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Quenched Large Deviations for Multiscale Diffusion Processes in Random Environments
Konstantinos Spiliopoulos
We consider multiple time scales systems of stochastic differential equations with small noise in random environments. We prove a quenched large deviations principle with explicit…
Non-asymptotic performance analysis of importance sampling schemes for small noise diffusions
Konstantinos Spiliopoulos
In this note we develop a prelimit analysis of performance measures for importance sampling schemes related to small noise diffusion processes. In importance sampling the performan…
Fluctuation analysis and short time asymptotics for multiple scales diffusion processes
Konstantinos Spiliopoulos
We consider the limiting behavior of fluctuations of small noise diffusions with multiple scales around their homogenized deterministic limit. We allow full dependence of the coeff…
Filtering the Maximum Likelihood for Multiscale Problems
Andrew Papanicolaou, Konstantinos Spiliopoulos
Filtering and parameter estimation under partial information for multiscale problems is studied in this paper. After proving mean square convergence of the nonlinear filter to a fi…
Fluctuation Analysis for the Loss From Default
Konstantinos Spiliopoulos, Justin A. Sirignano, Kay Giesecke
We analyze the fluctuation of the loss from default around its large portfolio limit in a class of reduced-form models of correlated firm-by-firm default timing. We prove a weak co…
Escaping from an attractor: Importance sampling and rest points I
Paul Dupuis, Konstantinos Spiliopoulos, Xiang Zhou
We discuss importance sampling schemes for the estimation of finite time exit probabilities of small noise diffusions that involve escape from an equilibrium. A factor that complic…
Maximum likelihood estimation for small noise multiscale diffusions
Konstantinos Spiliopoulos, Alexandra Chronopoulou
We study the problem of parameter estimation for stochastic differential equations with small noise and fast oscillating parameters. Depending on how fast the intensity of the nois…