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pro vyhledávání: '"Issoglio, Elena"'
This paper is concerned with numerical solutions of one-dimensional SDEs with the drift being a generalised function, in particular belonging to the Holder-Zygmund space $C^{-\gamma}$ of negative order $-\gamma<0$ in the spacial variable. We design a
Externí odkaz:
http://arxiv.org/abs/2309.11396
Autor:
Issoglio, Elena, Russo, Francesco
This paper investigates a class of PDEs with coefficients in negative Besov spaces and whose solutions have linear growth. We show existence and uniqueness of mild and weak solutions, which are equivalent in this setting, and several continuity resul
Externí odkaz:
http://arxiv.org/abs/2212.04293
Autor:
Issoglio, Elena, Russo, Francesco
We consider SDEs with (distributional) drift in negative Besov spaces and random initial condition and investigate them from two different viewpoints. In the first part we set up a martingale problem and show its well-posedness.We then prove further
Externí odkaz:
http://arxiv.org/abs/2208.10799
We study a class of zero-sum games between a singular-controller and a stopper over finite-time horizon. The underlying process is a multi-dimensional (locally non-degenerate) controlled stochastic differential equation (SDE) evolving in an unbounded
Externí odkaz:
http://arxiv.org/abs/2203.06247
Autor:
Issoglio, Elena, Russo, Francesco
The paper investigates existence and uniqueness for a stochastic differential equation (SDE) with distributional drift depending on the law density of the solution. Those equations are known as McKean SDEs. The McKean SDE is interpreted in the sense
Externí odkaz:
http://arxiv.org/abs/2107.14453
Autor:
Chamorro, Diego, Issoglio, Elena
We consider a parabolic-type PDE with a diffusion given by a fractional Laplacian operator and with a quadratic nonlinearity of the 'gradient' of the solution, convoluted with a singular term b. Our first result is the well-posedness for this problem
Externí odkaz:
http://arxiv.org/abs/2007.04588
In this paper we present a scheme for the numerical solution of one-dimensional stochastic differential equations (SDEs) whose drift belongs to a fractional Sobolev space of negative regularity (a subspace of Schwartz distributions). We obtain a rate
Externí odkaz:
http://arxiv.org/abs/1906.11026
Akademický článek
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Autor:
Issoglio, Elena
We consider a non-linear parabolic partial differential equation (PDE) on $\mathbb R^d$ with a distributional coefficient in the non-linear term. The distribution is an element of a Besov space with negative regularity and the non-linearity is of qua
Externí odkaz:
http://arxiv.org/abs/1808.01959
In this note we consider generalized diffusion equations in which the diffusivity coefficient is not necessarily constant in time, but instead it solves a nonlinear fractional differential equation involving fractional Riemann-Liouville time-derivati
Externí odkaz:
http://arxiv.org/abs/1807.04642