# zbMATH — the first resource for mathematics

## Scalas, Enrico

Compute Distance To:
 Author ID: scalas.enrico Published as: Scalas, E.; Scalas, Enrico
 Documents Indexed: 44 Publications since 1993, including 4 Books
all top 5

#### Co-Authors

 3 single-authored 6 Garibaldi, Ubaldo 6 Mainardi, Francesco 6 Raberto, Marco 5 Gorenflo, Rudolf 4 Germano, Guido 3 Pagnini, Gianni 3 Politi, Mauro 3 Trinh, Mailan 2 Băleanu, Dumitru I. 2 Cincotti, Silvano 2 Diethelm, Kai 2 Donadio, Sébastien 2 Fulger, Daniel 2 Giesl, Peter 2 Gudmundsson, Skuli 2 Hafstein, Sigurður Freyr 2 Leonenko, Nikolai N. 2 Polito, Federico 2 Reverberi, Andrea Pietro 2 Trujillo, Juan J. 2 Viano, Giovanni Alberto 2 Viles, Noèlia 1 Angle, John 1 Björnsson, Hjörtur 1 Chen, Jiawen 1 Di Nardo, Elvira 1 Dose, Christian 1 Eom, Cheoljun 1 Focardi, Sergio M. 1 Gerardo-Giorda, Luca 1 Hawkes, Alan Geoffrey 1 Inoue, Junichi 1 Kaizoji, Taisei 1 Kim, Cheol-Hyun 1 Kim, Kyungsik 1 Kim, Soo Yong 1 Livan, Giacomo 1 Luckock, Hugh 1 Mantelli, Maurizio 1 Nielsen, François 1 Park, Chung Hyun 1 Pichl, Lukáš 1 Ponta, Linda 1 Radivojević, Tijana 1 Schilling, René Leander 1 Vegliò, F. 1 Viarengo, Paolo
all top 5

#### Serials

 4 The European Physical Journal B. Condensed Matter and Complex Systems 4 Communications in Applied and Industrial Mathematics 3 Fractional Calculus & Applied Analysis 2 Fractals 2 Quantitative Finance 2 Discrete and Continuous Dynamical Systems. Series B 1 Inverse Problems 1 Journal of Mathematical Physics 1 Physica A 1 Chaos, Solitons and Fractals 1 Journal of Applied Probability 1 Statistics & Probability Letters 1 Journal of Physics A: Mathematical and General 1 Stochastic Processes and their Applications 1 Electronic Communications in Probability 1 Vietnam Journal of Mathematics 1 Communications in Nonlinear Science and Numerical Simulation 1 International Journal of Modern Physics C 1 Journal of Statistical Mechanics: Theory and Experiment 1 International Journal of Applied Nonlinear Science
all top 5

#### Fields

 24 Probability theory and stochastic processes (60-XX) 19 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 9 Real functions (26-XX) 7 Numerical analysis (65-XX) 6 Partial differential equations (35-XX) 5 Special functions (33-XX) 5 Statistical mechanics, structure of matter (82-XX) 4 Statistics (62-XX) 3 General and overarching topics; collections (00-XX) 2 History and biography (01-XX) 2 Ordinary differential equations (34-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Integral transforms, operational calculus (44-XX) 1 Field theory and polynomials (12-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Functions of a complex variable (30-XX) 1 Integral equations (45-XX) 1 Operator theory (47-XX) 1 Systems theory; control (93-XX)

