TY - JOUR AU - Sikolya, Eszter TI - Reaction-diffusion equations on metric graphs with edge noise JF - ANALYSIS MATHEMATICA J2 - ANAL MATH PY - 2024 SN - 0133-3852 DO - 10.1007/s10476-024-00006-z UR - https://m2.mtmt.hu/api/publication/34749280 ID - 34749280 AB - 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. LA - English DB - MTMT ER - TY - JOUR AU - Kovács, Mihály AU - Sikolya, Eszter TI - On the parabolic Cauchy problem for quantum graphs with vertex noise JF - ELECTRONIC JOURNAL OF PROBABILITY J2 - ELECTRON J PROBAB VL - 28 PY - 2023 SN - 1083-6489 DO - 10.1214/23-EJP962 UR - https://m2.mtmt.hu/api/publication/34048342 ID - 34048342 N1 - Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, Gothenburg, Sweden Department of Differential Equations, Budapest University of Technology and Economics, Budapest, Hungary Hungary and Faculty of Information Technology and Bionics, Pázmány Péter Catholic University, Budapest, Hungary Institute of Mathematics, Eötvös Loránd University, Budapest, Hungary Export Date: 6 July 2023 AB - 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. LA - English DB - MTMT ER - TY - JOUR AU - Kovács, Mihály AU - Sikolya, Eszter TI - Corrigendum to "On the stochastic Allen–Cahn equation on networks with multiplicative noise" [Electron. J. Qual. Theory Differ. Equ. 2021, No. 7, 1–24] JF - ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS J2 - ELECTRON J QUAL THEOR DIFFER EQUAT PY - 2021 IS - 52 SP - 1 EP - 4 PG - 4 SN - 1417-3875 DO - 10.14232/ejqtde.2021.1.52 UR - https://m2.mtmt.hu/api/publication/32152022 ID - 32152022 AB - 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. LA - English DB - MTMT ER - TY - JOUR AU - Kovács, Mihály AU - Sikolya, Eszter TI - Stochastic reaction–diffusion equations on networks JF - JOURNAL OF EVOLUTION EQUATIONS J2 - J EVOL EQU VL - 21 PY - 2021 IS - 4 SP - 4213 EP - 4260 PG - 48 SN - 1424-3199 DO - 10.1007/s00028-021-00719-w UR - https://m2.mtmt.hu/api/publication/32082271 ID - 32082271 N1 - Faculty of Information Technology and Bionics, Pázmány Péter Catholic University, Budapest, Hungary Chalmers University of Technology and University of Gothenburg, Gothenburg, 412 96, Sweden Department of Applied Analysis and Computational Mathematics, Eötvös Loránd University, Budapest, Hungary Alfréd Rényi Institute of Mathematics, Reáltanoda Street 13–15, Budapest, 1053, Hungary Export Date: 19 November 2021 Correspondence Address: Sikolya, E.; Department of Applied Analysis and Computational Mathematics, Hungary; email: eszter.sikolya@ttk.elte.hu Funding details: Marsden Fund, 18-UOO-143, 2017-04274 Funding details: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, NKFIH, K-131501 Funding text 1: M. Kovács was supported by Marsden Fund of the Royal Society of New Zealand Grant No. 18-UOO-143, VR Grant Number 2017-04274 and NKFI Grant Number K-131501. LA - English DB - MTMT ER - TY - JOUR AU - Csomós, Petra AU - Sikolya, Eszter TI - Numerical analysis view on the general Trotter-Kato product formulae JF - ACTA SCIENTIARUM MATHEMATICARUM (SZEGED) J2 - ACTA SCI MATH (SZEGED) VL - 87 PY - 2021 IS - 1-2 SP - 307 EP - 329 PG - 23 SN - 0001-6969 DO - 10.14232/actasm-020-140-3 UR - https://m2.mtmt.hu/api/publication/32039480 ID - 32039480 N1 - Eötvös Loránd University, Institute of Mathematics, MTA-ELTE Numerical Analysis and Large Networks Research Group, Pázmány Péter