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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
Probability Theory and Related Fields, ISSN 0178-8051, 6/2011, Volume 150, Issue 1, pp. 295 - 319
Journal Article
by Cass, T and Lim, N
ANNALS OF PROBABILITY, ISSN 0091-1798, 01/2019, Volume 47, Issue 1, pp. 1 - 60
Given a Gaussian process X, its canonical geometric rough path lift X, and a solution Y to the rough differential equation (RDE) dY(t) = V (Y-t) circle dX(t),... 
Rough paths theory | RESPECT | generalized Ito-Stratonovich correction formulas | CALCULUS | STOCHASTIC INTEGRATION | STATISTICS & PROBABILITY | DIFFERENTIAL-EQUATIONS DRIVEN | Malliavin calculus
Journal Article
Discrete and Continuous Dynamical Systems - Series B, ISSN 1531-3492, 08/2018, Volume 23, Issue 6, pp. 2245 - 2263
The mild Ito formula proposed in Theorem 1 in [Da Prato, G., Jentzen, A., & Rockner, M., A mild Ito formula for SPDEs, arXiv : 1009.3526 (2012), To appear in... 
MATHEMATICS, APPLIED | Stochastic analysis | MODELS | Ito formula | mild solution | EQUATIONS | CONVERGENCE | Nemytskii operators | Banach spaces | EXPONENTIAL INTEGRATORS
Journal Article
Stochastic Processes and their Applications, ISSN 0304-4149, 08/2019
Journal Article
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 11/2014, Volume 414, pp. 154 - 162
In the paper, we first extend the discrete time quantum random walk (DQRW) to continuous time quantum random walk (CQRW). Then we establish an Itô formula for... 
DQRW | Tanaka’s formula | Itô formula | CQRW | Tanaka's formula | STOCHASTIC CALCULUS | PHYSICS, MULTIDISCIPLINARY | Ito formula
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 10/2015, Volume 430, Issue 2, pp. 1163 - 1174
Extending Itô's formula to non-smooth functions is important both in theory and applications. One of the fairly general extensions of the formula, known as... 
Itô's formula | Finite variation Lévy process | Weak derivative | PIDE | ItÔ's formula | MATHEMATICS | MATHEMATICS, APPLIED | Finite variation Levy process | Ito's formula
Journal Article
Mathematische Nachrichten, ISSN 0025-584X, 12/2016, Volume 289, Issue 17-18, pp. 2192 - 2222
The paper studies a class of Ornstein–Uhlenbeck processes on the classical Wiener space. These processes are associated with a diffusion type Dirichlet form... 
Infinite dimensional Ornstein–Uhlenbeck process | weak approximation | Itô formula | quadratic variation | Secondary: 60G15 | Primary: 60J60 | MATHEMATICS | SPACE VALUED PROCESSES | PATH SPACE | Ito formula | Infinite dimensional Ornstein-Uhlenbeck process | RIEMANNIAN MANIFOLD | COVARIATION | Naturvetenskap | Mathematics | Natural Sciences | Matematik
Journal Article
Statistics and Probability Letters, ISSN 0167-7152, 04/2014, Volume 87, Issue 1, pp. 48 - 53
We prove an Itô's formula for Walsh's Brownian motion in the plane with angles according to a probability measure μ on [0, 2π [. This extends Freidlin-Sheu... 
Harmonic functions | Stochastic flows | Itô's formula | Walsh's Brownian motion | STATISTICS & PROBABILITY | FLOWS | Ito's formula
Journal Article
PROBABILITY AND MATHEMATICAL STATISTICS-POLAND, ISSN 0208-4147, 2019, Volume 39, Issue 1, pp. 39 - 60
For symmetric Levy processes, if the local times exist, the Tanaka formula has already been constructed via the techniques in the potential theory by Salminen... 
stable process | Ito's stochastic calculus | STATISTICS & PROBABILITY | Local time
Journal Article
Stochastic Processes and their Applications, ISSN 0304-4149, 08/2015, Volume 125, Issue 8, pp. 2989 - 3022
We derive a generalised Itō formula for stochastic processes which are constructed by a convolution of a deterministic kernel with a centred Lévy process. This... 
Skorokhod integral | [formula omitted]-transform | Fractional Lévy process | Stochastic convolution | Itō formula | Ito formula | S-transform
Journal Article
Stochastic Processes and their Applications, ISSN 0304-4149, 11/2014, Volume 124, Issue 11, pp. 3869 - 3885
In this paper, we show that the integration of a stochastic differential equation driven by -Brownian motion ( -SDE for short) in can be reduced to the... 
[formula omitted]-Itô’s formula | Comparison theorem | [formula omitted]-Brownian motion | [formula omitted]-SDE | G-SDE | G-Itô's formula | G-Brownian motion | THEOREM | STATISTICS & PROBABILITY | FORMULA | G-Ito's formula | Analysis | Differential equations
Journal Article
Random Operators and Stochastic Equations, ISSN 0926-6364, 06/2017, Volume 25, Issue 2, pp. 79 - 105
Journal Article
Alea, ISSN 1980-0436, 2018, Volume 15, Issue 1, pp. 703 - 753
We investigate Bochner integrabilities of generalized Wiener functionals. We further formulate an Ito formula for a diffusion in a distributional setting, and... 
Distributional Itô's formula | Hölder continuity of diffusion local times | Malliavin calculus | Smoothing effect brought by time-integral | SOBOLEV SPACES | SMOOTHNESS | LOCAL TIME | STATISTICS & PROBABILITY | Holder continuity of diffusion local times | Distributional Ito's formula
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 10/2012, Volume 64, Issue 7, pp. 2302 - 2311
We apply a variant of a discretised Itô formula to develop sharp conditions for the global a.s. asymptotic stability of the equilibrium solution of a... 
a.s. asymptotic stability | Random sequence | Stochastic difference equations | Discrete Itô formula multiplicative noise | a.s. asymptotic stability | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Discrete Ito formula multiplicative noise | Differential equations
Journal Article
The Annals of Probability, ISSN 0091-1798, 1/2013, Volume 41, Issue 1, pp. 109 - 133
Journal Article
Stochastic Processes and their Applications, ISSN 0304-4149, 2009, Volume 119, Issue 10, pp. 3356 - 3382
Journal Article
Mathematical and Computer Modelling, ISSN 0895-7177, 2011, Volume 54, Issue 1, pp. 221 - 232
In this paper, we explore a stochastic SIR model and show that this model has a unique global positive solution. Furthermore, we investigate the asymptotic... 
Brownian motion | Stochastic SIR model | It [formula omitted]’s formula | Global positive solution | Asymptotic behavior | Itô's formula | MATHEMATICS, APPLIED | Ito's formula
Journal Article
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