My main research interests lie in the field of stochastic analysis with strong links to the theory of PDEs. In particular I study
SPDEs driven by fractional Brownian motion: I use pathwise approach to solve linear transport equations driven by fractional noises. Main techniques used are fractional calculus, semigroup theory and theory of parabolic PDEs.
SDEs with singular drift: My results on deterministic PDEs with singular coefficients are exploited to tackle n-dimensional SDEs with singular drift.
Backward SDES and forward-backward SDEs with singular coefficients: techniques similar to the ones used for singular SDEs have inspired me to treat signular BSDEs. The main analytical tools are pointwise products, fractional Sobolev spaces and semigroup theory, and these are used in conjunction with classical stochastic analysis tools.
Numerics for Stochastic PDEs: I recently started to look at numerical schemes to approximate stochastic PDEs, in particular PDEs with distributional coefficients.
SPDEs on metric measure spaces: The pathwise approach for SPDEs is extended to SPDEs in metric measure spaces. Main techniques used are fractional Sobolev spaces generalized to measure spaces and fractional integrals and derivatives.
SDEs in Banach spaces: I study cylindrical processes in infinite dimensional spaces, in particular cylindrical fBm and related stochastic calculus in Banach spaces. Application to SPDEs considered as abstract Cauchy problems.
List of publications:
- Flandoli F., Issoglio E., Russo F. Multidimensional stochastic differential equations with distributional drift, Transactions of the American Mathematical Society, 369 (2017), 1665-1688
- Issoglio E, Zaehle M, Regularity of the solutions to SPDEs in metric measure spaces Stochastic Partial Differential Equations: Analysis and Computations, Volume 3, Issue 2, pp 272-289, 2015
- Hinz M., Issoglio E., Zaehle M. Elementary pathwise methods for nonlinear parabolic and transport type SPDE with fractal noise Modern Stochastics and Applications, Springer Optimization and Its Applications, Volume 90, pp 123-141, 2014
- Issoglio E., Riedle M. SDEs in Banach spaces driven by cylindrical fractional Brownian motions Stochastic Processes and their Applications, 124(11), pp 3507-3534, 2014
- Issoglio E. Transport equations with fractal noise – existence, uniqueness and regularity of the solution J. Analysis and its App. 32(1), pp 37-53, 2013
- Issoglio E. SPDEs with fractal noises: two different approaches (PhD Thesis) 2012
- Venturino E., Isaia M., Bona F., Issoglio E., Triolo V., Badino G. Modelling the spiders ballooning effect on the vineyard ecology Math. Model. Nat. Phenom. 1, no. 1, 137-159 (electronic), 2006
- Issoglio E., Jing S. Forward-Backward SDEs with distributional coefficients Arxiv preprint 2016
Work In Progress:
- Armstrong J., Issoglio E., Voss J., Numerical methods for stochastic PDEs
- Issoglio E., Russo F., Notes on Backward SDEs with generalised coefficients
- Issoglio E., On a non-linear transport-diffusion equation with distributional
Supervision of PhD Students:
- Paul Smith (joint supervision with J. Voss) 2016 – present
- Jason Susanna Anquandah (joint supervision with L. Bogachev and T. De Angelis) 2016 – present
I collaborate with a number of mathematicians including (in chronological order):
– Martina Zaehle (Univesity of Jena)
– Michael Hinz (Bielefeld University)
– Markus Riedle (King’s College London)
– Franco Flandoli (University of Pisa)
– Francesco Russo (ENSTA-ParisTech)
– Shuai Jing (Central University of finance and Economics, Beijing)
– John Armstrong (King’s College London)
– Jochen Voss (University of Leeds)