#### Citations contained in zbMATH Open

31 Publications have been cited 1,130 times in 1,005 Documents Cited by Year
Fractional calculus. Models and numerical methods. Zbl 1248.26011
Baleanu, Dumitru; Diethelm, Kai; Scalas, Enrico; Trujillo, Juan J.
2012
Waiting-times and returns in high-frequency financial data: An empirical study. Zbl 1001.91033
Raberto, Marco; Scalas, Enrico; Mainardi, Francesco
2002
Fractional calculus and continuous-time finance. III: The diffusion limit. Zbl 1138.91444
Gorenflo, Rudolf; Mainardi, Francesco; Scalas, Enrico; Raberto, Marco
2001
A fractional generalization of the Poisson processes. Zbl 1087.60064
Mainardi, Francesco; Gorenflo, Rudolf; Scalas, Enrico
2004
Five years of continuous-time random walks in econophysics. Zbl 1183.91135
Scalas, Enrico
2006
Fractional calculus. Models and numerical methods. 2nd expanded edition. Zbl 1347.26006
Baleanu, Dumitru; Diethelm, Kai; Scalas, Enrico; Trujillo, Juan J.
2017
A generalization of the space-fractional Poisson process and its connection to some Lévy processes. Zbl 1338.60129
Polito, Federico; Scalas, Enrico
2016
The fractional non-homogeneous Poisson process. Zbl 1416.60054
Leonenko, Nikolai; Scalas, Enrico; Trinh, Mailan
2017
Statistical equilibrium in simple exchange games. I. Zbl 1189.91129
Scalas, E.; Garibaldi, U.; Donadio, S.
2006
Finitary probability methods in econophysics. Zbl 1285.91001
Garibaldi, Ubaldo; Scalas, Enrico
2010
Revisiting the derivation of the fractional diffusion equation. Zbl 1050.35163
Scalas, Enrico; Gorenflo, Rudolf; Mainardi, Francesco; Raberto, Marco
2003
A class of CTRWs: compound fractional Poisson processes. Zbl 1300.60053
Scalas, Enrico
2012
Statistical equilibrium in simple exchange games II. The redistribution game. Zbl 1189.91118
Garibaldi, U.; Scalas, E.; Viarengo, P.
2007
Anomalous waiting times in high-frequency financial data. Zbl 1409.62216
Scalas, Enrico; Gorenflo, Rudolf; Luckock, Hugh; Mainardi, Francesco; Mantelli, Maurizio; Raberto, Marco
2004
A renewal process of Mittag-Leffler type. Zbl 1191.60101
Mainardi, Francesco; Gorenflo, Rudolf; Scalas, Enrico
2004
Mixtures of compound Poisson processes as models of tick-by-tick financial data. Zbl 1142.60392
Scalas, Enrico
2007
Limit theorems for the fractional nonhomogeneous Poisson process. Zbl 1418.60025
Leonenko, Nikolai; Scalas, Enrico; Trinh, Mailan
2019
A functional limit theorem for stochastic integrals driven by a time-changed symmetric $$\alpha$$-stable Lévy process. Zbl 1301.60034
Scalas, Enrico; Viles, Noèlia
2014
On the convergence of quadratic variation for compound fractional Poisson processes. Zbl 1278.60067
Scalas, Enrico; Viles, Noèlia
2012
Performance of information criteria for selection of Hawkes process models of financial data. Zbl 1405.62137
Chen, J.; Hawkes, A. G.; Scalas, E.; Trinh, M.
2018
