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We study path-dependent SDEs in Hilbert spaces. By using methods based on contractions in Banach spaces, we prove existence and uniqueness of mild solutions, continuity of mild solutions with respect… (More)

- Mauro Rosestolato, Karl Sabelfeld, +4 authors Rayna Georgieva
- 2013

We consider a real-valued stochastic dynamics y(x0, x1) solving an SDE with infinite delay appearing in the coefficients, given the value x0 at time 0, and its past x1 from −∞ up to time 0. The aim… (More)

We provide a version of the stochastic Fubini's theorem which does not depend on the particular stochastic integrator chosen as far as the stochastic integration is built as a continuous linear… (More)

Path-dependent PDEs (PPDEs) are natural objects to study when one deals with non Markovian models. Recently, after the introduction of the so-called pathwise (or functional or Dupire) calculus (see… (More)

We introduce a new definition of viscosity solution to path-dependent partial differential equations, which is a slight modification of the definition introduced in [8]. With the new definition, we… (More)

In this paper, we consider a generalisation of the Hobson–Rogers model proposed by Foschi and Pascucci (Decis Eocon Finance 31(1):1–20, 2008) for financial markets where the evolution of the prices… (More)

We present and apply a theory of one parameter $C_0$-semigroups of linear operators in locally convex spaces. Replacing the notion of equicontinuity considered by the literature with the weaker… (More)

We present and apply a theory of one parameter $C_0$-semigroups of linear operators in locally convex spaces. Replacing the notion of equicontinuity considered by the literature with the weaker… (More)

Recently, functional It\=o calculus has been introduced and developed in finite dimension for functionals of continuous semimartingales. With different techniques, we develop a functional It\=o… (More)

Abstract We study value functions which are viscosity solutions of certain Kolmogorov equations. Using PDE techniques we prove that they are C 1 + α regular on special finite dimensional subspaces.… (More)