Pedro Jose Catuogno

Research

I am a mathematician working in stochastic analysis and differential geometry. 

Teaching (Portuguese)

1) Primeiro semestre 2024. 

MA141Z - Geometria Analitica  

MM597 - Calculo Estocastico

2) Segundo semestre 2024

MM419 - Análise Real I

Notas de Aula:

1. Calculo Estocastico: SPDE1.pdf  ;  SPDE2.pdf  ; SPDE3.pdf  ; SPDE4.pdf  ; SPDE5.pdf  ; SPDE6.pdf  ; SPDE7.pdf  ; SPDE8.pdf 

2. Geometria Analitica: geometriaanalitica0  ; geometriaanalitica1.pdf  ; geometriaanalitica2.pdf  ;  geometriaanalitica3.pdf  ; geometriaanalitica4.pdf  ;  geometriaanalitica5.pdf  ; geometriaanalitica6.pdf  ; geometriaanalitica7.pdf  ; geometriaanalitica8.pdf  ; geometriaanalitica9.pdf  ; geometriaanalitica10.pdf  ; geometriaanalitica11.pdf  ; geometriaanalitica12.pdf  ; geometriaanalitica13.pdf  ; geometriaanalitica14.pdf  ; geometriaanalitica15.pdf  ; geometriaanalitica16.pdf  ; geometriaanalitica17.pdf  ; geometriaanalitica18.pdf 

3. Analise I:   AR1.pdf  ; AR2.pdf  ;  AR3.pdf  ; AR4.pdf  ; AR5.pdf  ;  AR6.pdf  ; AR7.pdf  ; AR8 .pdf 

Papers & Preprints

1. Castrequini, R. ; Catuogno, P.  ; Machado Hernandez, A.  An It^o-Wentzell formula for rough paths. Preprint arxiv 2206.09905 , 2022.

2. Catuogno, P. ; Stelmastchuk, S. Martingales on principal fiber bundles. Proyecciones  42 (2023), 4, 1051-1065. https://doi.org/10.22199/issn.0717-6279-5893

3. Oliveira Gomes, A. ; Catuogno, P.  Large deviations for L\'evy diffusions in the small noise regime. Preprint authorea https://www.authorea.com/doi/full/10.22541/au.165475804.43359405, 2022. Aceito Stochastics and Dynamics 2023.

4. Catuogno, P. ; Ledesma, D. Weak solutions for stochastic differential equations with additive fractional noise. Physica D. 458, 134015, 2024. https://doi.org/10.1016/j.physd.2023.134015 

5.  Lima, L. ; Ruffino, P. Catuogno, P.  Geometric aspects of Young Integral: decomposition of flows. Mediterranean Journal of Mathematics 20, article number 335, 2023. https://doi.org/10.1007/s00009-023-02539-3 1660-5446/23/060001-20 

6.  Oliveira Gomes, A. ; Catuogno, P.  Moderate averaged deviations for a multi-scale system with jumps and memory. Dynamics 2023, 3 (1), 171-201; https://doi.org/10.3390

7. Catuogno, P. ; Castrequini, R.  A generalized change of variable formula for the Young integral. Chaos Solitons Fractals 158 (2022), Paper No. 112064, 8 pp.

8.  Colombeau, J. F. ; Aragona, J. ; Catuogno, P. ; Juriaans, S. O. ; Olivera, C. Multiplication of distributions and nonperturbative calculations of transition probabilities. Quantum theory and symmetries with Lie theory and its applications in physics. Vol. 1, 393-401, Springer Proc. Math. Stat., 263, Springer, Singapore, 2018.

9.  Catuogno, P. ; Colombeau, J. F. ; Olivera, C. Generalized solutions of the multidimensional stochastic Burgers equation. J. Math. Anal. Appl. 464 (2018), no. 2, 1375-1382.

10. Catuogno, P. ; Molina, S. ; Olivera, C. Generalized functions and Laguerre expansions. Monatsh. Math. 184 (2017), no. 1, 51-75.

11.  Catuogno, P. ; Ledesma, D. ; Ruffino, P. R. Harmonic measures in embedded foliated manifolds. Stoch. Dyn. 17 (2017), no. 4, 1750026, 13 pp. 

12. Catuogno, P. ; Stelmastchuk, S. A stochastic transport theorem. Commun. Stoch. Anal. 10 (2016), no. 1, Article 3, 31-38. 

13. Aragona, J. ; Catuogno, P. ; Colombeau, J. F. ; Juriaans, S. O.; Olivera, C. Multiplication of distributions in mathematical physics. Lie theory and its applications in physics, 583-589, Springer Proc. Math. Stat., 191, Springer, Singapore, 2016.