Historical notes on the M-Wright/Mainardi function. Zbl 1329.26004
Pagnini, Gianni; Scalas, Enrico
2014
Itô and Stratonovich integrals on compound renewal processes: the normal/Poisson case. Zbl 1221.60129
Germano, Guido; Politi, Mauro; Scalas, Enrico; Schilling, René L.
2010
The Hausdorff moments in statistical mechanics. Zbl 0799.44006
Scalas, E.; Viano, G. A.
1993
Lyapunov function computation for autonomous linear stochastic differential equations using sum-of-squares programming. Zbl 1395.60060
Hafstein, Sigurdur; Gudmundsson, Skuli; Giesl, Peter; Scalas, Enrico
2018
Large scale simulation of synthetic markets. Zbl 1329.91150
Gerardo-Giorda, Luca; Germano, Guido; Scalas, Enrico
2014
Random numbers from the tails of probability distributions using the transformation method. Zbl 1312.65004
Fulger, Daniel; Scalas, Enrico; Germano, Guido
2013
A note on intraday option pricing. Zbl 1287.91146
Scalas, Enrico; Politi, Mauro
2013
Spectral densities of Wishart-Lévy free stable random matrices. Zbl 1188.15038
Politi, M.; Scalas, E.; Fulger, D.; Germano, G.
2010
Erratum: Statistical equilibrium in simple exchange games. I. Zbl 1189.91128
Scalas, E.; Garibaldi, U.; Donadio, S.
2007
Numerical solution of moving boundary problems in diffusion processes with attractive and repulsive interactions. Zbl 0996.65086
Reverberi, A. P.; Scalas, E.; Vegliò, F.
2002
Surface selective deconstruction: A Monte Carlo study. Zbl 0925.00044
Reverberi, A. P.; Scalas, E.
1997
Limit theorems for the fractional nonhomogeneous Poisson process. Zbl 1418.60025
Leonenko, Nikolai; Scalas, Enrico; Trinh, Mailan
2019
Performance of information criteria for selection of Hawkes process models of financial data. Zbl 1405.62137
Chen, J.; Hawkes, A. G.; Scalas, E.; Trinh, M.
2018
Lyapunov function computation for autonomous linear stochastic differential equations using sum-of-squares programming. Zbl 1395.60060
Hafstein, Sigurdur; Gudmundsson, Skuli; Giesl, Peter; Scalas, Enrico
2018
Fractional calculus. Models and numerical methods. 2nd expanded edition. Zbl 1347.26006
Baleanu, Dumitru; Diethelm, Kai; Scalas, Enrico; Trujillo, Juan J.
2017
The fractional non-homogeneous Poisson process. Zbl 1416.60054
Leonenko, Nikolai; Scalas, Enrico; Trinh, Mailan
2017
A generalization of the space-fractional Poisson process and its connection to some Lévy processes. Zbl 1338.60129
Polito, Federico; Scalas, Enrico
2016
A functional limit theorem for stochastic integrals driven by a time-changed symmetric $$\alpha$$-stable Lévy process. Zbl 1301.60034
Scalas, Enrico; Viles, Noèlia
2014
Historical notes on the M-Wright/Mainardi function. Zbl 1329.26004
Pagnini, Gianni; Scalas, Enrico
2014
Large scale simulation of synthetic markets. Zbl 1329.91150
Gerardo-Giorda, Luca; Germano, Guido; Scalas, Enrico
2014
