Research Interests

• Infinite dimensional analysis
• Mathematical physics
• Stochastic analysis
• Interacting particle systems

List of Publications

An uniqueness result for a class of Wiener space valued stochastic differential equations.
Potential Anal. 11 (1) (1999), 77--99.

A generalized Clark-Ocone formula (with M. de Faria and L. Streit).
Random Oper. Stoch. Equ. 8 (2) (2000), 163--174.

Intersection local times of independent Brownian motions as generalized white noise functionals (with S. Albeverio and L. Streit).
Acta Appl. Math. 69 (3) (2001), 221--241.

Analytic aspects of Poissonian white noise analysis (with Yu. G. Kondratiev and T. Kuna).
Methods Funct. Anal. Topology 8 (4) (2002), 15--48.

On the relations between Poissonian white noise analysis and harmonic analysis on configuration spaces (with Yu. G. Kondratiev and T. Kuna).
J. Funct. Anal. 213 (1) (2004), 1--30.

Feynman integrals for non-smooth and rapidly growing potentials (with M. de Faria and L. Streit).
J. Math. Phys. 46 (6) (2005), Art. No. 063505.

Holomorphic Bogoliubov functionals for interacting particle systems in continuum (with Yu. G. Kondratiev and T. Kuna).
J. Funct. Anal. 238 (2) (2006), 375--404.

A data-reconstructed fractional volatility model (with R. Vilela Mendes).
Economics Discussion Papers 2, No. 2008-22 (2008).

Extension of explicit formulas in Poissonian white noise analysis using harmonic analysis on configuration spaces (with Yu. G. Kondratiev and T. Kuna).
Condens. Matter Phys. 11 No. 2 (54) (2008), 237--246.

Markov evolutions and hierarchical equations in the continuum. I: one-component systems (with D. L. Finkelshtein and Yu. G. Kondratiev).
J. Evol. Equ. 9 (2) (2009), 197--233.

Intersection local times of independent fractional Brownian motions as generalized white noise functionals (with J. L. Silva and L. Streit).
Acta Appl. Math. 113 (1) (2011), 17--39.

Self-avoiding fractional Brownian motion - The Edwards model (with M. Grothaus, J. L. Silva and L. Streit).
J. Stat. Phys. 145 (6) (2011), 1513--1523.

Glauber dynamics in the continuum via generating functionals evolution (with D. L. Finkelshtein and Yu. G. Kondratiev).
Complex Anal. Oper. Theory 6 (4) (2012), 923--945.

Kawasaki dynamics in the continuum via generating functionals evolution (with D. L. Finkelshtein and Yu. G. Kondratiev).
Methods Funct. Anal. Topology 18 (1) (2012), 55--67.

Markov evolutions and hierarchical equations in the continuum. II: multicomponent systems (with D. L. Finkelshtein and Yu. G. Kondratiev).
Rep. Math. Phys. 71 (1) (2013), 123--148.

Dynamical Widom-Rowlinson model and its mesoscopic limit (with D. Finkelshtein, Yu. Kondratiev and O. Kutoviy).
J. Stat. Phys. 158 (1) (2015), 57--86.

No-arbitrage, leverage and completeness in a fractional volatility model (with R. Vilela Mendes and A. M. Rodrigues).
Phys. A 419 (2015), 470--478.

Polymer measure: Varadhan's renormalization revisited (with W. Bock, J. L. Silva and L. Streit).
Rev. Math. Phys. 27 (3) (2015), 1550009.

Chaos decomposition and gap renormalization of Brownian self-intersection local times (with J. Bornales and L. Streit).
Rep. Math. Phys. 77 (2) (2016), 141--152.

An infinite dimensional umbral calculus (with D. Finkelshtein, Y. Kondratiev and E. Lytvynov).
J. Funct. Anal. 276 (12) (2019), 3714--3766.

Sheffer homeomorphisms of spaces of entire functions in infinite dimensional analysis (with D. Finkelshtein, Y. Kondratiev, E. Lytvynov and L. Streit).
J. Math. Anal. Appl. 479 (1) (2019), 162--184.

Stirling operators in spatial combinatorics (with D. Finkelshtein, Y. Kondratiev, E. Lytvynov).
J. Funct. Anal. 282 (2) (2022), 109285.

Analysis on the cone of discrete Radon measures (with D. Finkelshtein, Y. Kondratiev, P. Kuchling, E. Lytvynov).
Pure Appl. Funct. Anal. (accepted), 2024.

Books: Edition and Chapters

Stochastic and Infinite Dimensional Analysis C. Bernido, M. V. Carpio-Bernido, M. Grothaus, T. Kuna, M. J. Oliveira, J. L. da Silva (eds.) Trends in Mathematics, Birkhäuser, 2016. ISBN: 978-3-319-07244-9

White Noise Analysis: An Introduction In T. Hida and L. Streit (eds.), Let Us Use White Noise, pp. 1--36. World Scientific Publ. Co., 2017. ISBN: 978-981-3220-93-5

Proceedings

Intersection local times of fractional Brownian motions with H∈(0,1) as generalized white noise functionals (with C. Drumond and J. L. Silva).
In C. C. Bernido and M. V. Bernido (Eds.), 5th Jagna International Workshop "Stochastic and Quantum Dynamics of Biomolecular Systems", Jagna, Bohol (Philippines), 3--5 January 2008. AIP Conf. Proc. vol. 1021 (1), 34--45. American Institute of Physics, Melville NY, 2008.

Fractional Brownian polymers - some first results (with J. Bornales, S. Eleutério and L. Streit).
Int. J. Mod. Phys. Conf. Ser. 17 (2012), 54--65.

Studies in fractional Poisson measures (with J. L. Silva).
Int. J. Mod. Phys. Conf. Ser. 17 (2012), 122--129.

Self-repelling fractional Brownian motion - a generalized Edwards model for chain polymers (with J. Bornales and L. Streit).
In L. Accardi, W. Freudenberg, M. Ohya (Eds.), Quantum Bio-Informatics V. Proceedings of Quantum Bio-Informatics 2011. Quantum Probability and White Noise Analysis vol. 30, 389--401. World Scientific Publ. Co., Singapure, New Jersey, London, 2013.

A survey on Bogoliubov generating functionals for interacting particle systems in the continuum (with D. L. Finkelshtein).
In C. Bernardin and P. Gonçalves (Eds.), From Particle Systems to Partial Differential Equations. Particle Systems and PDEs, Braga, Portugal, December 2012. Springer Proc. Math. Stat. vol. 75 (2014), 161--177.

Fractional Boson gas and fractional Poisson measure in infinite dimensions (with R. Vilela Mendes).
In P. Gonçalves and A. J. Soares (Eds.), From Particle Systems to Partial Differential Equations II. Particle Systems and PDEs II, Braga, Portugal, December 2013. Springer Proc. Math. Stat. vol. 129 (2015), 293--312.

An infinite dimensional umbral calculus. Oberwolfach Rep. 14 (Issue 1), 800--803, 2017.

Results about the free Kawasaki dynamics of continuous particle systems in infinite volume: long-time asymptotics and hydrodynamic limit (with Y. G. Kondratiev, T. Kuna, J. L. Silva, L. Streit). In E. Carlen, P. Gonçalves and A. J. Soares (Eds.), From Particle Systems to Partial Differential Equations. PSPDE X, Braga, Portugal, June 2022. Springer Proc. Math. Stat. vol. 465 (2024), 149--185.

List of Preprints

Finite difference calculus in the continuum (with D. Finkelshtein, Y. Kondratiev, E. Lytvynov).
arXiv:math-ph/2410.23847 (2024)