14.  Catuogno, P. ; Ledesma, D. ; Ruffino, P. Foliated stochastic calculus: harmonic measures. Trans. Amer. Math. Soc. 368 (2016), no. 1, 563-579. 

15.  Vieira, M. G. O.; Kizil, E.; Catuogno, P. Regular trajectories of Young systems. J. Dyn. Control Syst. 21 (2015), no. 4, 539–558. 

16. Catuogno, P. ; Olivera, C. Renormalized-generalized solutions for the KPZ equation. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 17 (2014), no. 4, 1450027, 11 pp.

17. Catuogno, P. ; Lucinger, L. Random Lie-point symmetries. J. Nonlinear Math. Phys. 21 (2014), no. 2, 149-165.

18. Catuogno, P.; Olivera, C. Strong solution of the stochastic Burgers equation. Appl. Anal. 93 (2014), no. 3, 646-652.

19.  Catuogno, P. ; Olivera, C. Time-dependent tempered generalized functions and Itô's formula. Appl. Anal. 93 (2014), no. 3, 539-550. 

20. Catuogno, P. ; Ledesma, D. ; Ruffino, P. A note on stochastic calculus in vector bundles. Séminaire de Probabilités XLV, 353-364, Lecture Notes in Math., 2078, Springer, Cham, 2013.

21. Catuogno, P.; da Silva, F.; Ruffino, P. Decomposition of stochastic flows in manifolds with complementary distributions. Stoch. Dyn. 13 (2013), no. 4, 1350009, 12 pp.

22. Vieira, M. G. O.; Kizil, E.; Catuogno, P. Monotonic homotopy for trajectories of Young systems. J. Dyn. Control Syst. 19 (2013), no. 3, 405-420.

23. Catuogno, P. ; Olivera, C. $L^p$-solutions of the stochastic transport equation. Random Oper. Stoch. Equ. 21 (2013), no. 2, 125-134.

24.  Catuogno, P. ; da Silva, F. ; Ruffino, P. R. Decomposition of stochastic flows with automorphism of subbundles component. Stoch. Dyn. 12 (2012), no. 2, 1150013, 15 pp.

25. Catuogno, P. ; Olivera, C. On stochastic generalized functions. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 14 (2011), no. 2, 237-260. 

26. Catuogno, P. ; Olivera, C. Tempered generalized functions and Hermite expansions. Nonlinear Anal. 74 (2011), no. 2, 479-493.

27. Catuogno, P. ; Gonzalez A. L. ; Ferrando, S. H-systems for efficient hedging and approximation of derivatives. Proceedings of the third Brazilian Conference on Statistical Modelling in Insurance and Finance. (2007) Ed. C. Fernandes, H. Schmidli and N. Kolev.  pp 108-113.  

28. Catuogno, P. ; Ledesma, D. ; Ruffino, P. R. C. Relative rotation number for stochastic systems: dynamical and topological applications. Dyn. Syst. 23 (2008), no. 4, 425-435.

29. Catuogno, P. ; Ferrando, S. E.; Gonzalez, A. L. Adaptive martingale approximations. J. Fourier Anal. Appl. 14 (2008), no. 5-6, 712-743.

30.  Catuogno, P. ; Martínez, F. ; Molina, S. Laguerre expansions and products of distributions. Commun. Korean Math. Soc. 23 (2008), no. 2, 201-209.  

31.  Catuogno, P. ; Stelmastchuk, S. Martingales on frame bundles. Potential Anal. 28 (2008), no. 1, 61-69. 

32. Catuogno, P. ; Gonzalez A. L. ; Ferrando, S. Efficient Hedging of Options with Probabilistic Haar Wavelets. 

33.  Catuogno, P. A geometric Itô formula. Workshop on Differential Geometry. Mat. Contemp. 33 (2007), 85-99. 

34.  Catuogno, P. ; Ruffino, P. R. C. Product of harmonic maps is harmonic: a stochastic approach. Séminaire de Probabilités XL, 227–233, Lecture Notes in Math., 1899, Springer, Berlin, 2007.

35. Catuogno, P. ; Molina, S. ; Olivera, C. Hermite expansions and products of tempered distributions. Integral Transforms Spec. Funct. 18 (2007), no. 3-4, 233-243.

36. Catuogno, P. Second order connections and stochastic horizontal lifts. J. Geom. Phys. 56 (2006), no. 9, 1637-1653. 

37.  Catuogno, P. ; Ruffino, P. R. C. Geometry of stochastic delay differential equations. Electron. Comm. Probab. 10 (2005), 190-195.

38. Ferrando, S. E. ; Catuogno, P. ; Gonzalez, A. L. Lower bounds for generalized upcrossings of ergodic averages. Illinois J. Math. 47 (2003), no. 3, 633-648.

