54 citations · 124 across the 10 of their papers we have counts for
11 papers
A Gaussian Markov alternative to fractional Brownian motion for pricing financial derivatives
Daniel Conus, Mackenzie Wildman
Replacing Black-Scholes' driving process, Brownian motion, with fractional Brownian motion allows for incorporation of a past dependency of stock prices but faces a few major downf…
Weak convergence rates of spectral Galerkin approximations for SPDEs with nonlinear diffusion coefficients
Daniel Conus, Arnulf Jentzen, Ryan Kurniawan
Strong convergence rates for (temporal, spatial, and noise) numerical approximations of semilinear stochastic evolution equations (SEEs) with smooth and regular nonlinearities are…
Intermittency for the wave and heat equations with fractional noise in time
Raluca M. Balan, Daniel Conus
In this article, we consider the stochastic wave and heat equations driven by a Gaussian noise which is spatially homogeneous and behaves in time like a fractional Brownian motion…
A note on intermittency for the fractional heat equation
Raluca Balan, Daniel Conus
The goal of the present note is to study intermittency properties for the solution to the fractional heat equation $$\frac{\partial u}{\partial t}(t,x) = -(-Δ)^{β/2} u(t,x) + u(t,x…
Intermittency and chaos for a stochastic non-linear wave equation in dimension 1
Daniel Conus, Mathew Joseph, Davar Khoshnevisan +1
We consider a non-linear stochastic wave equation driven by space-time white noise in dimension 1. First of all, we state some results about the intermittency of the solution, whic…
On the chaotic character of the stochastic heat equation, II
Daniel Conus, Mathew Joseph, Davar Khoshnevisan +1
Consider the stochastic heat equation , where the solution is indexed by , and $\dot…
Initial measures for the stochastic heat equation
Daniel Conus, Mathew Joseph, Davar Khoshnevisan +1
We consider a family of nonlinear stochastic heat equations of the form , where denotes space-time white noise, the…
Correlation-length bounds, and estimates for intermittent islands in parabolic SPDEs
Daniel Conus, Mathew Joseph, Davar Khoshnevisan
We consider the nonlinear stochastic heat equation in one dimension. Under some conditions on the nonlinearity, we show that the "peaks" of the solution are rare, almost fractal li…
On the chaotic character of the stochastic heat equation, before the onset of intermitttency
Daniel Conus, Mathew Joseph, Davar Khoshnevisan
We consider a nonlinear stochastic heat equation , where denotes space-time white noise and $σ:\mathbf {R…
Weak nonmild solutions to some SPDEs
Daniel Conus, Davar Khoshnevisan
We study the nonlinear stochastic heat equation driven by space-time white noise in the case that the initial datum is a (possibly signed) measure. In this case, one cannot o…
On the existence and position of the farthest peaks of a family of stochastic heat and wave equations
Daniel Conus, Davar Khoshnevisan
We study a family of non-linear stochastic heat equations in (1+1) dimensions, driven by the generator of a Lévy process and space-time white noise. We assume that the underlying L…