Random numbers from the tails of probability distributions using the transformation method. Zbl 1312.65004
Fulger, Daniel; Scalas, Enrico; Germano, Guido
2013
A note on intraday option pricing. Zbl 1287.91146
Scalas, Enrico; Politi, Mauro
2013
Fractional calculus. Models and numerical methods. Zbl 1248.26011
Baleanu, Dumitru; Diethelm, Kai; Scalas, Enrico; Trujillo, Juan J.
2012
A class of CTRWs: compound fractional Poisson processes. Zbl 1300.60053
Scalas, Enrico
2012
On the convergence of quadratic variation for compound fractional Poisson processes. Zbl 1278.60067
Scalas, Enrico; Viles, Noèlia
2012
Finitary probability methods in econophysics. Zbl 1285.91001
Garibaldi, Ubaldo; Scalas, Enrico
2010
Itô and Stratonovich integrals on compound renewal processes: the normal/Poisson case. Zbl 1221.60129
Germano, Guido; Politi, Mauro; Scalas, Enrico; Schilling, René L.
2010
Spectral densities of Wishart-Lévy free stable random matrices. Zbl 1188.15038
Politi, M.; Scalas, E.; Fulger, D.; Germano, G.
2010
Statistical equilibrium in simple exchange games II. The redistribution game. Zbl 1189.91118
Garibaldi, U.; Scalas, E.; Viarengo, P.
2007
Mixtures of compound Poisson processes as models of tick-by-tick financial data. Zbl 1142.60392
Scalas, Enrico
2007
Erratum: Statistical equilibrium in simple exchange games. I. Zbl 1189.91128
Scalas, E.; Garibaldi, U.; Donadio, S.
2007
Five years of continuous-time random walks in econophysics. Zbl 1183.91135
Scalas, Enrico
2006
Statistical equilibrium in simple exchange games. I. Zbl 1189.91129
Scalas, E.; Garibaldi, U.; Donadio, S.
2006
A fractional generalization of the Poisson processes. Zbl 1087.60064
Mainardi, Francesco; Gorenflo, Rudolf; Scalas, Enrico
2004
Anomalous waiting times in high-frequency financial data. Zbl 1409.62216
Scalas, Enrico; Gorenflo, Rudolf; Luckock, Hugh; Mainardi, Francesco; Mantelli, Maurizio; Raberto, Marco
2004
A renewal process of Mittag-Leffler type. Zbl 1191.60101
Mainardi, Francesco; Gorenflo, Rudolf; Scalas, Enrico
2004
Revisiting the derivation of the fractional diffusion equation. Zbl 1050.35163
Scalas, Enrico; Gorenflo, Rudolf; Mainardi, Francesco; Raberto, Marco
2003
Waiting-times and returns in high-frequency financial data: An empirical study. Zbl 1001.91033
Raberto, Marco; Scalas, Enrico; Mainardi, Francesco
2002
Numerical solution of moving boundary problems in diffusion processes with attractive and repulsive interactions. Zbl 0996.65086
Reverberi, A. P.; Scalas, E.; Vegliò, F.
2002
Fractional calculus and continuous-time finance. III: The diffusion limit. Zbl 1138.91444
Gorenflo, Rudolf; Mainardi, Francesco; Scalas, Enrico; Raberto, Marco
2001
Surface selective deconstruction: A Monte Carlo study. Zbl 0925.00044
Reverberi, A. P.; Scalas, E.
1997
The Hausdorff moments in statistical mechanics. Zbl 0799.44006
Scalas, E.; Viano, G. A.
1993
all top 5