39. Catuogno, P. ; Ferrando, S. E. Pointwise asymptotics for the jumps of ergodic averages. New York J. Math. 7 (2001), 59-69. 

40. de la Torre, A. ; Maltz, A. ; Martin, M. ; Catuogno, P. ; Garcia Matta, I. Random walk with an exponentially varying step. Physics Review E (2000) 62, 6, 7748-7754.

41. Catuogno, P. On stochastic parallel transport and prolongation of connections. Rev. Un. Mat. Argentina 41 (1999), no. 3, 107-118. 

42. Catuogno, P. Stochastic parallel transport and connections of $H^2M$. Arch. Math. (Brno) 35 (1999), no. 4, 305-315.

43. Catuogno, P. Composition and factorization of diffusions on principal fiber bundles. Proceedings of the Fourth "Dr. Antonio A. R. Monteiro'' Congress on Mathematics (Bahía Blanca, 1997), 59-70, Univ. Nac. del Sur, Bahía Blanca, 1997. 

44. Catuogno, P. ; de la Torre, A. ; Ferrando, S. Non separability and non commutativity. Found. of Phys. Lett. 4 (1991) 1, 49-59.  

45.  Hack, H. ; González, A. L. ; Catuogno, P. ; Moure, M ; Campbell, A. A computer semantics of Spanish using the theories of R. Montague. (Spanish) Theoria (San Sebastián) (2) 5 (1990), no. 12-13, 171-191.

46.  de la Torre, A. C. ; Catuogno, P. ; Ferrando, S. Uncertainty and nonseparability. Found. Phys. Lett. 2 (1989), no. 3, 235-244.

47.  Catuogno, P. Two characterizations of lattices with union. (Spanish) Mat. Mar del Plata No. 4 (1983), Exp. No. G, 7 pp.

48.  Catuogno, P. A connection between sup-irreducibles and lattices with partial operations. (Spanish) Mat. Mar del Plata No. 4 (1983), Exp. No. D, 6 pp.

49. Batbedat, A. ; Catuogno, P. Elementary, chained lattices with difference, of height $n≤4$. (Spanish) Mat. Mar del Plata No. 2 (1983), Exp. No. J, 12 pp.

50. Catuogno, P. Cutting hypergraphs and lattices. (Spanish) Mat. Mar del Plata No. 2 (1983), Exp. No. F, 13 pp. 

51. Catuogno, P. The sup-irreducibles for the inf-hypergraphs. (Spanish) Mat. Mar del Plata No. 2 (1983), Exp. No. E, 14 pp.

52. Catuogno, P. The operator EXTAT. (Spanish) Mat. Mar del Plata No. 2 (1983), Exp. No. D, 12 pp.

Students

• Alvaro Machado Hernadez (PhD advisor)  Rough paths em variedades. UNICAMP, in progress.

• Alexandre do Nascimento Oliveira Sousa (Posdoc position, advisor) FAPESP, 2022.

• Claudia Lorena Duarte Espitia (Posdoc position, advisor) FAPESP, in progress.

• Gustavo Fróes Do Vale (Undergraduate advisor) Uma introdução a simulações e equações diferenciais estocásticas. (PICME) UNICAMP, 2022.

• Clayton Alves Luis (Undergraduate advisor) Uma introdução a simulações e financas.(PICME) UNICAMP, in progress.

• Mauro de Andrade Pinto (Undergraduate advisor) Uma introdução a simulações. (PICME) UNICAMP, in progress.

• Felipe Batista de Lima Araujo (Undergraduate advisor) Introdução à precificação de derivativos em tempo discreto.(FAPESP) UNICAMP, in progress.

• Vinicius Franco Vasconcelos (Ms, advisor) Análise Não-Standard: Aplicações à Análise Harmônica e à Probabilidade. UNICAMP, 2021.

• Andre de Oliveira Gomes (Posdoc position, advisor) FAPESP, 2021.

• Alvaro Enrique Machado Hernandez (Ms, advisor) Equacao de Burgers estocastica. UNICAMP, 2019.

• Lucas de Figueiredo Costa de Queiroz (Undergraduate advisor) Teoria das distribuicoes. UNICAMP, 2018. 

• Gustavo do Nascimento Costa (Ms, advisor) Equações diferenciais estocasticas backward: Uma aplicação a finanças. UNICAMP, 2018. 

• Marco Antonio Rosa (Ms, advisor)  A importancia das relações de recorrência para melhoria do ensino aprendizagem na matemática discreta. PROFMAT/UNICAMP, 2017. 

