Results 171 to 180 of about 474 (215)

ON STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS

Mathematics of the USSR-Sbornik, 1975
In this paper we consider the Cauchy problem for second-order stochastic partial differential equations of parabolic type. We study linear and nonlinear equations for filtering Markov diffusion processes. Theorems on the existence, uniqueness and smoothness of solutions are proved.Bibliography: 21 items.
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Stochastic Partial Differential Equations

2015
A natural generalisation of the finite-dimensional diffusions are stochastic partial differential equations. In this chapter we focus on the Allen-Cahn equation introduced in Section 5.7 in one spatial dimension. Section 5.7 gives the main theorem and a rough outline of its proof.
Anton Bovier, Frank den Hollander
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Stochastic Partial Differential Equations

2003
The purpose of this chapter is to give an introduction to stochastic partial differential equations from a computational point of view. The presented tools provide a consistent quantitative way of relating uncertainty in input to uncertainty in output for PDE-based models.
H. P. Langtangen, H. Osnes
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MULTIVALUED STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS VIA BACKWARD DOUBLY STOCHASTIC DIFFERENTIAL EQUATIONS

Stochastics and Dynamics, 2008
In this paper, we establish by means of Yosida approximation, the existence and uniqueness of the solution of a backward doubly stochastic differential equation whose coefficient contains the subdifferential of a convex function. We will use this result to prove the existence of stochastic viscosity solution for some multivalued parabolic stochastic ...
Boufoussi, B., Mrhardy, N.
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On stochastic partial differential equations with Unbounded coefficients

Potential Analysis, 1992
Existence, uniqueness and approximations of parabolic Itô equations are considered. The well-weighted Sobolev spaces are used. In particular stochastic partial differential equations (SPDE) with unbounded coefficients, SPDE whose coefficients grow faster than linear functions and SPDE on manifolds are discussed.
Gyöngy, István, Krylov, Nicolai V.
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INVARIANT FOLIATIONS FOR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS

Stochastics and Dynamics, 2008
In this paper, we study the existence of an invariant foliation for a class of stochastic partial differential equations with a multiplicative white noise. This invariant foliation is used to trace the long term behavior of all solutions of these equations.
Lu, Kening, Schmalfuß, Björn
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Fully Nonlinear Stochastic Partial Differential Equations

SIAM Journal on Mathematical Analysis, 1996
The authors are concerned with the following stochastic partial differential equation: \[ du(t, .)= L(t, ., u, Du, D^2u) dt+ \langle b(t, .)Du+ h(t, .)u, dW(t) \rangle, \qquad u(0)= u_0, \tag{1} \] where \(L\), \(b\) and \(h\) are suitable functions and \(W\) is an \(\mathbb{R}^N\)-valued Brownian motion.
G. Da Prato, Tubaro, Luciano
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Stochastic Partial Differential Equations

2007
Preliminaries Introduction Some Examples Brownian Motions and Martingales Stochastic Integrals Stochastic Differential Equations of Ito Type Levy Processes and Stochastic Integrals Stochastic Differential Equations of Levy Type Comments Scalar Equations of First Order Introduction Generalized Ito's Formula Linear Stochastic Equations Quasilinear ...
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Stochastic Partial Differential Equations

2012
A brief discussion on the relevance of stochastic partial differential equations (SPDEs) in Sect. 9.1 is followed by a review of the type of SPDEs studied in the mathematical literature (Sect. 9.2). Section 9.3 shows that SPDEs can be solved by the methods in Chaps. 7 and 8 via time and space discretization.
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Balancing of partially-observed stochastic differential equations

2008 47th IEEE Conference on Decision and Control, 2008
We study balanced truncation for stochastic differential equations. In doing so, we adopt ideas from large deviations theory and discuss notions of controllability and observability for dissipative Hamiltonian systems with degenerate noise term, also known as Langevin equations.
Carsten Hartmann 0001, Christof Schütte
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