st. 1/C, Budapest, H-1117, Hungary Eötvös Loránd University, Institute of Mathematics, Pázmány Péter st. 1/C, Budapest, H-1117, Hungary Alfréd Rényi Institute of Mathematics, Reáltanoda u. 13-15., Budapest, H-1053, Hungary Export Date: 23 May 2022 LA - English DB - MTMT ER - TY - JOUR AU - Kovács, Mihály AU - Sikolya, Eszter TI - On the stochastic Allen–Cahn equation on networks with multiplicative noise JF - ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS J2 - ELECTRON J QUAL THEOR DIFFER EQUAT PY - 2021 IS - 7 SP - 1 EP - 24 PG - 24 SN - 1417-3875 DO - 10.14232/ejqtde.2021.1.7 UR - https://m2.mtmt.hu/api/publication/31855780 ID - 31855780 N1 - Funding Agency and Grant Number: Marsden Fund of the Royal Society of New ZealandRoyal Society of New ZealandMarsden Fund (NZ) [18-UOO-143]; Swedish Research Council (VR)Swedish Research Council [2017-04274]; NKFIH [131545] Funding text: M. Kovacs acknowledges the support of the Marsden Fund of the Royal Society of New Zealand through grant no. 18-UOO-143, the Swedish Research Council (VR) through grant no. 2017-04274 and the NKFIH through grant no. 131545. Faculty of Information Technology and Bionics, Pázmány Péter Catholic University, Práter u. 50/A., Budapest, H–1083, Hungary Chalmers University of Technology and University of Gothenburg, Gothenburg, SE-412 96, Sweden Institute of Mathematics, Eötvös Loránd University, Pázmány Péter stny. 1/c, Budapest, H–1117, Hungary Alfréd Rényi Institute of Mathematics, Reáltanoda street 13–15, Budapest, H-1053, Hungary Export Date: 22 May 2021 Correspondence Address: Kovács, M.; Faculty of Information Technology and Bionics, Práter u. 50/A., Hungary; email: mihaly@chalmers.se Correspondence Address: Kovács, M.; Chalmers University of Technology and University of GothenburgSweden; email: mihaly@chalmers.se Funding details: Vetenskapsrådet, VR, 2017-04274 Funding details: Marsden Fund, 18-UOO-143 Funding details: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, NKFIH, 131545 Funding text 1: The authors would like to thank the anonymous referee for her/his useful comments that helped them to improve the presentation of the paper. M. Kov?cs acknowledges the support of the Marsden Fund of the Royal Society of New Zealand through grant no. 18-UOO-143, the Swedish Research Council (VR) through grant no. 2017-04274 and the NKFIH through grant no. 131545. Funding text 2: M. Kovács acknowledges the support of the Marsden Fund of the Royal Society of New Zealand through grant no. 18-UOO-143, the Swedish Research Council (VR) through grant no. 2017-04274 and the NKFIH through grant no. 131545. LA - English DB - MTMT ER - TY - JOUR AU - Andreianov, B AU - Fijavz, MK AU - Peperko, A AU - Sikolya, Eszter TI - Semigroups of max-plus linear operators (vol 94, pg 463, 2017) JF - SEMIGROUP FORUM J2 - SEMIGROUP FORUM VL - 94 PY - 2017 IS - 2 SP - 477 EP - 479 PG - 3 SN - 0037-1912 DO - 10.1007/s00233-017-9870-9 UR - https://m2.mtmt.hu/api/publication/3402467 ID - 3402467 N1 - LMPT CNRS UMR7350, Université de Tours, Parc Grandmont, Tours, 37200, France Faculty of Civil and Geodetic Engineering, University of Ljubljana, Jamova 2, Ljubljana, 1000, Slovenia Institute of Mathematics, Physics, and Mechanics, Jadranska 19, Ljubljana, 1000, Slovenia Faculty of Mechanical Engineering, University of Ljubljana, Aškerčeva 6, Ljubljana, 1000, Slovenia Department of Applied