Stochastic systems with memory and jumps

DOI10.1016/j.jde.2018.10.052zbMath1412.34228arXiv1603.00272OpenAlexW2963172535WikidataQ128939968 ScholiaQ128939968MaRDI QIDQ1736185

Francesco Giuseppe Cordoni, Luca Di Persio, Giulia Di Nunno, Elin Engen Røse, David R. Baños

Publication date: 26 March 2019

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.00272

zbMATH Keywords

stochastic delay equationsItô formulamemoryjump diffusionsmoment estimatescalculus via regularisation

Mathematics Subject Classification ID

Stochastic functional-differential equations (34K50) Stochastic calculus of variations and the Malliavin calculus (60H07)

Related Items (13)

Applications of anticipated BSDEs driven by time-changing Lévy noises ⋮ A nonlinear Kolmogorov equation for stochastic functional delay differential equations with jumps ⋮ Stability of stochastic functional differential systems with semi-Markovian switching and Lévy noise by functional Itô's formula and its applications ⋮ Bilateral teleoperation of stochastic port‐Hamiltonian systems using energy tanks ⋮ Feynman-Kac formula for BSDEs with jumps and time delayed generators associated to path-dependent nonlinear Kolmogorov equations ⋮ Stability of stochastic time-delay systems involving delayed impulses ⋮ Weak Dirichlet processes and generalized martingale problems ⋮ Existence and smoothness of the densities of stochastic functional differential equations with jumps ⋮ Fusion of PDF compensation and gain-scheduled control for discrete stochastic systems with randomly occurring nonlinearities ⋮ Delay tolerance for stable hybrid stochastic differential equations with Lévy noise based on Razumikhin technique ⋮ An explicit approximation for super-linear stochastic functional differential equations ⋮ Stochastic control of memory mean-field processes ⋮ A BSDE with delayed generator approach to pricing under counterparty risk and collateralization

Cites Work

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• Optimal control of systems with noisy memory and BSDEs with Malliavin derivatives
• An infinite-dimensional approach to path-dependent Kolmogorov equations
• Generalized covariation for Banach space valued processes, Itō formula and applications
• On stochastic calculus related to financial assets without semimartingales
• Delay differential equations: with applications in population dynamics
• Delay differential equations driven by Lévy processes: stationarity and Feller properties
• Gaussian approximation of multivariate Lévy processes with applications to simulation of tempered stable processes
• Change of variable formulas for non-anticipative functionals on path space
• The European option with hereditary price structures
• Weak Dirichlet processes with jumps
• Optimal control of forward-backward mean-field stochastic delayed systems
• Delay equations. Functional-, complex-, and nonlinear analysis
• Applied functional analysis. Main principles and their applications
• The generalized covariation process and Itô formula
• Ito formula for \(C^ 1\)-functions of semimartingales
• Functional Itō calculus and stochastic integral representation of martingales
• The pricing of options for securities markets with delayed response
• Infinite-dimensional Black-Scholes equation with hereditary structure
• Approximations of small jumps of Lévy processes with a view towards simulation
• Modeling and Pricing of Swaps for Financial and Energy Markets with Stochastic Volatilities
• Computation of the Delta in Multidimensional Jump-Diffusion Setting with Applications to Stochastic Volatility Models
• GENERALIZED COVARIATION AND EXTENDED FUKUSHIMA DECOMPOSITION FOR BANACH SPACE-VALUED PROCESSES: APPLICATIONS TO WINDOWS OF DIRICHLET PROCESSES
• Higher moments of Banach space valued random variables
• Functional Itô versus Banach space stochastic calculus and strict solutions of semilinear path-dependent equations
• Stochastic Equations with Delay: Optimal Control via BSDEs and Regular Solutions of Hamilton–Jacobi–Bellman Equations
• Diffusion approximation of Lévy processes with a view towards finance
• A Delayed Black and Scholes Formula
• Lévy Processes and Stochastic Calculus
• One-Parameter Semigroups for Linear Evolution Equations
• Calculus via regularizations in Banach spaces and Kolmogorov-type path-dependent equations
• A Stochastic Calculus for Systems with Memory

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