UMA Home page for Francesco Russo
Teaching/Research
Professor
Professor
Research Habilitation 1993
Ph.D. 1988
EMAIL_TEMPLATE
Research activities
- Stochastic analysis.
- Financial mathematics.
- Probabilistic models in mathematical physics.
For publications see: Site personnel
Research gate: https://www.researchgate.net/profile/Francesco_Russo11
SDAIM (Stochastic and Deterministic Analysis of Irregular Models)
Project (2023-27) founded by the ANR (french national research agency) and FAPESP (Sao Paulo state research agency).
- SDAIM web site
- Coordinator (France): Francesco RUSSO (ENSTA Paris)
- French teams: ENSTA Paris, CMAP (Polytechnique), CentraleSupélec, EDF, Université de Lille
- Coordinator (Brazil): Christian OLIVERA (UNICAMP)
- Brazilian team: UNICAMP (Campinas, Sao Paulo, Brazil)
Publications
Papers in peer-reviewed journals
Submitted
- A PDE WITH DRIFT OF NEGATIVE BESOV INDEX AND LINEAR GROWTH SOLUTIONS
and
submitted [
] 
- An entropy penalized approach for stochastic control problems. Complete version
, and
submitted [ ] - Characteristics and Itô's formula for weak Dirichlet processes: an equivalence result
and
submitted [ ] - Path-dependent Hamilton-Jacobi-Bellman equation: Uniqueness of Crandall-Lions viscosity solutions
, , and
Preprint hal-03285204, submitted [ ] - Path-dependent SDEs with jumps and irregular drift: well-posedness and Dirichlet properties
and
submitted [ ] - Reduced dissipation effect in stochastic transport by Gaussian noise with regularity greater than 1/2
and
submitted [ ] - SDEs WITH SINGULAR COEFFICIENTS: THE MARTINGALE PROBLEM VIEW AND THE STOCHASTIC DYNAMICS VIEW
and
submitted [ ] - Weak Dirichlet processes and generalized martingale problems
and
Preprint HAL 01241073, submitted [ ]
To appear
- Rough paths and symmetric-Stratonovich integrals driven by singular covariance Gaussian processes.
and
To appear: Bernoulli, to appear [ ]
2023
- McKean SDEs with singular coefficients
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Annales de l'Institut Henri Poincaré. Probabilités et Statistiques., vol. 59 (3), pp. 1530–1548, sep, 2023 [ ] 
- On SDEs for Bessel Processes in low dimension and path-dependent extensions
, and
ALEA, Lat. Am. J. Probab. Math. Sta., vol. 20, pp. 1111-1138, 2023 [ ]
2022
- Backward Stochastic Differential Equations with no driving martingale, Markov processes and associated Pseudo Partial Differential Equations.
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Journal of Stochastic Analysis (JOSA)., vol. 3, Nr. 1, mar, 2022 [ ] - Crandall-Lions viscosity solutions for path-dependent PDEs: the case of heat equation.
and
Bernoulli, vol. 28, pp. 481-503, jan, 2022 [ ] - Fokker-Planck equations with terminal condition and related McKean probabilistic representation
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Nonlinear Differential Equations and Applications NoDEA, jan, 2022 [ ] - Gâteaux type path-dependent PDEs and BSDEs with Gaussian forward processes
and
Stochastics and Dynamics, vol. 22, pp. 2250007, jan, 2022 [ ] - On some path-dependent SDEs involving distributional drifts
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Modern Stochastics: Theory and Applications, vol. 9 (1), pp. 65-87, jan, 2022 [ ]
2021
- A fully backward representation of semilinear PDEs applied to the control of thermostatic loads in power systems
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Monte-Carlo methods and applications., vol. 27 (4), pp. 347-371, oct, 2021 [ ] - Backward Stochastic Differential Equations with no driving martingale, Markov processes and associated Pseudo Partial Differential Equations. Part II: Decoupled mild solutions and Examples.
