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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
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 02/2013, Volume 398, Issue 1, pp. 315 - 334
In this paper, we study the notion of local time and obtain the Tanaka formula for the -Brownian motion. Moreover, the joint continuity of the local time of... 
[formula omitted]-expectation | Tanaka formula | [formula omitted]-Brownian motion | Local time | Quadratic variation | G-expectation | G-Brownian motion | MATHEMATICS | MATHEMATICS, APPLIED | THEOREM | STOCHASTIC CALCULUS | EXPECTATIONS | Mathematics - Probability
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
THEORY OF PROBABILITY AND ITS APPLICATIONS, ISSN 0040-585X, 2019, Volume 64, Issue 2, pp. 264 - 289
For a symmetric stable process Z = (Z(t))(t >= 0) of index 0 < alpha < 2, any alpha is an element of R, and gamma is an element of (0, 2) satisfying alpha - 1... 
mollifiers | Fourier transform | STATISTICS & PROBABILITY | STOCHASTIC DIFFERENTIAL-EQUATIONS | Tanaka's formula | symmetric stable processes
Journal Article
ANNALS OF PROBABILITY, ISSN 0091-1798, 07/2017, Volume 45, Issue 4, pp. 2377 - 2397
We establish a Krylov-type estimate and an Ito-Krylov change of variable formula for the solutions of one-dimensional quadratic backward stochastic... 
Quadratic backward stochastic differential equations | STOCHASTIC DIFFERENTIAL-EQUATIONS | COEFFICIENT | nonlinear quadratic PDEs | Tanaka's formula | GROWTH | SOLVABILITY | Krylov's inequality | STATISTICS & PROBABILITY | Ito-Krylov's formula | local time | 2 REFLECTING BARRIERS
Journal Article
Journal of Theoretical Probability, ISSN 0894-9840, 6/2016, Volume 29, Issue 2, pp. 590 - 616
We prove an Itô–Tanaka formula and existence of pathwise stochastic integrals for a wide class of Gaussian processes. Motivated by financial applications, we... 
Generalized Lebesgue–Stieltjes integral | Mathematical finance | Gaussian processes | 91G20 | Probability Theory and Stochastic Processes | Mathematics | Statistics, general | 60H05 | Itô–Tanaka formula | Pathwise stochastic integral | 60G15 | Föllmer integral
Journal Article
by Wang, J and Pyrz, R
Composites Science and Technology, ISSN 0266-3538, 2004, Volume 64, Issue 7, pp. 925 - 934
Journal Article
The Annals of Probability, ISSN 0091-1798, 07/2017, Volume 45, Issue 4, pp. 2377 - 2397
Journal Article
Journal of Computational and Theoretical Nanoscience, ISSN 1546-1955, 07/2013, Volume 10, Issue 7, pp. 1579 - 1582
We present an Ito's formula for the one-dimensional discrete-time quantum walk and give some examples including a Tanaka's formula by using the formula.... 
Tanaka's Formula | Itô's Formula | Quantum Walk | STOCHASTIC CALCULUS | PHYSICS, CONDENSED MATTER | Ito's Formula
Journal Article
Stochastic Processes and their Applications, ISSN 0304-4149, 11/2014, Volume 124, Issue 11, pp. 3846 - 3868
The derivative of self-intersection local time (DSLT) for Brownian motion was introduced by Rosen (2005) and subsequently used by others to study the and... 
Tanaka formula | Wiener chaos | Self-intersection local time | Fractional Brownian motion | WHITE-NOISE THEORY | FINANCE | CALCULUS | STATISTICS & PROBABILITY | CENTRAL-LIMIT-THEOREM
Journal Article
Journal of Theoretical Probability, ISSN 0894-9840, 07/2005, Volume 18, Issue 3, pp. 499 - 535
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 02/2011, Volume 217, Issue 12, pp. 5774 - 5783
In this paper, some new properties and interesting estimations of mutual variation process for G-Brownian motion are presented, Kunita–Watanabe inequalities... 
Mutual variation process | Tanaka formula | Kunita–Watanabe inequalities | G-Brownian motion | Kunita-Watanabe inequalities | MATHEMATICS, APPLIED | Mathematical models | Computation | Mathematical analysis | Inequalities
Journal Article
Annales de l'institut Henri Poincare (B) Probability and Statistics, ISSN 0246-0203, 02/2018, Volume 54, Issue 1, pp. 1 - 21
We study a notion of local time for a continuous path, defined as a limit of suitable discrete quantities along a general sequence of partitions of the time... 
Itô-Tanaka formula | Pathwise local-Time | Brownian variation | Random partitions | BROWNIAN-MOTION | INTEGRATION | Pathwise local-time | Ito-Tanaka formula | PATHS | STATISTICS & PROBABILITY | TANAKA FORMULA
Journal Article
Electronic Journal of Probability, ISSN 1083-6489, 2015, Volume 20, pp. 1 - 15
Following a hedging based approach to model free financial mathematics, we prove that it should be possible to make an arbitrarily large profit by investing in... 
Tanaka formula | Itô formula | Model uncertainty | Local times | STATISTICS & PROBABILITY | INTEGRATION | Ito formula
Journal Article
Theory of Probability and its Applications, ISSN 0040-585X, 2012, Volume 56, Issue 3, pp. 443 - 456
Two generalizations of the classical Ito's formula for Brownian motion are derived in this paper. The first is valid for functions with a discontinuous... 
Brownian motion | Wiener process | Itô's formula | Itô's lemma | Discrete Itô's formula | Tanaka's formula | LOCAL TIME | Ito's lemma | discrete Ito's formula | STATISTICS & PROBABILITY | Ito's formula | Derivatives
Journal Article
Journal of the American Society of Hypertension, ISSN 1933-1711, 06/2018, Volume 12, Issue 6, pp. 457 - 469
Measurements of 24-hour urinary sodium (24hrUNa) and potassium (24hrUK) excretion are useful in hypertensives but 24-hour urine collection may be difficult or... 
Tanaka formula | Kawasaki formula | PAHO formula | spot urine measurement | POPULATION | VALIDATION | EQUATIONS | PERIPHERAL VASCULAR DISEASE | SAMPLES | SPOT URINE
Journal Article
Rendiconti del Seminario Matematico dell 'Universita' di Padova/Mathematical Journal of the University of Padova, ISSN 0041-8994, 2012, Volume 127, pp. 41 - 55
In the setting of finite reflection groups, we prove that the projection of a Brownian motion onto a closed Weyl chamber is another Brownian motion normally... 
MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
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