Zobrazeno 1 - 10
of 321
pro vyhledávání: '"Rozovskiĭ IS"'
Publikováno v:
SIAM J. Numer. Anal., 53(1): 153-183, 2015
We compare Wiener chaos and stochastic collocation methods for linear advection-reaction-diffusion equations with multiplicative white noise. Both methods are constructed based on a recursive multi-stage algorithm for long-time integration. We derive
Externí odkaz:
http://arxiv.org/abs/1505.03771
Autor:
Mikulevicius, R., Rozovskii, B. L.
The starting point of the current paper is a sequence of uncorrelated random variables. The distribution functions of these variables are assumed to be given but no assumptions on the types or the structure of these distributions are made. The above
Externí odkaz:
http://arxiv.org/abs/1406.5952
Publikováno v:
SIAM J. Sci. Comp. V. 36 (2014), No 4, pp. A1652-A1677
We consider a sparse grid collocation method in conjunction with a time discretization of the differential equations for computing expectations of functionals of solutions to differential equations perturbed by time-dependent white noise. We first an
Externí odkaz:
http://arxiv.org/abs/1310.5605
Autor:
Mikulevicius, R., Rozovskii, B. L.
A random perturbation of a deterministic Navier-Stokes equation is considered in the form of an SPDE with Wick type nonlinearity. The nonlinear term of the perturbation can be characterized as the highest stochastic order approximation of the origina
Externí odkaz:
http://arxiv.org/abs/1008.3554
The Malliavin derivative, divergence operator, and the Ornstein-Uhlenbeck operator are extended from the traditional Gaussian setting to generalized processes from the higher-order chaos spaces.
Externí odkaz:
http://arxiv.org/abs/1007.0569
Autor:
Lototsky, S. V., Rozovskii, B. L.
We study stochastic evolution equations driven by Gaussian noise. The key features of the model are that the operators in the deterministic and stochastic parts can have the same order and the noise can be time-only, space-only, or space-time. Even t
Externí odkaz:
http://arxiv.org/abs/0709.2975
Autor:
Lototsky, S. V., Rozovskii, B. L.
A procedure is described for defining a generalized solution for stochastic differential equations using the Cameron-Martin version of the Wiener Chaos expansion. Existence and uniqueness of this Wiener Chaos solution is established for parabolic sto
Externí odkaz:
http://arxiv.org/abs/0706.2390
Publikováno v:
Annals of Applied Probability 2006, Vol. 16, No. 3, 1633-1652
This paper is concerned with nonlinear filtering of the coefficients in asset price models with stochastic volatility. More specifically, we assume that the asset price process $S=(S_{t})_{t\geq0}$ is given by \[ dS_{t}=m(\theta_{t})S_{t} dt+v(\theta
Externí odkaz:
http://arxiv.org/abs/math/0612212
Explicit conditions are presented for the existence, uniqueness and ergodicity of the strong solution to a class of generalized stochastic porous media equations. Our estimate of the convergence rate is sharp according to the known optimal decay for
Externí odkaz:
http://arxiv.org/abs/math/0512259
This paper is concerned with nonlinear filtering of the coefficients in asset price models with stochastic volatility. More specifically, we assume that the asset price process $ S=(S_{t})_{t\geq0} $ is given by \[ dS_{t}=r(\theta_{t})S_{t}dt+v(\thet
Externí odkaz:
http://arxiv.org/abs/math/0509503