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Large Deviations for Multiscale Diffusions via Weak Convergence Methods
Paul Dupuis, Konstantinos Spiliopoulos
We study the large deviations principle for locally periodic stochastic differential equations with small noise and fast oscillating coefficients. There are three possible regimes…
Large Deviations Principle for a Large Class of One-Dimensional Markov Processes
Konstantinos Spiliopoulos
We study the large deviations principle for one dimensional, continuous, homogeneous, strong Markov processes that do not necessarily behave locally as a Wiener process. Any strong…
Recovery Rates in investment-grade pools of credit assets: A large deviations analysis
Konstantinos Spiliopoulos, Richard B. Sowers
We consider the effect of recovery rates on a pool of credit assets. We allow the recovery rate to depend on the defaults in a general way. Using the theory of large deviations, we…
Reaction Diffusion Equations with Nonlinear Boundary Conditions in Narrow Domains
Mark Freidlin, Konstantinos Spiliopoulos
Second initial boundary problem in narrow domains of width for linear second order differential equations with nonlinear boundary conditions is considered in this paper. U…
A Note on the Smoluchowski-Kramers Approximation for the Langevin Equation with Reflection
Konstantinos Spiliopoulos
According to the Smoluchowski-Kramers approximation, the solution of the equation converges to the so…
Wiener Process with Reflection in Non-Smooth Narrow Tubes
Konstantinos Spiliopoulos
Wiener process with instantaneous reflection in narrow tubes of width ε<<1 around axis x is considered in this paper. The tube is assumed to be (asymptotically) non-smooth in the f…