On the exact and \(\varepsilon\)-strong simulation of (jump) diffusions

DOI10.3150/14-BEJ676zbMath1343.60099arXiv1302.6964OpenAlexW3101800103MaRDI QIDQ265272

Adam M. Johansen, Gareth O. Roberts, Murray Pollock

Publication date: 1 April 2016

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.6964

zbMATH Keywords

simulationstochastic differential equationsadaptive exact algorithmsbarrier crossing probabilitiesBrownian path space probabilitiesfirst hitting timesjump diffusionskilled diffusions

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Diffusion processes (60J60) Sample path properties (60G17) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)

Related Items

Piecewise deterministic Markov processes for continuous-time Monte Carlo, An Exact Auxiliary Variable Gibbs Sampler for a Class of Diffusions, Unbiased simulation of rare events in continuous time, Reducing Bias in Event Time Simulations via Measure Changes, Consistency of Bayesian nonparametric inference for discretely observed jump diffusions, The computational cost of blocking for sampling discretely observed diffusions, Strong approximation of Bessel processes, \(\varepsilon\)-strong simulation of the convex minorants of stable processes and meanders, Numerical aspects of shot noise representation of infinitely divisible laws and related processes, Exact simulation of multidimensional reflected Brownian motion, Monte Carlo fusion, On logarithmically optimal exact simulation of max-stable and related random fields on a compact set, Exact simulation of the first passage time through a given level of jump diffusions, ɛ-Strong Simulation of Fractional Brownian Motion and Related Stochastic Differential Equations, Exact simulation of coupled Wright–Fisher diffusions

Cites Work

• The Pricing of Options and Corporate Liabilities
• Discretization of processes.
• Exact simulation of jump-diffusion processes with Monte Carlo applications
• A factorisation of diffusion measure and finite sample path constructions
• Numerical solution of stochastic differential equations with jumps in finance
• Bayesian inference for nonlinear multivariate diffusion models observed with error
• Discretization error in simulation of one-dimensional reflecting Brownian motion
• \(\varepsilon\)-strong simulation of the Brownian path
• The Itô-Ventzell formula and forward stochastic differential equations driven by Poisson random measures
• Closed-form likelihood expansions for multivariate diffusions
• Simple simulation of diffusion bridges with application to likelihood inference for diffusions
• Simulation of Brownian motion at first-passage times
• Exact simulation of diffusions
• Retrospective exact simulation of diffusion sample paths with applications
• Boundary crossing probability for Brownian motion
• Stochastic Differential Mixed-Effects Models
• A Modification of the Sequential Probability Ratio Test to Reduce the Sample Size
• Exact and Computationally Efficient Likelihood-Based Estimation for Discretely Observed Diffusion Processes (with Discussion)
• Markov Chain Monte Carlo for Exact Inference for Diffusions
• Exact Sampling of Jump Diffusions
• Localization and Exact Simulation of Brownian Motion-Driven Stochastic Differential Equations
• Option pricing when underlying stock returns are discontinuous
• Applied stochastic control of jump diffusions
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