# Fr\'{e}chet derivatives of expected functionals of solutions to stochastic differential equations

@inproceedings{Lie2021FrechetDO, title={Fr\'\{e\}chet derivatives of expected functionals of solutions to stochastic differential equations}, author={Han Cheng Lie}, year={2021} }

In the analysis of stochastic dynamical systems described by stochastic differential equations (SDEs), it is often of interest to analyse the sensitivity of the expected value of a functional of the solution of the SDE with respect to perturbations in the SDE parameters. In this paper, we consider path functionals that depend on the solution of the SDE up to a stopping time. We derive formulas for Fréchet derivatives of the expected values of these functionals with respect to bounded…

## References

SHOWING 1-10 OF 21 REFERENCES

### Fréchet differentiable drift dependence of Perron–Frobenius and Koopman operators for non-deterministic dynamics

- MathematicsNonlinearity
- 2019

We prove the Fréchet differentiability with respect to the drift of Perron–Frobenius and Koopman operators associated to time-inhomogeneous ordinary stochastic differential equations. This result…

### Randomised one-step time integration methods for deterministic operator differential equations

- MathematicsCalcolo
- 2022

This work proves pathwise and expected error bounds on the random trajectories, given an assumption on the local truncation error of the underlying deterministic time integration and an assumption that the absolute moments of the random variables decay with the time step.

### Introduction to Stochastic Analysis and Malliavin Calculus

- Mathematics
- 2007

This volume presents an introductory course on differential stochastic equations and Malliavin calculus. The material of the book has grown from a series of courses delivered at the Scuola Normale…

### Computation and Optimal Perturbation of Finite-Time Coherent Sets for Aperiodic Flows Without Trajectory Integration

- MathematicsSIAM J. Appl. Dyn. Syst.
- 2020

This work considers the relevant transfer operators and their infinitesimal generators on an augmented space-time manifold to compute coherent sets from an aperiodic time-dependent dynamical system and obtains explicit solutions for these optimization problems using Lagrange multipliers.

### Efficient rare event simulation by optimal nonequilibrium forcing

- Physics
- 2012

Rare event simulation and estimation for systems in equilibrium are among the most challenging topics in molecular dynamics. As was shown by Jarzynski and others, nonequilibrium forcing can…

### The Malliavin Calculus and Related Topics

- Mathematics
- 1995

Analysis on the Wiener space.- Regularity of probability laws.- Anticipating stochastic calculus.- Transformations of the Wiener measure.- Fractional Brownian motion.- Malliavin Calculus in finance.-…

### Elements of Information Theory

- Computer Science
- 1991

The author examines the role of entropy, inequality, and randomness in the design of codes and the construction of codes in the rapidly changing environment.

### Monte Carlo and Quasi-Monte Carlo Sampling

- Mathematics, Physics
- 2009

The Monte Carlo method.- Sampling from known distributions.- Pseudorandom number generators.- Variance reduction techniques.- Quasi-Monte Carlo constructions.- Using quasi-Monte Carlo constructions.-…

### with an appendix by

- Mathematics
- 2013

We prove that cubulated hyperbolic groups are virtually special. The proof relies on results of Haglund and Wise which also imply that they are linear groups, and quasi-convex subgroups are…