ASYMPTOTIC MINIMAX ESTIMATION IN NONLINEAR STOCHASTIC DIFFERENTIAL EQUATIONS FROM DISCRETE OBSERVATIONS

2001 ◽  
Vol 19 (2) ◽  
Author(s):  
M.N. Mishra ◽  
B.L.S. Prakasa Rao
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Minimax Estimation ◽  
Discrete Observations ◽  
Nonlinear Stochastic Differential Equations ◽  
Asymptotic Minimax

A variational approach to nonlinear stochastic differential equations with linear multiplicative noise

2019 ◽  
Vol 25 ◽  
pp. 71
Author(s):  
Viorel Barbu
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Parabolic Equations ◽  
Optimization Problem ◽  
Multiplicative Noise ◽  
Generalized Solution ◽  
Convex Optimization Problem ◽  
Nonlinear Stochastic Differential Equations ◽  
Infinite Dimensional ◽  
Wiener Processes

One introduces a new concept of generalized solution for nonlinear infinite dimensional stochastic differential equations of subgradient type driven by linear multiplicative Wiener processes. This is defined as solution of a stochastic convex optimization problem derived from the Brezis-Ekeland variational principle. Under specific conditions on nonlinearity, one proves the existence and uniqueness of a variational solution which is also a strong solution in some significant situations. Applications to the existence of stochastic total variational flow and to stochastic parabolic equations with mild nonlinearity are given.

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