and
Journal of Theoretical Probabililty., vol. 34, pp. 1110-1148, may, 2021 [ ] - Martingale driven BSDEs, PDEs and other related deterministic problems
and
Stochastic Processes and their Applications, vol. 133, 193-228, feb, 2021 [ ] - McKean Feynman-Kac probabilistic representations of non-linear partial differential equations
, and
Geometry and Invariance in Stochastic Dynamics. Eds. S. Ugolini et al., vol. 378, pp. 187-212, Springer, dec, 2021 [ ] - Rough paths and regularization
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Journal of Stochastic Analysis (JOSA)., vol. 2 (4), pp. 1-21, dec, 2021 [ ] - Smoothness of densities for path-dependent SDEs under Hörmander’s condition
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Journal of Functional Analysis, vol. 281, pp. 109-225, Elsevier, nov, 2021
2020
- A Feynman-Kac result via Markov BSDEs with generalised drivers
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Bernoulli, vol. 26, pp. 728-766, jan, 2020 [ ] - About classical solutions of the path-dependent heat equation.
and
Random Operators Stochastic Equations (ROSE), vol. 1, pp. 35-62, jan, 2020 [ ] - Decoupled mild solutions of path-dependent PDEs and Integro PDEs represented by BSDEs driven by cadlag martingales
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Potential Analysis., vol. 53, pp. 449-481, jul, 2020 [ ] - Discrete-type approximations for non-Markovian optimal stopping problems: Part II
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Methodology and Computing in Applied Probability, vol. 22, pp. 1221-1255, nov, 2020 [ ] - The identification problem for BSDEs driven by possibly non quasi-left-continuous random measures
and
Stochastics and Dynamics, vol. 20, jan, 2020 [ ]
2019
- Discrete-type approximations for non-Markovian optimal stopping problems: Part I
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Journal of Applied Probability, vol. 56, pp. 981-1005, apr, 2019 [ ] - Forward Feynman-Kac type representation for semilinear nonconservative Partial Differential Equations
, and
Stochastics: An International Journal Of Probability And Stochastic Processes, Vol. 91, Issue 8, aug, 2019 [ ] - On the well-posedness of a class of McKean Feynman-Kac equations
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Markov Processes and Related Fields., vol. 25, pp. 821-862, oct, 2019 [ ] - Path-dependent Martingale Problems and Additive Functionals
and
Stochastics and Dynamics, vol. 19 (4), pp. 1950027 (39 pages), apr, 2019 [ ] - Path-dependent equations driven by Hölder processes
and
Stochastic analysis and their applications., vol. 37 (3), pp. 480-498, oct, 2019 [ ] - Strong-viscosity solutions: semilinear parabolic PDEs and path-dependent PDEs
and
Osaka Journal of Mathematics., vol. 56, No.2, pp. 323-373, apr, 2019 [ ]
2018
- Gas storage valuation and hedging. A quantification of the model risk.
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International Journal of Financial Studies. Special Issue "Finance, Financial Risk Management and their Applications"., vol. 6(1), pp. 27, mar, 2018 [ ] 
- Infinite-dimensional calculus under weak spatial regularity of the processes
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Journal of Theoretical Probability, vol. 31, pp. 789-826, 2018 [ ] - Monte-Carlo Algorithms for Forward Feynman-Kac type representation for semilinear nonconservative Partial Differential Equations
, and
Monte Carlo Methods and Applications., vol. 24 no 1, pp. 55-70, mar, 2018 [ ] - Special weak Dirichlet processes and BSDEs driven by a random measure.
and
Bernoulli, vol. 24(4A), pp. 2569-2609, 2018 [ ] - Srishti Dhar Chatterji, my Ph.D. advisor
Expositiones Mathematicae, vol. 36, pp. 257-258, dec, 2018 [ ]
2017
- A note on time-dependent additive functionals
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Communications on Stochastic Analysis, vol. 11 no 3, pp. 313-334, sep, 2017 [ ] - Doubly probabilistic representation for the stochastic porous media type equation.
