Uncertainty Quantification and Stochastic Partial Differential Equations
Wiener chaos expansion and numerical solutions of stochastic partial differential equations
... the stochastic finite element method for solving stochastic elliptic equations, and resolved a few technical difficulties in this ap- ...for uncertainty quantification in subsurface ...
225
Multiscale Model Reduction Methods for Deterministic and Stochastic Partial Differential Equations
... the uncertainty quantification. Recently, a data-driven stochastic method [15, 60] was proposed by constructing a problem-dependent stochastic basis to solve these ...the stochastic ...
118
Quasilinear Stochastic Partial Differential Equations
... Quasilinear stochastic PDE’s occur in applications such as the stochastic Navier-Stokes equation for which there is a complete answer to existence and uniqueness of ...The stochastic term in each of ...
88
The Osgood condition for stochastic partial differential equations
... Theorem 1.3. Suppose that Assumption 1.1 holds. If almost surely the solution to (1.2) blows up in finite time then b satisfies the Osgood condition (1.3). Together with the result of Bonder and Groisman, this can be ...
19
Optimization governed by stochastic partial differential equations
... SPDEs are partial differential equations for which the input data (i.e. forcing terms, diffu- sion/advection/reaction coefficients, domain) are uncertain. This uncertainty could arise [r] ...
142
Discretisations of rough stochastic partial differential equations
... My research and a wider understanding of related topics was influenced by many people from Warwick and abroad. Particularly, I am grateful to Peter Friz for his enormous endeavor to establish connections between ...
166
Stochastic partial differential equations with fractal noise
... Also the fractional Brownian motion is a.s. nowhere differentiable, but it is known to be a.s. H 0 -H¨ older continuous for any 0 < H 0 < H. The standard Brownian motion appears for H = 1/2, the only case where the ...
110
Adaptive algorithms for partial differential equations with parametric uncertainty
... applications. Partial differential equations (PDEs) with parametric uncertainty are ubiquitous in such mathematical models as they evermore represent the starting point of the investigation ...
176
Stochastic partial differential equations with coefficients depending on VaR
... as a suitable model. Since then a number of other stochastic processes have been used to model price processes. Let us consider an asset pricing model, where the price of a single asset is determined through a ...
98
Strong solutions of semilinear stochastic partial differential equations
... In particular, under the hypothesis that all the coefficients are suffi- ciently smooth and have bounded derivatives, we consider the equation in the context of power scale generated by a strongly elliptic ...
21
Stochastic partial differential equations driven by colored noise
... of stochastic integral introduced by Walsh in [91] if Γ(t, x) is a real- valued function or Dalang’s extension of Walsh integral (see [24]) when Γ is a ...bounded partial derivatives of all orders, |σ (z)| ...
294
The exponential stability for stochastic delay partial differential equations
... Keywords: Stochastic partial functional differential equations; Energy solutions; Energy equation; Exponential stability ...Recently stochastic partial differential ...
15
On multilevel quadrature for elliptic stochastic partial differential equations
... Abstract In the present article, we show that the multilevel Monte Carlo method for elliptic stochastic partial differential equations can be interpreted as a sparse grid approximation. By ...
19
Stochastic control for mean-field Stochastic Partial Differential Equations with jumps
... mean-field stochastic partial differen- tial equations (stochastic evolution equations) driven by a Brownian motion and an independent Poisson random measure, in the case of ...
26
Stochastic Volterra equations in Banach spaces and stochastic partial differential equation
... integral equations in Banach spaces by using the corresponding semigroup and the variation-of-constants formula ...which stochastic integrals are well ...of stochastic integrals in 2-smooth Banach ...
65
Regularity and representation of viscosity solutions of partial differential equations via backward stochastic differential equations
... parabolic partial differential equation with Lipschitz coefficients by using its connection with a forward backward stochastic differential equation (in short FBSDE) and we give a ...
21
Degenerate Parabolic Stochastic Partial Differential Equations: Quasilinear case
... parabolic stochastic partial differential equation driven by a cylindrical Wiener ...cerning stochastic hyperbolic conservation laws ...
41
Supremum estimates for degenerate, quasilinear stochastic partial differential equations
... In the above theorem V 1 and V 2 are functions that can be regarded as dominating any existing “free terms” coming from the drift part and the noise part of the equation, respectively (cf. Assumption 2.1 below). A key ...
32
Martingale solutions and Markov selections for stochastic partial differential equations
... solving stochastic porous medium equations and stochastic Navier–Stokes equations in the sense of martingale ...3D stochastic Navier–Stokes equations, ...for stochastic ...
40
Dynamics of stochastic partial differential equations with dynamical boundary conditions
... original stochastic partial differential equation into a non–autonomous partial differential equation, which generates a random dynamical system, to get the random fix ...
145