#### Cited by 1,428 Authors

 102 Băleanu, Dumitru I. 38 Ntouyas, Sotiris K. 36 Ahmad, Bashir 28 Machado, José António Tenreiro 26 Meerschaert, Mark M. 19 Benchohra, Mouffak 18 Tariboon, Jessada 17 Gómez-Aguilar, José Francisco 17 Jafari, Hossein 17 Wang, Guotao 15 Abdeljawad, Thabet 15 Leonenko, Nikolai N. 15 Mainardi, Francesco 15 Yang, Xiao-Jun 14 Abbas, Said 14 Al-saedi, Ahmed Eid Salem 13 Agarwal, Ravi P. 13 Liu, Fawang 13 Polito, Federico 12 Beghin, Luisa 12 Nieto Roig, Juan Jose 12 Scalas, Enrico 12 Zhang, Lihong 11 Vellaisamy, Palaniappan 10 Bäumer, Boris 10 Bhrawy, Ali Hassan 10 Li, Changpin 10 Lopes, António M. 10 Salahshour, Soheil 10 Sun, Haiwei 10 Wei, Ting 9 Ahmadian, Ali 9 Gorenflo, Rudolf 9 Trujillo, Juan J. 8 Atangana, Abdon 8 Torres, Delfim Fernando Marado 8 Turner, Ian William 7 Debbouche, Amar 7 Escobar-Jiménez, Ricardo Fabricio 7 Jiang, Xiaoyun 7 Lei, Siulong 7 Toscani, Giuseppe 7 Wu, Guocheng 6 Anh, Vo V. 6 Duan, Junsheng 6 Jarad, Fahd 6 Liu, Sanyang 6 Luca, Rodica 6 Macci, Claudio 6 Nane, Erkan 6 Orsingher, Enzo 6 Pang, Hong-Kui 6 Pedas, Arvet 6 Sikorskii, Alla 6 Straka, Peter 6 Tarasov, Vasily E. 6 Wang, Hong 6 Xu, Chuanju 6 Zeng, Shengda 6 Zhang, Xianmin 5 Abbasbandy, Saeid 5 Cernea, Aurelian 5 Garra, Roberto 5 Golmankhaneh, Alireza Khalili 5 Jajarmi, Amin 5 Kataria, Kuldeep Kumar 5 Kolokoltsov, Vassili N. 5 Kovács, Mihály 5 Lukashchuk, Stanislav Yur’evich 5 Maheshwari, Aditya 5 Momani, Shaher M. 5 Olivares-Peregrino, Victor Hugo 5 Pagnini, Gianni 5 Rui, Hongxing 5 Sakhno, Lyudmyla Mykhaĭlivna 5 Sayevand, Khosro 5 Srivastava, Hari Mohan 5 Sun, Zhizhong 5 Tamme, Enn 5 Tarasova, Valentina V. 5 Wang, Jungang 5 Yépez-Martínez, Huitzilin 5 Zhou, Yong 4 Agarwal, Praveen 4 Cattani, Carlo 4 Dassios, Ioannis K. 4 Deng, Weihua 4 Ding, Wenbin 4 Fernandez, Arran 4 Garrappa, Roberto 4 Hajipour, Mojtaba 4 Henderson, Johnny Lee 4 Henry, Bruce I. 4 Ibrahim, Rabha Waell 4 Karthikeyan, Anitha 4 Khan, Rahmat Ali 4 Kobayashi, Kei 4 Li, Hong 4 Liu, Lishan 4 Liu, Yang ...and 1,328 more Authors
all top 5