, and
Annales de l'Institut Henri Poincare. Section Probabilites et Statistiques, vol. 53 No. 4, pp. 2043-2073, nov, 2017 [ ] - Elliptic PDEs with distributional drift and backward SDEs driven by a càdlàg martingale with random terminal time
and
Stochastics and Dynamics., vol. 17, pp. 1750030, aug, 2017 [ ] - HJB equations in infinite dimension and optimal control of stochastic evolution equations via generalized Fukushima decomposition
and
SIAM Journal on Control and Optimization, vol. 55(6), pp. 4072–4091, jun, 2017 [ ] - Infinite dimensional weak Dirichlet processes and convolution type processes.
and
Stochastic Processes and its Applications, vol. 127 (1), pp. 325-357, jan, 2017 [ ] - Multidimensional stochastic differential equations with distributional drift.
, and
Transactions of the American Mathematical Society, vol. 369 (3), pp. 1655-1688, mar, 2017 [ ] - Particle system algorithm and chaos propagation related to non-conservative McKean type stochastic differential equations.
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Stochastics and partial differential equations: Analysis and Computation., vol. 5 (1), pp. 1-37, Springer-Verlag, mar, 2017 [ ] - Uniqueness for a class of stochastic Fokker-Planck and porous media equations
and
Journal of Evolution Equations, vol. 17 (3), pp. 1049-1062, Springer-Verlag, oct, 2017 [ ] - Weak Dirichlet processes with jumps.
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Stochastic Processes and their applications, vol. 12, pp. 4139--4189, 2017 [ ]
2016
- BSDEs, càdlàg martingale problems and orthogonalisation under basis risk.
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SIAM Journal on Financial Mathematics., vol. 7, pp. 308-356, may, 2016 [ ] - Calculus via regularizations in Banach spaces and Kolmogorov-type path-dependent equations
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vol. 668, pp. 43-65, Probability on Algebraic and Geometric Structures, June 5-7 2014, Contemporary Mathematics 668, 2016 [ ] - Functional Itô versus Banach space stochastic calculus and strict solutions of semilinear path-dependent equations
and
Infinite Dimensional Analysis, Quantum Probability and Related Topics, vol. 19 (4), pp. 1650024, 2016 [ ] - Probabilistic representation of a class of non conservative nonlinear Partial Differential Equations.
, and
ALEA (Latin American Journal Of Probability And Mathematical Statistics), vol. 13, pp. 1189–1233, nov, 2016 [ ]
2015
- Functional and Banach Space Stochastic Calculi: Path-Dependent Kolmogorov Equations Associated with the Frame of a Brownian Motion
and
vol. 138, pp. 27-80, Springer Proceedings in Mathematics and Statistics. F.E. Benth and G. Di Nunno (eds.), Stochastics of Environmental and Financial Economics,, oct, 2015 [ ] - Gaussian and non-Gaussian processes of zero power variation and related stochastic calculus
and
ESAIM P & S, vol. 19, pp. 414-439, sep, 2015 [ ] - On countably skewed Brownian motion with accumulation point.
, and
Electronic Journal in Probability., vol. 20 (82), pp. 1-27, aug, 2015 [ ] - Second Order PDEs with Dirichlet White Noise Boundary Conditions.
, , and
Journal of Evolution Equations., vol. 15 (1), pp. 1-26, jan, 2015 [ ] - The Stochastic Porous Media Equations in $\R^d$
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Journal de Mathematiques Pures et Appliquees., vol. 103 (4), pp. 1024-1052, apr, 2015 [ ]
2014
- BSDEs under partial information and financial applications.
, and
Stochastic processes and applications., vol. 124 (8), pp. 2628–2653, mar, 2014 [ ] - GKW representation theorem and linear BSDEs under restricted information. An application to risk-minimization.
, and
Stochastics and Dynamics, vol. 14(2), pp. 1350019, may, 2014 [ ] - Generalized covariation for Banach space valued processes and Itô formula
and
Osaka Journal of Mathematics, vol. 51(3), jun, 2014 [ ] - Probabilistic representation for solutions of a porous media type equation with Neumann boundary condition: the case of the half-line.
and
Differential and Integral Equations. Advances in Differential Equations., vol. 27 1/2, pp. 181-200, jan, 2014 [ ] - The covariation for Banach space valued processes and applications.
