Quadratic covariation and an extension of Itô's formula

From MaRDI portal
Publication:1903608

DOI10.2307/3318684zbMath0851.60048OpenAlexW1528471277MaRDI QIDQ1903608

Hans Föllmer, Philip E. Protter, Albert N. Shiryaev

Publication date: 12 December 1995

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.bj/1186078365




Related Items

Generalized integration and stochastic ODEsBackward problems for stochastic differential equations on the Sierpinski gasketA central bank strategy for defending a currency pegGeneralization of Itô's formula for smooth nondegenerate martingales.Integration with respect to local time and Itô's formula for smooth nondegenerate martingalesSemimartingale integral representationThe quadratic variation for mixed-fractional Brownian motionOn time-dependent functionals of diffusions corresponding to divergence form operatorsThe generalized quadratic covariation for fractional Brownian motion with Hurst index less than 1/2Derivative for the intersection local time of two independent fractional Brownian motionsNonsemimartingales: stochastic differential equations and weak Dirichlet processesThe functional Meyer–Tanaka formulaA change of variable formula with applications to multi-dimensional optimal stopping problemsA central limit theorem for the realised covariation of a bivariate Brownian semistationary processOptimal stopping under ambiguity in continuous timeApproximation of Optimal Stopping Problems and Variational Inequalities Involving Multiple Scales in Economics and FinanceStochastic integration with respect to additive functionals of zero quadratic variationSome Remarks on Davie’s Uniqueness TheoremThe generalized Bouleau-Yor identity for a sub-fractional Brownian motionQuadratic covariation estimates in non-smooth stochastic calculusGeneralized covariations, local time and Stratonovich Itô's formula for fractional Brownian motion with Hurst index \(H\geq\frac 1 4\).Integration with respect to the \(G\)-Brownian local timeOnline drift estimation for jump-diffusion processesSome remarks on local time-space calculusOn Itô's formula for elliptic diffusion processesHedging options in market models modulated by the fractional Brownian motionOn Chernoff's test for a fractional Brownian motionFinite expiry Russian optionsDistributional It\^o's Formula and Regularization of Generalized Wiener FunctionalsOn arbitrage and Markovian short rates in fractional bond marketsLocal time-space stochastic calculus for Lévy processesA Dirichlet process characterization of a class of reflected diffusionsQuadratic covariation and Itô's formula for smooth nondegenerate martingalesTemporal variation for fractional heat equations with additive white noiseNonlinear stochastic partial differential equations with singular diffusivity and gradient Stratonovich noiseStratonovich stochastic differential equation with irregular coefficients: Girsanov's example revisitedStochastic bifurcation modelsIntegration with respect to fractional local time with Hurst index \(1/2 < \text H < 1\)An extension of Itô's formula for elliptic diffusion processesQuadratic covariations for the solution to a stochastic heat equation with space-time white noiseOn local times of Ornstein-Uhlenbeck processesA Bayesian sequential test for the drift of a fractional Brownian motionA change-of-variable formula with local time on curvesThe quadratic covariation for a weighted fractional Brownian motionItô's formula for finite variation Lévy processes: the case of non-smooth functions