8 papers
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…
Lyapunov Criteria for the Feller-Dynkin Property of Martingale Problems
David Criens
We give necessary and sufficient criteria for the Feller-Dynkin property of solutions to martingale problems in terms of Lyapunov functions. Moreover, we derive a Khasminskii-type…
No Arbitrage in Continuous Financial Markets
David Criens
We derive integral tests for the existence and absence of arbitrage in a financial market with one risky asset which is either modeled as stochastic exponential of an Ito process o…