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The Annals of Probability, ISSN 0091-1798, 1/2013, Volume 41, Issue 1, pp. 109 - 133
Journal Article
Differential Equations, ISSN 0012-2661, 4/2018, Volume 54, Issue 4, pp. 557 - 561
For a stochastic differential equation of the heat equation type, we obtain a Feynman–Kac formula to which the method of analytic continuation with respect to... 
Difference and Functional Equations | Mathematics | Ordinary Differential Equations | Partial Differential Equations | MATHEMATICS | Formulas (mathematics) | Schroedinger equation | Differential equations
Journal Article
Stochastics and Dynamics, ISSN 0219-4937, 08/2016, Volume 16, Issue 4
Dupire [16] introduced a notion of smoothness for functionals of paths and arrived at a generalization of Ito's formula that applies to functionals with a... 
Pathwise stochastic calculus | functional Itō formula | VISCOSITY SOLUTIONS | STATISTICS & PROBABILITY | functional Ito formula
Journal Article
Stochastics and Dynamics, ISSN 0219-4937, 08/2018, Volume 18, Issue 4
The functional Ito formula, firstly introduced by Bruno Dupire for continuous semi-martingales, might be extended in two directions: different dynamics for the... 
Functional Itô calculus | mollification | max-martingales | Meyer-Tanaka formula | running maximum | local time | MARTINGALES | VISCOSITY SOLUTIONS | Functional Ito calculus | CALCULUS | ITOS FORMULA | STATISTICS & PROBABILITY | SPACE | SEMIMARTINGALES | Mathematics - Probability
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 2008, Volume 245, Issue 1, pp. 30 - 58
Journal Article
Stochastic Processes and their Applications, ISSN 0304-4149, 03/2016, Volume 126, Issue 3, pp. 735 - 766
This paper introduces path derivatives, in the spirit of Dupire’s functional Itô calculus, for controlled rough paths in rough path theory with possibly... 
Functional Itô calculus | Rough path | Itô–Ventzell formula | Path derivatives | Characteristics | Rough differential equations | Rough PDEs | Stochastic PDEs | 60H10 | MSC 60H05 | 60G17 | 60G05 | 60H15 | STOCHASTIC VISCOSITY SOLUTIONS | Functional Ito calculus | PARTIAL-DIFFERENTIAL-EQUATIONS | Ito-Ventzell formula | STATISTICS & PROBABILITY | DRIVEN
Journal Article
Stochastic Processes and their Applications, ISSN 0304-4149, 07/2015, Volume 125, Issue 7, pp. 2820 - 2855
In this paper we establish the pathwise Taylor expansions for random fields that are “regular” in terms of Dupire’s path-derivatives [6]. Using the language of... 
Stochastic partial differential equations | Pathwise Taylor expansion | Path derivatives | Functional Itô formula | Itô–Wentzell formula | Ito-Wentzell formula | STATISTICS & PROBABILITY | Functional Ito formula
Journal Article
2016, Advanced Courses in Mathematics - CRM Barcelona, ISBN 9783319271279, Issue DOI: 10.1007/978-3-319-27128-6, 213
This volume contains lecture notes from the courses given by Vlad Bally and Rama Cont at the Barcelona Summer School on Stochastic Analysis (July 2012).The... 
Probability Theory and Stochastic Processes | Mathematics | Ordinary Differential Equations | Partial Differential Equations | Probability
eBook
The Annals of Probability, ISSN 0091-1798, 3/2014, Volume 42, Issue 2, pp. 497 - 526
Journal Article
Journal Article
Infinite Dimensional Analysis, Quantum Probability and Related Topics, ISSN 0219-0257, 12/2016, Volume 19, Issue 4
Journal Article
Neurocomputing, ISSN 0925-2312, 05/2014, Volume 131, pp. 157 - 163
Journal Article
IEEE Transactions on Automatic Control, ISSN 0018-9286, 8/2019, pp. 1 - 1
Given an unstable hybrid stochastic differential equation (SDE), can we design a feedback control, based on the discrete-time observations of the state at... 
Markov chain | Asymptotic stability | Symmetric matrices | Lyapunov functional | Highly nonlinear | Stability criteria | Ito formula | Differential equations | Markov processes | Control systems | Feedback control
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 2010, Volume 259, Issue 4, pp. 1043 - 1072
We derive a change of variable formula for non-anticipative functionals defined on the space of R d -valued right-continuous paths with left limits. The... 
Itô formula | Functional derivative | Dirichlet process | Malliavin calculus | Semimartingale | Cadlag functions | Functional calculus | Stochastic integral | Quadratic variation | MATHEMATICS | Ito formula | DIRICHLET PROCESSES | Functional Analysis | Probability | Mathematics
Journal Article
Potential Analysis, ISSN 0926-2601, 1/2019, Volume 50, Issue 1, pp. 1 - 42
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 02/2018, Volume 458, Issue 2, pp. 1390 - 1408
This paper is concerned with the almost sure exponential stability of the n-dimensional nonlinear hybrid stochastic functional differential equation (SFDE)... 
Brownian motion | Markov chain | Stability | Itô formula | Hybrid stochastic differential functional equations | MATHEMATICS | MATHEMATICS, APPLIED | Ito formula | STABILIZATION | DESTABILIZATION | SYSTEMS | DELAY EQUATIONS | NOISE
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2009, Volume 359, Issue 2, pp. 482 - 498
In this paper, we consider a predator–prey model with modified Leslie–Gower and Holling-type II schemes with stochastic perturbation. We show there is a unique... 
Globally stable in time average | Itô's formula | Persistent in mean | Extinction | COMPLEX DYNAMICS | MATHEMATICS, APPLIED | STABILITY | BEHAVIOR | Ito's formula | FUNCTIONAL-RESPONSE | MATHEMATICS | IMPULSIVE PERTURBATIONS | LOTKA-VOLTERRA MODEL | SYSTEMS
Journal Article
JOURNAL OF STATISTICAL PHYSICS, ISSN 0022-4715, 02/2020, Volume 178, Issue 3, pp. 666 - 681
We consider the Dean-Kawasaki equation with smooth drift interaction potential and show that measure-valued solutions exist only in certain parameter regimes... 
Wasserstein diffusion | BROWNIAN PARTICLES | Dean-Kawasaki equation | Langevin dynamics | Ito formula for measure-valued processes | MODEL | DENSITY-FUNCTIONAL THEORY | PHYSICS, MATHEMATICAL
Journal Article
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