9 papers · 1 filter
The Martingale Problem Method Revisited
David Criens, Peter Pfaffelhuber, Thorsten Schmidt
We use the abstract method of (local) martingale problems in order to give criteria for convergence of stochastic processes. Extending previous notions, the formulation we use is n…
On the Feller-Dynkin and the Martingale Property of One-Dimensional Diffusions
David Criens
We show that a one-dimensional regular continuous Markov process \(\X\) with scale function \(s\) is a Feller--Dynkin process precisely if the space transformed process \(s (X)\) i…
On a Theorem by A.S. Cherny for Semilinear Stochastic Partial Differential Equations
David Criens, Moritz Ritter
We consider analytically weak solutions to semilinear stochastic partial differential equations with non-anticipating coefficients driven by cylindrical Brownian motion. The soluti…
A Dual Yamada-Watanabe Theorem for Levy driven stochastic differential equations
David Criens
We prove a dual Yamada-Watanabe theorem for one-dimensional stochastic differential equations driven by quasi-left continuous semimartingales with independent increments. In partic…
On Absolute Continuity and Singularity of Multidimensional Diffusions
David Criens
Consider two laws \(P\) and \(Q\) of multidimensional possibly explosive diffusions with common diffusion coefficient \(\mathfrak{a}\) and drift coefficients \(\mathfrak{b}\) and \…
On the Existence of Semimartingales with Continuous Characteristics
David Criens
We prove the existence of quasi-left continuous semimartingales with continuous local semimartingale characteristics which satisfy a Lyapunov-type or a linear growth condition, whe…