Mimicking the marginal distributions of a semimartingale

Abstract

We exhibit conditions under which the flow of marginal distributions of a discontinuous semimartingale $\xi$ can be matched by a Markov process, whose infinitesimal generator is expressed in terms of the local characteristics of $\xi$. Our construction applies to a large class of semimartingales, including smooth functions of a Markov process. We use this result to derive a partial integro-differential equation for the one-dimensional distributions of a semimartingale, extending the Kolmogorov forward equation to a non-Markovian setting.

Revision: 2012

References in corpus (1)

• Stochastic differential equations with jumps

Cited by in corpus (9)

• Mimicking an Itô process by a solution of a stochastic differential equation
• Forward equations for option prices in semimartingale models
• On the martingale problem for degenerate-parabolic partial differential operators with unbounded coefficients and a mimicking theorem for Ito processes
• Short-time asymptotics for marginal distributions of semimartingales
• Existence and uniqueness results for time-inhomogeneous time-change equations and Fokker--Planck equations
• Accelerating Convergence of Replica Exchange Stochastic Gradient MCMC via Variance Reduction
• Automated Importance Sampling via Optimal Control for Stochastic Reaction Networks: A Markovian Projection-based Approach
• Risk aggregation and stochastic claims reserving in disability insurance
• Performance of tail hedged portfolio with third moment variation swap