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Applicable Analysis, ISSN 0003-6811, 03/2014, Volume 93, Issue 3, pp. 539 - 550
The paper introduces a novel Itô's formula for time- dependent tempered generalized functions. As an application, we study the heat equation when initial... 
Itô's formula | Hermite expansions | generalized functions | Hermite functions | COLOMBEAU ALGEBRAS | MATHEMATICS, APPLIED | TOPOLOGICAL STRUCTURES | Ito's formula | Initial conditions | Proving | Heat equations
Journal Article
Bulletin of the Georgian National Academy of Sciences, ISSN 0132-1447, 2011, Volume 5, Issue 3, pp. 11 - 16
Journal Article
Stochastic Analysis and Applications, ISSN 0736-2994, 11/2015, Volume 33, Issue 6, pp. 1020 - 1049
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
Siberian Advances in Mathematics, ISSN 1055-1344, 1/2016, Volume 26, Issue 1, pp. 17 - 29
For the first time we present a complete proof (from the standpoint of stochastic analysis) of the generalized Itô–Venttsel’ formula whose ideas were adduced... 
Itô–Venttsel’ formula | Poisson measure | δ-sequence | mean-square convergence | generalized Itô equation | Mathematics, general | Mathematics | Methods | Differential equations
Journal Article
Stochastic Processes and their Applications, ISSN 0304-4149, 1999, Volume 79, Issue 1, pp. 45 - 67
Stability of stochastic differential equations with Markovian switching has recently received a lot of attention. For example, stability of linear or... 
Brownian motion | M-matrix | Generalized Itô’s formula | Markov chain generator | Lyapunov exponent | Generalized Itô's formula | M -matrix | STATISTICS & PROBABILITY | generalized Ito's formula | Lyapunov exponent Generalized Ito's formula Brownian motion Markov chain generator M-matrix
Journal Article
Systems & Control Letters, ISSN 0167-6911, 02/2013, Volume 62, Issue 2, pp. 178 - 187
One of the important issues in the study of hybrid SDDEs is the automatic control, with consequent emphasis being placed on the asymptotic analysis of... 
Brownian motion | Markov chain | Asymptotic boundedness | Generalized Itô’s formula | Exponential stability | Generalized Itô's formula | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | INTERVAL SYSTEMS | Generalized Ito's formula | AUTOMATION & CONTROL SYSTEMS | DEPENDENT STABILITY
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2011, Volume 376, Issue 1, pp. 11 - 28
In this paper, we prove that a stochastic logistic population under regime switching controlled by a Markov chain is either stochastically permanent or... 
Brownian motion | Generalized Itô's formula | Markov chain | Stochastic permanence | Stochastic differential equation | MATHEMATICS, APPLIED | STABILITY | PERSISTENCE | BEHAVIOR | ENVIRONMENT | DIFFERENTIAL-EQUATIONS | NOISE | Generalized Ito's formula | RANDOM PERTURBATION | MATHEMATICS | LOTKA-VOLTERRA MODEL | DYNAMICS | SYSTEMS | Markov processes | Analysis | Extinction (Biology)
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
Stochastic Processes and their Applications, ISSN 0304-4149, 09/2017, Volume 127, Issue 9, pp. 2816 - 2840
Within the framework of the previous paper (Bonaccorsi and Mazzucchi, 2015), we develop a generalized stochastic calculus for processes associated to higher... 
Generalized Itô calculus | Probabilistic representation of solutions of PDEs | Stochastic processes on the complex plane | PDE | EQUATIONS | STATISTICS & PROBABILITY | Generalized Ito calculus | SIGNED MEASURE | FORMULA | Stochastic processes
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 09/2015, Volume 266, pp. 539 - 559
In this paper, we investigate the stochastic permanence and extinction of a stochastic ratio-dependent prey–predator model controlled by a Markov chain. In the... 
Brownian motion | Markov chain | Generalized Itô’s formula | Ratio-dependent prey-predator model | Stochastic differential equation | Generalized Itô's formula | MATHEMATICS, APPLIED | II SCHEMES | DIFFERENTIAL-EQUATIONS | MODEL | Generalized Ito's formula | MODIFIED LESLIE-GOWER | QUALITATIVE-ANALYSIS | DYNAMICS | CONVERGENCE | Markov processes | Analysis
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 2009, Volume 232, Issue 2, pp. 427 - 448
In this paper, we investigate a Lotka–Volterra system under regime switching d x ( t ) = diag ( x 1 ( t ) , … , x n ( t ) ) [ ( b ( r ( t ) ) + A ( r ( t ) ) x... 
Brownian motion | Markov chain | Generalized Itô’s formula | Stochastic permanence | Stochastic differential equation | Generalized Itô's formula | EXISTENCE | MATHEMATICS, APPLIED | GLOBAL STABILITY | POSITIVE SOLUTIONS | PERSISTENCE | ENVIRONMENT | DIFFERENTIAL-EQUATIONS | MODEL | Generalized Ito's formula | RANDOM PERTURBATION | UNIQUENESS | LOGISTIC EQUATION | Markov processes | Analysis
Journal Article
Stochastic Processes and their Applications, ISSN 0304-4149, 2008, Volume 118, Issue 8, pp. 1385 - 1406
Journal Article
Siberian Advances in Mathematics, ISSN 1055-1344, 7/2015, Volume 25, Issue 3, pp. 191 - 205
We deduce an analog of the Itô–Venttsel’ formula for an Itô system of generalized stochastic differential equations (GSDE) with noncentered measure on the... 
generalized stochastic differential equation | stochastic first integral | Mathematics, general | Mathematics | kernel of an integral invariant | Itô–Venttsel formula | noncentered Poisson measure
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 05/2019, Volume 348, pp. 338 - 354
Journal Article
Infinite Dimensional Analysis, Quantum Probability and Related Topics, ISSN 0219-0257, 12/2016, Volume 19, Issue 4
Functional Ito calculus was introduced in order to expand a functional F(t, X.+(t), X-t) depending on time t, past and present values of the process X. Another... 
Functional Itô calculus | strict solutions | Banach space valued stochastic calculus | calculus via regularization | path-dependent partial differential equation | MATHEMATICS, APPLIED | BACKWARD | Functional Ito calculus | VALUED PROCESSES | REPRESENTATION | STATISTICS & PROBABILITY | FORMULA | PHYSICS, MATHEMATICAL | GENERALIZED COVARIATION
Journal Article
IEEE Transactions on Automatic Control, ISSN 0018-9286, 09/2013, Volume 58, Issue 9, pp. 2319 - 2332
Journal Article
Stochastic Processes and their Applications, ISSN 0304-4149, 2003, Volume 103, Issue 2, pp. 277 - 291
Stability of stochastic differential equations with Markovian switching has recently been discussed by many authors, for example, Basak et al. (J. Math. Anal.... 
Generalized Itô's formula | Brownian motion | Markov chain | Asymptotic stability in distribution | STATISTICS & PROBABILITY | generalized Ito's formula | asymptotic stability in distribution | Generalized Ito's formula Brownian motion Markov chain Asymptotic stability in distribution
Journal Article
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