• Michele Calefe (Ms, advisor) Construcao de conjuntos numericos: Dos numeros inteiros aos numeros infinitesimais. PROFMAT/UNICAMP, 2016.

• Clovis Rodrigues Vilas-Boas (Ms, advisor)  Introducao ao estudo dos grafos: origem e aplicacoes. PROFMAT/UNICAMP, 2016.

• David Chipana Mollinedo (PhD advisor) Equação estocástica de reação-difusão e equação estocástica de transporte com coeficientes irregulares. UNICAMP, 2015. 

• Carla Cristina Fonte (Ms, advisor) Introducao aos grafos no ensino medio. PROFMAT/UNICAMP, 2014.

• MIke Botazzo (Undergraduate advisor) Compressive sensing. UNICAMP, 2014.

• Rafael Andretto Castrequini (PhD advisor) Uma formula de Ito-Ventzel para caminhos Holder. UNICAMP, 2014. 

• Rodrigo de Sousa Serafim da Silva (Undergraduate advisor) Modelo binomial em financas. UNICAMP, 2014.

• Ian Dick de Paula (Undergraduate advisor) Teorema do ponto fixo e aplicacoes. UNICAMP, 2014.

• Jamil Gomes de Abreu Jr (PhD co-advisor) Solução de conjectura de Weiss estocástica para semigrupos analíticos. UNICAMP, 2013.

• Eduardo de Amorim Neves (PhD advisor) Difusões dependendo diferenciavelmente de Métricas e Conexões. UNICAMP, 2013.

• Elizeu Franca (Ms, advisor)  Simetrias de LIe de equações parciais. UNICAMP, 2012. 

• Luis Roberto Lucinger de Almeida (PhD advisor) Simetrias de Lie estocásticas. UNICAMP, 2012. 

• David Alexander Chipana Mollinedo (Ms, advisor) Fluxos estocásticos e teorema do limite de Kunita. UNICAMP, 2011. 

• Christian Horacio Olivera (Posdoc position, advisor) FAPESP, 2010.

• Roberta Rodrigues Albuquerque (Ms, advisor)Transporte paralelo estocastico. UNICAMP, 2010. 

• Ana Candida Martins (Undergraduate advisor) Calculo e variaçao de funçoes. UNICAMP, 2010. 

• Diego Sebastian Ledesma (PhD co-advisor) Calculo Estocastico en Variedades Folhadas. UNICAMP, 2009.

• Marcelo Gonçalves Oliveira Viera (PhD advisor) Homotopia entre trajetorias de equaçoes dirigidas por caminhos rugosos. UNICAMP, 2009.

• Rafael Andretto Castrequini (Ms, advisor) Teoria de Rough Paths via Integração Algébrica. UNICAMP, 2009. 

• Luciano Vianna Felix (Ms, advisor) Geometria dos caminhos em grupos de LIe. UNICAMP, 2009. 

• Luiz Roberto Lucinger de Almeida (Ms, advisor) Distribuições temperadas e cálculo estócastico. UNICAMP, 2008. 

• Jamil Gomes de Abreu Junior  (Undergraduate advisor)  Introdução ao cálculo de Malliavin e aplicações. UNICAMP, 2008.

• Simão Nicolau Stelmastchuk (PhD advisor) Martingales no fibrado de bases e seções harmônicas via cálculo estocástico. UNICAMP, 2007.

• Rafael Andreto Castrequini (Undergraduate advisor) Análise no Espaço de Wiener e Aplicações. UNICAMP, 2007. 

• Odail Pagliardi (PhD co-advisor) Estudo analógico de fenomenos mecânicos térmicos, hidrologicos, econômicos e movimento browniano por meio do modelo de Black-Scholes. FEAGRI/UNICAMP 2007. 

• Marcelo Gonçalves Oliveira Vieira (Ms, advisor) Homotopia de trajetorias de sistemas dinamicos. UNICAMP, 2005. 

• Federico Martinez (Undergraduate, advisor) N-representacion y producto de distribuciones soportadas en $[0,\infty)$. UNMDP, 2006. 

• Christian Olivera (Undergraduate, advisor) N-representacion y producto de distribuciones. UNMDP, 2004. 

• Diego Sebastian Ledesma (Undergraduate, advisor) Numero de rotacion. UNMDP, 2004. 

• Natalia Sturniolo (Undergraduate, co-advisor) Modelos Probabilisticos para valuacion de opciones financieras. UNMDP, 2002. 

• Jorge Nicolas Lopez (Undergraduate, advisor) Haces fibrados sobre esferas. UNMDP, 2000. 

• Mariela Fernandez (Undergraduate, co-advisor) Modelos matematicos en finanzas de opciones americanas en tiempo discreto. UNMDP, 2000.