• Corpus ID: 209516409

Positivity of mild solution to stochastic evolution equations with an application to forward rates

@article{Marinelli2019PositivityOM,
  title={Positivity of mild solution to stochastic evolution equations with an application to forward rates},
  author={Carlo Marinelli},
  journal={arXiv: Analysis of PDEs},
  year={2019}
}
  • Carlo Marinelli
  • Published 28 December 2019
  • Mathematics
  • arXiv: Analysis of PDEs
We prove a maximum principle for mild solutions to stochastic evolution equations with (locally) Lipschitz coefficients and Wiener noise on weighted $L^2$ spaces. As an application, we provide sufficient conditions for the positivity of forward rates in the Heath-Jarrow-Morton model, considering the associated Musiela SPDE on a homogeneous weighted Sobolev space. 
View PDF on arXiv
5 Citations
Background Citations
1

5 Citations

Singular perturbations and asymptotic expansions for SPDEs with an application to term structure models

Reaction-Diffusion Equations with Transport Noise and Critical Superlinear Diffusion: Local Well-Posedness and Positivity

. In this paper we consider a class of stochastic reaction-diffusion equations. The main results are concerned with local well-posedness, regularity, and positivity of solutions. Some of the novelties…

Invariant cones for jump-diffusions in infinite dimensions

. In this paper we provide sufficient conditions for stochastic invariance of closed convex cones for stochastic partial differential equations (SPDEs) of jump-diffusion type, and clarify when these…

On pointwise Malliavin differentiability of solutions to semilinear parabolic SPDEs

We obtain estimates on the first-order Malliavin derivative of mild solutions, evaluated at fixed points in time and space, to a class of parabolic dissipative stochastic PDEs on bounded domain of R.…

On the Positivity of Local Mild Solutions to Stochastic Evolution Equations

We provide sufficient conditions on the coefficients of a stochastic evolution equation on a Hilbert space of functions driven by a cylindrical Wiener process ensuring that its mild solution is…

References

SHOWING 1-10 OF 28 REFERENCES

Approximation and convergence of solutions to semilinear stochastic evolution equations with jumps

LOCAL WELL‐POSEDNESS OF MUSIELA’S SPDE WITH LÉVY NOISE

We determine sufficient conditions on the volatility coefficient of Musiela’s stochastic partial differential equation driven by an infinite dimensional Lévy process so that it admits a unique local…

Comparison of systems of stochastic partial differential equations

Comparison methods for a class of function valued stochastic partial differential equations

SummaryA comparison theorem is derived for a class of function valued stochastic partial differential equations (SPDE's) with Lipschitz coefficients driven by cylindrical and regular Hilbert space…

Term Structure Models Driven by Wiener Processes and Poisson Measures: Existence and Positivity

This work investigates term structure models driven by Wiener processes and Poisson measures with forward curve dependent volatilities and characterize positivity preserving models by means of the characteristic coefficients.

One-parameter semigroups for linear evolution equations

Linear Dynamical Systems.- Semigroups, Generators, and Resolvents.- Perturbation and Approximation of Semigroups.- Spectral Theory for Semigroups and Generators.- Asymptotics of Semigroups.-…

Second order partial differential equations in Hilbert spaces

Part I. Theory in the Space of Continuous Functions: 1. Gaussian measures 2. Spaces of continuous functions 3. Heat equation 4. Poisson's equation 5. Elliptic equations with variable coefficients 6.…

Trotter’s formula for transition semigroups

Continuity properties and Trotter’s formula for the transition semigroups corresponding to Markov processes are discussed. Applications to stochastic invariance are given as well. The research was…

Kolmogorov Equations For Stochastic Pdes

1 Introduction and Preliminaries.- 1.1 Introduction.- 1.2 Preliminaries ix.- 1.2.1 Some functional spaces.- 1.2.2 Exponential functions.- 1.2.3 Gaussian measures.- 1.2.4 Sobolev spaces W1,2 (H, ?)…

Consistency Problems For Heath Jarrow Morton Interest Rate Models

Thank you for downloading consistency problems for heath jarrow morton interest rate models. Maybe you have knowledge that, people have look numerous times for their chosen books like this…