Zobrazeno 1 - 10
of 55
pro vyhledávání: '"Conus, Daniel"'
Publikováno v:
In Applied Mathematics and Computation 1 February 2025 486
Autor:
Conus, Daniel, Wildman, Mackenzie
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 downfalls, including the occurrence of arbitrage when implemented in the fi
Externí odkaz:
http://arxiv.org/abs/1608.03428
Publikováno v:
Ann. Appl. Probab. 29 (2019), no. 2, 653-716
Strong convergence rates for (temporal, spatial, and noise) numerical approximations of semilinear stochastic evolution equations (SEEs) with smooth and regular nonlinearities are well understood in the scientific literature. Weak convergence rates f
Externí odkaz:
http://arxiv.org/abs/1408.1108
Publikováno v:
The Annals of Applied Probability, 2019 Apr 01. 29(2), 653-716.
Externí odkaz:
https://www.jstor.org/stable/26581802
Autor:
Balan, Raluca, Conus, Daniel
The goal of the present note is to study intermittency properties for the solution to the fractional heat equation $$\frac{\partial u}{\partial t}(t,x) = -(-\Delta)^{\beta/2} u(t,x) + u(t,x)\dot{W}(t,x), \quad t>0,x \in \bR^d$$ with initial condition
Externí odkaz:
http://arxiv.org/abs/1311.0023
Autor:
Balan, Raluca M., Conus, Daniel
Publikováno v:
Annals of Probability 2016, Vol. 44, No. 2, 1488-1534
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 with Hurst index $H>1/2$. The solutions of these equations are interpr
Externí odkaz:
http://arxiv.org/abs/1311.0021
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, which have only been carefully studied in some particular cases so far. Th
Externí odkaz:
http://arxiv.org/abs/1112.1909
Consider the stochastic heat equation $\partial_t u = (\frac{\varkappa}{2})\Delta u+\sigma(u)\dot{F}$, where the solution $u:=u_t(x)$ is indexed by $(t,x)\in (0, \infty)\times\R^d$, and $\dot{F}$ is a centered Gaussian noise that is white in time and
Externí odkaz:
http://arxiv.org/abs/1111.4728
We consider a family of nonlinear stochastic heat equations of the form $\partial_t u=\mathcal{L}u + \sigma(u)\dot{W}$, where $\dot{W}$ denotes space-time white noise, $\mathcal{L}$ the generator of a symmetric L\'evy process on $\R$, and $\sigma$ is
Externí odkaz:
http://arxiv.org/abs/1110.4079
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 like. We also provide an upper bound on the length of the "islands," the
Externí odkaz:
http://arxiv.org/abs/1110.3012