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- Paul Dupuis, Konstantinos Spiliopoulos, Hui Wang
- Multiscale Modeling & Simulation
- 2012

We construct importance sampling schemes for stochastic differential equations with small noise and fast oscillating coefficients. Standard Monte Carlo methods perform poorly for these problems inâ€¦ (More)

Ornstein-Uhlenbeck processes driven by general LÃ©vy process are considered in this paper. We derive strongly consistent estimators for the moments of the underlying LÃ©vy process and for the meanâ€¦ (More)

- Andrew Papanicolaou, Konstantinos Spiliopoulos
- Multiscale Modeling & Simulation
- 2014

Filtering and parameter estimation under partial information for multiscale diffusion problems are studied in this paper. The nonlinear filter converges in the mean-square sense to a filter ofâ€¦ (More)

In recent papers it has been demonstrated that sampling a Gibbs distribution from an appropriate time-irreversible Langevin process is, from several points of view, advantageous when compared toâ€¦ (More)

- Mark Freidlin, Konstantinos Spiliopoulos
- Asymptotic Analysis
- 2008

Second initial boundary problem in narrow domains of width Ç« â‰ª 1 for linear second order differential equations with nonlinear boundary conditions is considered in this paper. Using probabilisticâ€¦ (More)

- Paul Dupuis, Konstantinos Spiliopoulos, Hui Wang
- Proceedings of the 2011 Winter Simulationâ€¦
- 2011

A rough energy landscape can be modeled by a potential function superimposed by another fast oscillating function. Modeling motion in such a rough energy landscape by a small noise stochasticâ€¦ (More)

- Justin A. Sirignano, Konstantinos Spiliopoulos
- SIAM J. Financial Math.
- 2017

We consider stochastic gradient descent for continuous-time models. Traditional approaches for the statistical estimation of continuous-time models, such as batch optimization, can be impractical forâ€¦ (More)

According to the Smoluchowski-Kramers approximation, the solution of the equation Î¼qÌˆ t = b(q Î¼ t ) âˆ’ qÌ‡ t + Î£(q t )áº†t, q 0 = q, qÌ‡ 0 = p converges to the solution of the equation qÌ‡t = b(qt) +â€¦ (More)

- Konstantinos Spiliopoulos
- Multiscale Modeling & Simulation
- 2015

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 convergence resultâ€¦ (More)