#### Cited in 228 Serials

 79 Abstract and Applied Analysis 71 Advances in Difference Equations 58 Fractional Calculus & Applied Analysis 49 Applied Mathematics and Computation 37 Journal of Computational and Applied Mathematics 36 Computers & Mathematics with Applications 27 Chaos, Solitons and Fractals 25 Journal of Computational Physics 21 Nonlinear Dynamics 18 Mathematical Problems in Engineering 16 Advances in Mathematical Physics 13 Journal of Statistical Physics 13 Applied Numerical Mathematics 13 Communications in Nonlinear Science and Numerical Simulation 12 Statistics & Probability Letters 12 Applied Mathematical Modelling 12 Computational and Applied Mathematics 11 Stochastic Processes and their Applications 11 Discrete Dynamics in Nature and Society 10 Physica A 10 Journal of Scientific Computing 10 Journal of Applied Mathematics and Computing 9 Numerical Algorithms 9 Boundary Value Problems 9 Open Mathematics 8 Journal of Applied Probability 8 Mathematical Modelling of Natural Phenomena 8 Journal of Nonlinear Science and Applications 8 International Journal of Applied and Computational Mathematics 7 International Journal of Computer Mathematics 7 Fractional Differential Calculus 6 Journal of Mathematical Analysis and Applications 6 Stochastic Analysis and Applications 6 Applied Mathematics Letters 6 Theory of Probability and Mathematical Statistics 6 Mathematics 5 Journal of Optimization Theory and Applications 5 Proceedings of the American Mathematical Society 5 Journal of Integral Equations and Applications 5 SIAM Journal on Scientific Computing 5 Chaos 5 Mediterranean Journal of Mathematics 5 The European Physical Journal B. Condensed Matter and Complex Systems 5 Journal of Function Spaces 4 Advances in Applied Probability 4 Reports on Mathematical Physics 4 Numerical Methods for Partial Differential Equations 4 Turkish Journal of Mathematics 4 Complexity 4 Engineering Analysis with Boundary Elements 4 Differential Equations and Dynamical Systems 4 Methodology and Computing in Applied Probability 4 International Journal of Nonlinear Sciences and Numerical Simulation 4 Cubo 4 Modern Stochastics. Theory and Applications 3 Journal of the Franklin Institute 3 The Annals of Probability 3 Transactions of the American Mathematical Society 3 Circuits, Systems, and Signal Processing 3 Journal of Theoretical Probability 3 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 3 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 3 Quantitative Finance 3 Advances in Complex Systems 3 Fixed Point Theory and Applications 3 Discrete and Continuous Dynamical Systems. Series S 3 International Journal of Biomathematics 3 Tbilisi Mathematical Journal 3 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 3 Palestine Journal of Mathematics 3 East Asian Journal on Applied Mathematics 2 Computers and Fluids 2 Computer Physics Communications 2 International Journal of Theoretical Physics 2 Journal of Mathematical Physics 2 Physics Letters. A 2 Journal of Statistical Planning and Inference 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Physica D 2 SIAM Journal on Applied Mathematics 2 Taiwanese Journal of Mathematics 2 Lobachevskii Journal of Mathematics 2 Nonlinear Analysis. Real World Applications 2 Nonlinear Analysis. Modelling and Control 2 Journal of Evolution Equations 2 Discrete and Continuous Dynamical Systems. Series B 2 Journal of Applied Mathematics 2 Journal of Function Spaces and Applications 2 Boletim da Sociedade Paranaense de Matemática. Terceira Série 2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 Communications in Mathematical Analysis 2 Vestnik Samarskogo Gosudarstvennogo Tekhnicheskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki 2 SIAM Journal on Financial Mathematics 2 Science China. Mathematics 2 Symmetry 2 Iranian Journal of Mathematical Chemistry 2 Analysis and Mathematical Physics 2 Afrika Matematika 2 Axioms 2 Journal of Mathematical Modeling ...and 128 more Serials
all top 5

#### Cited in 44 Fields

 349 Ordinary differential equations (34-XX) 348 Partial differential equations (35-XX) 317 Numerical analysis (65-XX) 274 Real functions (26-XX) 168 Probability theory and stochastic processes (60-XX) 77 Integral equations (45-XX) 76 Operator theory (47-XX) 60 Special functions (33-XX) 59 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 41 Biology and other natural sciences (92-XX) 40 Systems theory; control (93-XX) 35 Fluid mechanics (76-XX) 33 Statistical mechanics, structure of matter (82-XX) 30 Calculus of variations and optimal control; optimization (49-XX) 26 Dynamical systems and ergodic theory (37-XX) 24 Difference and functional equations (39-XX) 20 Integral transforms, operational calculus (44-XX) 19 Information and communication theory, circuits (94-XX) 17 Approximations and expansions (41-XX) 17 Statistics (62-XX) 12 Mechanics of deformable solids (74-XX) 12 Operations research, mathematical programming (90-XX) 10 Linear and multilinear algebra; matrix theory (15-XX) 10 Mechanics of particles and systems (70-XX) 9 Computer science (68-XX) 7 Functional analysis (46-XX) 6 Quantum theory (81-XX) 6 Geophysics (86-XX) 5 Combinatorics (05-XX) 5 Number theory (11-XX) 5 Measure and integration (28-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 5 Optics, electromagnetic theory (78-XX) 4 History and biography (01-XX) 3 Functions of a complex variable (30-XX) 3 Differential geometry (53-XX) 3 Classical thermodynamics, heat transfer (80-XX) 2 General and overarching topics; collections (00-XX) 2 General topology (54-XX) 2 Relativity and gravitational theory (83-XX) 1 Potential theory (31-XX) 1 Abstract harmonic analysis (43-XX) 1 Geometry (51-XX) 1 Global analysis, analysis on manifolds (58-XX)