Asymptotic expansions of solutions of stochastic differential equations driven by multivariate fractional Brownian motions having Hurst indices greater than 1/3

DOI10.1080/07362994.2018.1483247zbMath1420.60075OpenAlexW2899294270WikidataQ129020132 ScholiaQ129020132MaRDI QIDQ4634144

I. V. Kachan, Maksim Vaskouski

Publication date: 7 May 2019

Published in: Stochastic Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/07362994.2018.1483247

zbMATH Keywords

stochastic differential equationasymptotic expansionsrough path integralmultivariate fractional Brownian motion

Mathematics Subject Classification ID

Fractional processes, including fractional Brownian motion (60G22) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10)

Related Items

Finiteness of moments of solutions to mixed-type stochastic differential equations driven by standard and fractional Brownian motions ⋮ Stability of linear stochastic differential equations of mixed type with fractional Brownian motions ⋮ Existence and uniqueness of solutions of differential equations weakly controlled by rough paths with an arbitrary positive Hölder exponent ⋮ Analog of the Kolmogorov equations for one-dimensional stochastic differential equations controlled by fractional Brownian motion with Hurst exponent \(H\in (0,1)\)

Cites Work

• The Jain-Monrad criterion for rough paths and applications to random Fourier series and non-Markovian Hörmander theory
• Existence of weak solutions of stochastic differential equations with standard and fractional Brownian motion, discontinuous coefficients, and a partly degenerate diffusion operator
• Properties of solutions of stochastic differential equations with standard and fractional Brownian motions
• Large deviations and asymptotic methods in finance
• Trees and asymptotic expansions for fractional stochastic differential equations
• Ramification of rough paths
• Operators associated with a stochastic differential equation driven by fractional Brownian motions
• Existence of solutions of stochastic differential inclusions with standard and fractional Brownian motions
• Differential equations driven by rough signals
• Differential equations driven by fractional Brownian motion
• The existence and uniqueness of the solution of an integral equation driven by a \(p\)-semimartin\-gale of special type.
• Stochastic analysis, rough path analysis and fractional Brownian motions.
• Controlling rough paths
• Existence of weak solutions of stochastic differential equations with standard and fractional Brownian motions and with discontinuous coefficients
• Geometric versus non-geometric rough paths
• Stability and attraction of solutions of nonlinear stochastic differential equations with standard and fractional Brownian motions
• Stochastic calculus for fractional Brownian motion and related processes.
• Stochastic integral of divergence type with respect to fractional Brownian motion with Hurst parameter \(H \in (0,\frac {1}{2})\)
• General approach to filtering with fractional brownian noises — application to linear systems
• Existence and Uniqueness of the Solution of Stochastic Differential Equation Involving Wiener Process and Fractional Brownian Motion with Hurst IndexH > 1/2
• LONG RANGE DEPENDENCE, NO ARBITRAGE AND THE BLACK–SCHOLES FORMULA
• Multidimensional Stochastic Processes as Rough Paths
• Stochastic Differential Equations Driven by Fractional Brownian Motion and Standard Brownian Motion
• A course on rough paths. With an introduction to regularity structures