Elements of Stochastic Calculus via Regularization

By Francesco Russo, Pierre Vallois. 2006

152 citations recorded by the source corpus.

This paper first summarizes the foundations of stochastic calculus via regularization and constructs through this procedure Ito and Stratonovich integrals. In the second part, a survey and new results are presented in relation with finite quadratic variation processes, Dirichlet and weak Dirichlet processes.

Subfields: Applied Mathematics, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a97df01a2ee30ae83841af4ebe6aaa6443e8a85e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Ciprian A. Tudor
2. Kun He
3. Rama Cont
4. Litan Yan
5. Massimiliano Gubinelli
6. Nicolas Perkowski
7. Guangjun Shen
8. Joachim Lebovits

In Finance

1. Nicolas Perkowski
2. Massimiliano Gubinelli
3. Rama Cont
4. Guangjun Shen
5. Joachim Lebovits
6. Litan Yan
7. Kun He
8. Ciprian A. Tudor

In Mathematical Physics

1. Nicolas Perkowski
2. Massimiliano Gubinelli
3. Rama Cont
4. Guangjun Shen
5. Litan Yan
6. Ciprian A. Tudor
7. Kun He
8. Joachim Lebovits

Citations in the corpus

• Stochastic Calculus with Respect to Gaussian Processes (2014, background): “Let us also mention the stochastic calculus via regularization (see [45] and references therein), that is also a generalization of Itô integral.”
• Pathwise integration and change of variable formulas for continuous paths with arbitrary regularity (2018, methodology): “A notion similar to our definition of pth variation was introduced by Errami and Russo [13], in the (probabilistic and not pathwise) context of stochastic calculus via regularization [28].”
• Change of variable formulas for non-anticipative functionals on path space ✩ (2010, background): “This construction may in fact be carried out for a more general class of processes, including the class of Dirichlet processes [4,7,8, 11,15], in which case the integral (1) is the forward integral studied by Russo and Vallois [15].”
• Analysis of the Rosenblatt process (2006, background): “2 of the Russo and Vallois survey [38] that every f ∈ C2(R), the integrals ∫ t 0 f (X)dX, ∫ t 0 f (X)dX, ∫ t 0 f (X)dX exist and are equal and we have the Itô’s formula f(Xt) = f(X0) + ∫ t 0 f (X)dX.”
• Itô's formula for a sub-fractional Brownian motion (2011, methodology): “Russo, F. and Vallois, P.: Elements of Stochastic Calculus via Regularization, Séminaire de Probabilités XL (2007), 147–185.”
• Energy solutions of KPZ are unique (2015, background): “Dirichlet processes (wheter Markov or not) can be handled via the stochastic calculus via regularization developed by Russo and Vallois [11].”