Probability density function of SDEs with unbounded and path-dependent drift coefficient

DOI10.1016/j.spa.2020.03.006OpenAlexW3014223202MaRDI QIDQ2196367

Akihiro Tanaka, Dai Taguchi

Publication date: 2 September 2020

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

Full work available at URL: https://arxiv.org/abs/1811.07101

zbMATH Keywords

probability density functionEuler-Maruyama schemeparametrix methodGaussian two-sided boundMaruyama-Girsanov theoremunbiased simulation

Mathematics Subject Classification ID

Density estimation (62G07) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30) Heat kernel (35K08)

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Cites Work

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• The parametrix method for skew diffusions
• Euler approximations with varying coefficients: the case of superlinearly growing diffusion coefficients
• A Malliavin calculus method to study densities of additive functionals of SDE's with irregular drifts
• Strong convergence of an explicit numerical method for SDEs with nonglobally Lipschitz continuous coefficients
• Absolute continuity for some one-dimensional processes
• Unbiased simulation of stochastic differential equations using parametrix expansions
• On some non asymptotic bounds for the Euler scheme
• Smoothness and asymptotic estimates of densities for SDEs with locally smooth coefficients and applications to square root-type diffusions
• Continuity and Gaussian two-sided bounds of the density functions of the solutions to path-dependent stochastic differential equations via perturbation
• A note on tamed Euler approximations
• Hölder continuity property of the densities of SDEs with singular drift coefficients
• Euler scheme and tempered distributions
• A probabilistic interpretation of the parametrix method
• Sharp estimates for the convergence of the density of the Euler scheme in small time
• Examples of singular parabolic measures and singular transition probability densities
• Some estimates of the transition density of a nondegenerate diffusion Markov process
• On the convergence rate of Euler scheme for SDE with Lipschitz drift and constant diffusion
• Comparison theorem and estimates for transition probability densities of diffusion processes
• Sharp bounds for transition probability densities of a class of diffusions
• Towards the exact simulation using hyperbolic Brownian motion
• Convergence of the Euler-Maruyama method for multidimensional SDEs with discontinuous drift and degenerate diffusion coefficient
• Unbiased simulation of stochastic differential equations
• A simple method for the existence of a density for stochastic evolutions with rough coefficients
• Parabolic differential equations with unbounded coefficients -- A generalization of the parametrix method
• The Euler scheme with irregular coefficients
• The law of the Euler scheme for stochastic differential equations. I: Convergence rate of the distribution function
• Weak rate of convergence of the Euler-Maruyama scheme for stochastic differential equations with non-regular drift
• Weak uniqueness and density estimates for SDEs with coefficients depending on some path-functionals
• Density for solutions to stochastic differential equations with unbounded drift
• Hölder continuous densities of solutions of SDEs with measurable and path dependent drift coefficients
• Strong rate of convergence for the Euler-Maruyama approximation of SDEs with Hölder continuous drift coefficient
• Approximation for non-smooth functionals of stochastic differential equations with irregular drift
• Convergence and regularity of probability laws by using an interpolation method
• A representation formula for transition probability densities of diffusions and applications
• Two-sided estimates on the density of Brownian motion with singular drift
• Curvature and the eigenvalues of the Laplacian
• Continuous Markov processes and stochastic equations
• Strong rate of convergence for the Euler-Maruyama approximation of stochastic differential equations with irregular coefficients
• Joint distributions for stochastic functional differential equations
• STOCHASTIC VOLATILITY MODELS AND THE PRICING OF VIX OPTIONS
• Strong and weak divergence in finite time of Euler's method for stochastic differential equations with non-globally Lipschitz continuous coefficients
• Continuity of Solutions of Parabolic and Elliptic Equations
• Rate of Convergence of the Euler Approximation for Diffusion Processes
• The Malliavin Calculus and Related Topics
• ON STRONG SOLUTIONS AND EXPLICIT FORMULAS FOR SOLUTIONS OF STOCHASTIC INTEGRAL EQUATIONS
• Diffusions and Elliptic Operators
• Stochastic formulations of the parametrix method
• Edgeworth type expansions for Euler schemes for stochastic differential equations.
• Unbiased Monte Carlo estimate of stochastic differential equations expectations
• Stability of Densities for Perturbed Diffusions and Markov Chains
• Bounds for the fundamental solution of a parabolic equation
• Diffusion processes with continuous coefficients, I
• A TRANSFORMATION OF THE PHASE SPACE OF A DIFFUSION PROCESS THAT REMOVES THE DRIFT