Analysis and Computational Mathematics, ELTE TTK, Pázmány Péter sétány 1/C, Budapest, 1117, Hungary Cited By :1 Export Date: 22 May 2021 Correspondence Address: Fijavž, M.K.; Institute of Mathematics, Jadranska 19, Slovenia; email: marjeta.kramar@fgg.uni-lj.si AB - 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. LA - English DB - MTMT ER - TY - JOUR AU - Marjeta, Kramar Fijavž AU - Aljoša, Peperko AU - Sikolya, Eszter TI - Semigroups of max-plus linear operators JF - SEMIGROUP FORUM J2 - SEMIGROUP FORUM VL - 94 PY - 2017 IS - 2 SP - 463 EP - 476 PG - 14 SN - 0037-1912 DO - 10.1007/s00233-015-9761-x UR - https://m2.mtmt.hu/api/publication/2994266 ID - 2994266 N1 - Faculty of Civil and Geodetic Engineering, University of Ljubljana, Jamova 2, Ljubljana, 1000, Slovenia Institute of Mathematics, Physics, and Mechanics, Jadranska 19, Ljubljana, 1000, Slovenia Faculty of Mechanical Engineering, University of Ljubljana, Aškerčeva 6, Ljubljana, 1000, Slovenia Department of Applied Analysis and Computational Mathematics, Pázmány Péter sétány 1/C, Budapest, 1117, Hungary Cited By :1 Export Date: 22 May 2021 Correspondence Address: Fijavž, M.K.; Institute of Mathematics, Jadranska 19, Slovenia; email: marjeta.kramar@fgg.uni-lj.si Funding details: Javna Agencija za Raziskovalno Dejavnost RS, ARRS Funding details: Magyar Tudományos Akadémia, MTA Funding text 1: The authors thank J.A. Goldstein, R. Nagel and M. Kandi? for useful comments. The first and the second author were supported in part by Grant P1-0222 of the Slovenian Research Agency. The third author was supported by the Bolyai Grant of the Hungarian Academy of Sciences. LA - English DB - MTMT ER - TY - GEN AU - Simon L., Péter AU - Sikolya, Eszter TI - Ornstein-Uhlenbeck approximation of one-step processes: a differential equation approach PY - 2016 UR - https://m2.mtmt.hu/api/publication/31320185 ID - 31320185 LA - English DB - MTMT ER - TY - JOUR AU - Bátkai, András AU - Istvan, Z Kiss AU - Sikolya, Eszter AU - Simon L., Péter TI - Differential equation approximations of stochastic network processes: An operator semigroup approach JF - NETWORKS AND HETEROGENEOUS MEDIA J2 - NETW HETEROG MEDIA VL - 7 PY - 2012 IS - 1 SP - 43 EP - 58 PG - 16 SN - 1556-1801 DO - 10.3934/nhm.2012.7.43 UR - https://m2.mtmt.hu/api/publication/1878401 ID - 1878401 N1 - Admin megjegyzés-23365301 #JournalID1# Name: Netw. Heterog. Media ISSN: 1556-1801 #JournalID2# \n Loránd Eötvös University, Institute of Mathematics, Pázmány Péter Sétány 1C, H-1117 Budapest, Hungary \n School of Mathematical and Physical Sciences, Department of Mathematics, University of Sussex, Falmer, Brighton BN1 9RF, United Kingdom \n Cited By :8 \n Export Date: 13 November 2018 \n Correspondence Address: Bátkai, A.; Loránd Eötvös University, Institute of Mathematics, Pázmány Péter Sétány 1C, H-1117 Budapest, Hungary; email: batka@cs.elte.hu Loránd Eötvös University, Institute of Mathematics, Pázmány Péter Sétány 1C, H-1117 Budapest, Hungary School of Mathematical and Physical Sciences, Department of Mathematics, University of Sussex, Falmer, Brighton BN1 9RF, United Kingdom Cited By :10 Export Date: 22 May 2021 Correspondence Address: Bátkai, A.; Loránd Eötvös University, Pázmány Péter Sétány 1C, H-1117 Budapest, Hungary; email: batka@cs.elte.hu AB - 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. LA - English DB - MTMT ER -