Nonlinear filtering for the solution of certain stochastic differential equations

Spontaneous Breaking of Space-Time Symmetries

“…In (11), once again, the delta function δ(q 1 + q 2 + q 3 ) enforces the explicit translational invariance, and the dependence of B on the momentum respects both translational and rotational invariance.…”

“…There is a boundary renormalization group flow, which does not change the bulk central charge and therefore does not lead to all the problems associated with tachyons in the bulk. One can associate a term in the boundary which measures the effective number of degrees of freedom, this has been done by various authors [10], [12], [11].…”

“…Map of the preferred boundary conditions in the c = 1 moduli space, N stands for Neuman and D for Dirichlet boundary conditions [9] One can associate a term in the boundary which measures the effective number of degrees of freedom, this has been done by various authors [10], [12], [11].…”

Equivalence of the probability measures generated by the solutions of nonlinear evolution differential equations in a Hilbert space, disturbed by Gaussian processes. Part I

“…The existence of such densities allows an efficient solution of applied problems with the use of integration over known standard distributions (for example, Gaussian, Wiener, etc.) for which algorithms are available.The publications [1-42] address the absolute continuity and equivalence of probability measures for different classes of nonlinear transformations and nonlinear differential equations with Gaussian perturbation, which were applied to calculate optimal estimates in extrapolation and filtration problems for the solution of the differential equations [7,8,12,[34][35][36][37][38][39].The present paper can be considered as a continuation of the studies in this field for nonlinear evolution differential equations in a Hilbert space H and of the studies initiated in [44] for random fields being the solutions of Dirichlet and Neumann boundary-value problems for nonlinear elliptic differential equations in a finite-dimensional Euclidean space.In contrast to the previous studies, we will consider, for the first time, nonlinear differential equations with unbounded linear operators, which are a family of generating operators for the evolution family of bounded operators. We will use the concept of extended stochastic integral and the results from [9] to establish the sufficient conditions for the equivalence of the probability measures under study and to calculate explicitly the corresponding Radon-Nikodym densities.…”

“…The publications address the absolute continuity and equivalence of probability measures for different classes of nonlinear transformations and nonlinear differential equations with Gaussian perturbation, which were applied to calculate optimal estimates in extrapolation and filtration problems for the solution of the differential equations [7,8,12,[34][35][36][37][38][39].…”