT:32039480,
	title = {Numerical analysis view on the general Trotter-Kato product formulae},
	url = {https://m2.mtmt.hu/api/publication/32039480},
	author = {Csomós, Petra and Sikolya, Eszter},
	doi = {10.14232/actasm-020-140-3},
	journal-iso = {ACTA SCI MATH (SZEGED)},
	journal = {ACTA SCIENTIARUM MATHEMATICARUM (SZEGED)},
	volume = {87},
	unique-id = {32039480},
	issn = {0001-6969},
	year = {2021},
	pages = {307-329},
	orcid-numbers = {Csomós, Petra/0000-0002-7138-8407; Sikolya, Eszter/0000-0003-0636-4326}
}

@article{MTMT:31855780,
	title = {On the stochastic Allen–Cahn equation on networks with multiplicative noise},
	url = {https://m2.mtmt.hu/api/publication/31855780},
	author = {Kovács, Mihály and Sikolya, Eszter},
	doi = {10.14232/ejqtde.2021.1.7},
	journal-iso = {ELECTRON J QUAL THEOR DIFFER EQUAT},
	journal = {ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS},
	unique-id = {31855780},
	issn = {1417-3875},
	year = {2021},
	eissn = {1417-3875},
	pages = {1-24},
	orcid-numbers = {Kovács, Mihály/0000-0001-7977-9114; Sikolya, Eszter/0000-0003-0636-4326}
}

@article{MTMT:3402467,
	title = {Semigroups of max-plus linear operators (vol 94, pg 463, 2017)},
	url = {https://m2.mtmt.hu/api/publication/3402467},
	author = {Andreianov, B and Fijavz, MK and Peperko, A and Sikolya, Eszter},
	doi = {10.1007/s00233-017-9870-9},
	journal-iso = {SEMIGROUP FORUM},
	journal = {SEMIGROUP FORUM},
	volume = {94},
	unique-id = {3402467},
	issn = {0037-1912},
	abstract = {Boris Andreianov determined that the examples of max-additive and max-plus linear semigroups in the last section of the article [6] are given inaccurately, i.e., [6, Proposition 4.1] is not true as stated and [6, Proposition 4.2] does not hold without some additional assumptions. Jointly we are able to correct the issues as follows.. © 2017, Springer Science+Business Media New York.},
	keywords = {HAMILTON-JACOBI EQUATIONS; VISCOSITY SOLUTIONS},
	year = {2017},
	eissn = {1432-2137},
	pages = {477-479},
	orcid-numbers = {Sikolya, Eszter/0000-0003-0636-4326}
}

@article{MTMT:2994266,
	title = {Semigroups of max-plus linear operators},
	url = {https://m2.mtmt.hu/api/publication/2994266},
	author = {Marjeta, Kramar Fijavž and Aljoša, Peperko and Sikolya, Eszter},
	doi = {10.1007/s00233-015-9761-x},
	journal-iso = {SEMIGROUP FORUM},
	journal = {SEMIGROUP FORUM},
	volume = {94},
	unique-id = {2994266},
	issn = {0037-1912},
	year = {2017},
	eissn = {1432-2137},
	pages = {463-476},
	orcid-numbers = {Sikolya, Eszter/0000-0003-0636-4326}
}

@misc{MTMT:31320185,
	title = {Ornstein-Uhlenbeck approximation of one-step processes: a differential equation approach},
	url = {https://m2.mtmt.hu/api/publication/31320185},
	author = {Simon L., Péter and Sikolya, Eszter},
	unique-id = {31320185},
	year = {2016},
	orcid-numbers = {Simon L., Péter/0000-0002-2183-1853; Sikolya, Eszter/0000-0003-0636-4326}
}

@article{MTMT:1878401,
	title = {Differential equation approximations of stochastic network processes: An operator semigroup approach},
	url = {https://m2.mtmt.hu/api/publication/1878401},
	author = {Bátkai, András and Istvan, Z Kiss and Sikolya, Eszter and Simon L., Péter},
	doi = {10.3934/nhm.2012.7.43},
	journal-iso = {NETW HETEROG MEDIA},
	journal = {NETWORKS AND HETEROGENEOUS MEDIA},
	volume = {7},
	unique-id = {1878401},
	issn = {1556-1801},
	abstract = {The rigorous linking of exact stochastic models to mean-field approximations is studied. Starting from the differential equation point of view the stochastic model is identified by its master equation, which is a system of linear ODEs with large state space size (N). We derive a single non-linear ODE (called mean-field approximation) for the expected value that yields a good approximation as N tends to infinity. Using only elementary semigroup theory we can prove the order O(1/N) convergence of the solution of the system to that of the mean-field equation. The proof holds also for cases that are somewhat more general than the usual density dependent one. Moreover, for Markov chains where the transition rates satisfy some sign conditions, a new approach using a countable system of ODEs for proving convergence to the mean-field limit is proposed. © American Institute of Mathematical Sciences.},
	keywords = {Stochastic models; Markov processes; Ordinary differential equations; mean field approximation; mean field approximation; Dynamic network; Dynamic network; Semi-group; Stochastic networks; Birth-and-death process; One-parameter operator semigroup; Birth and death process; Countable systems; Mean-field equations; Semigroup approaches},
	year = {2012},
	eissn = {1556-181X},
	pages = {43-58},
	orcid-numbers = {Bátkai, András/0000-0002-9209-2779; Sikolya, Eszter/0000-0003-0636-4326; Simon L., Péter/0000-0002-2183-1853}
}