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Metrika, vol. 77, pp. 51-104, jan, 2014 [ ] - Variance Optimal Hedging for discrete time processes with independent increments. Application to Electricity Markets
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Journal of Computational Finance., vol. 17 (2), pp. 71-111, jan, 2014 [ ] - Variance optimal hedging for continuous time additive processes and applications
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Stochastics An International Journal of Probability and Stochastic Processes., vol. 81 (1), pp. 147--185, jan, 2014 [ ]
2013
- On some expectation and derivative operators related to integral representations of random variables with respect to a PII process.
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Stochastic Analysis and Applications, vol. 31, pp. 108--141, jan, 2013 [ ] - Probabilistic and deterministic algorithms for space multidimensional irregular porous media equation
, and
Stochastic Partial Differential Equations: Analysis and Computations, vol. 1 (1), pp. 3-62, mar, 2013 [ ]
2012
- Generalized covariation and extended Fukushima decompositions for Banach space valued processes. Application to windows of Dirichlet processes.
and
Infinite Dimensional Analysis, Quantum Probability and Related Topics (IDA-QP)., vol. 15(2), jun, 2012 [ ] - Uniqueness for Fokker-Planck equation with measurable coefficients and applications to the fast diffusion equation
and
Electronic Journal in Probability, vol. 17 (84), pp. 1-28, 2012
2011
- A probabilistic algorithm approximating solutions of a singular PDE of porous media type
, and
Monte Carlo Methods and Applications, vol. 17, pp. 317-369, oct, 2011 [ ] - Clark-Ocone type formula for non-semimartingales with finite quadratic variation
and
Comptes Rendus de l'Académie des Sciences., vol. 349(3-4), pp. 209 214, jan, 2011 [ ] - On stochastic calculus related to financial assets without semimartingales
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Bulletin Sciences Mathématiques, vol. 135, pp. 733774, jul, 2011 [ ] - Probabilistic representation for solutions of an irregular porous media type equation: the degenerate case.
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Probability Theory and Related Fields, vol. 151, 1-2, pp. 1-43, Springer, sep, 2011
2010
- Probabilistic representation for solutions of an irregular porous media type equation
, and
Annals of Probability, vol. 38, 5, pp. 18701900, 2010
Books
2022
- Stochastic calculus via regularizations
and
vol. 11, Bocconi & Springer Series, nov, 2022 [ ]
2015
- Stochastic analysis: a series of lectures, Centre Interfacultaire Bernoulli, January-June 2012, Ecole Polytechnique Federale, Lausanne (Switzerland)
, , and
vol. 68, Birkäuser Verlag, aug, 2015
2013
- Seminar on Stochastic Analysis, Random Fields and Applications VII
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vol. 67, pp. 469 p., Birkhäuser Applied Probability and Statistics (Springer), 2013
2011
- Seminar on stochastic analysis, random fields and applications VI
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vol. 63, pp. 482, Seminar on Stochastic Analysis, Random Fields and Applications VI, Birkäuser Verlag, may, 2011
Lecture notes
2014
- A regularization approach to functional Itô calculus and strong-viscosity solutions to path-dependent PDEs
and
HAL INRIA Preprint 00933678, jan, 2014 [ ] - A stochastic Fokker-Planck equation and double probabilistic representation for the stochastic porous media type equation.
, and
HAL-INRIA 00981113, 2014 [ ] - Infinite dimensional weak Dirichlet processes, stochastic PDEs and optimal control.
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feb, 2014 [ ] - Probabilistic representation of a class of non conservative nonlinear Partial Differential Equations.
, and
Arxiv, HAL-ENSTA, apr, 2014 [ ]
2010
- Infinite dimensional stochastic calculus via regularization.
and
Arxiv, apr, 2010 [ ] - Malliavin-Skorohod calculus and Paley-Wiener integral for covariance singular processes
and
HAL-INRIA, nov, 2010